ML032790030
| ML032790030 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| 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: ML032790030 (118) | |
Text
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 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: T. S. Brihmodesarn Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 76 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 inchhr.
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 nozle end.
Refpoint := 1544 To place the flow with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter 2)
- 3) The lower
- 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 eklvation from Nozzle Bottom. Enter this value below ULStrs.Dist :=1.704 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
1 S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 14 Page 2 of 11 Engineering Report M-EP-2003-00201 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 im.
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 t:= Ro-Rid t
Rrn: Rid+ +2 Timopr:= Years-365-24 CFinrfl
- = 1.417-105 Timopr Cblk =urn
=lim Prntblk :=50 L
Co := 2 RrM Rt=t
~-7496-Qg 1.103-T+49.67 Tref+459.67 Co C0
]a0 c Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Biihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Enginemng Programs Appendix "C"; Attachment 14 Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data In the table below. The column designations are as follows:
Column "0" = 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
o 0
-17.41
-13.55
-11.11
-8.88
-6.63 1
0.46
-8.49
-6.31
-4.92
-3.71
-2.54 2
0.83 0.09 0.18 0.11 0.19 0.28 3
1.13 7.03 6.95 6.31 5.21 4.65 4
1.36 8.22 10.95 10.85 9.51 5.65 5
1.55 13.27 16.41 16.06 17.13 25.26 6
1.7 20.63 22.24 25.41 43.58 53.78 7
1.83 29.04 28.83 31.29 53.55 64.08 8
1.95 33.95 30.93 36.41 61.6 71.01 9
2.07 29.59 31.79 40.54 64.61 76.42 10 2.19 23.26 29.74 41.2 64.19 79.63 AXLen:= AllData(°)
IDAII:= A11Data('>
0DA11:= AlIData(>
Stress Distribution Ind%
I u
.)
cn IDAII ODAII 50 I
I I :
I1.5441,704
~~~~~~~~~~~~.
/
II I
I1 I~~~~~~~~~~~~~~~~~~~~~~
I I
~ ~~~I I
0
-50 0 0.5 I
1.5 2
2.5 3
3.5 AXLen Axial Elevation above Bottom [inch]
Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 4 of 11 Engineering Report M-EP200302-01 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.
ype "Data and the Mathcad 'equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
A 1
A1 11_ I O-O GOA t'rOQ U
j,*qjq41
-11.i13
-0.08oq
_U.UZ8 Data :=
0.461
-8.494 0.83 0.089 1.126 7.025 1.363 8.215 1.552 13.266 1.704 20.627 1.825 29.036 1.946 33.945 2.066 29.591 2.187 23.26 10.954 10.85 9.512 5.646
-6.31
-4.924
-3.706 -2.541 0.179 0.11 0.186 0.284 6.953 6.314 5.208 4.646 16.41 16.061 17.131 25.256 22.237 25.413 43.58 53.784 28.83 31.285 53.547 64.082 30.929 36.407 61.6 71.01 31.788 40.536 64.612 76.418 29.738 41.2 64.193 79.626 )
AxI = Data(0)
MD := Data)
ID:= Data(])
TQ := Data(4)
QT := Data(2)
(5)
OD:= Data RID := regress(Axl, ID, 3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD:= regress(Axl,MD,3)
RTQ := regress(Axl,TQ,3)
FLCntr = Refpint -CO if Val =
Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c 0 otherwise UTiD := FLCntr + CO Developed by:
- 1. S. Buhmaodesam Incstrs.av -
ULSrs.Dist - UTip In Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 5 of 11 Engineering Report M-EP-2003-002-01 TV No User Input is required beyond this Point fiSat Aug 09 10:21:18AM 2003 Developed by.
J. S. Bnhmadesam Vetffled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 page 6 of 11 Engineering Report M-EP-2003-00201 ProPLength =
0.6 U
CL G.)
2 3
0.4 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 Operating Time {years}
3 3.5 4
Entergy-CEP Model "I
._A
'5 S-0.8 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 Developed by:
J. S. Bnhmadesam Verified by B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix "C"; Attachment 14 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors c
0 C) 4)
Cd S-2f 80 60 40 20 0
I I
I I
I I
I I
I I
I I
I I
0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model I Surface Point Entergy-CEP model Developed by:
J S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Prograins Appendix "C"; Attachment 14 Page 8 of 11 Engineering Report M-EP-2003-002-01 0.8 0.7 v) 0 Co up I.
c)
To cz c;
C 0.6 0.5 0.4 0.3 Influence Coefficients - Flaw 0.2 0.I 0o0 0.5 l
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray CON0
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 14 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi~k 8 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi (k, 6) 15.529 19.971 19.978 19.986 19.994 20.002 20.009 20.017 20.025 20.033 20.04 20.048 20.056 20.064 20.072 20.079 CGRsambi (k, 5) 11.322 14.55 14.555 14.56 14.565 14.57 14.575 14.58 14.585 14.59 14.595 14.6 14.605 14.61 14.615 14.62 Developed by:
J. S. Brihmadesam Vernied by:
. C. Gray
Entergy Operations Inc Central Engineering Programs 60 -
[
1 4 0 X
I 20 0- 03-
.I 0.2 I
0.1 0.0 Appendix "C"; Attachment 14 Page t0 of II Engineering Report M-EP-2003-002-01 0.0 0 5 1 0 1.5 2.0 2.5 3.0 Distanco from Nozzie Bottom finChsa) 0 1
2 3
4 O perating Time (years)
Developed by:e J. S. Brihmadesam Venffed by B. C. Gray
Entergy Operations Inc Central Engineering Programs 0.3-S 0 o, 0.2 2
1 (3
0 o o.
Appendix "C"; Attachment 14 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
0 p e ra tin g T im e (y e a rs )
F - S u rfa ce P o in tI{"c"-tip )l, 35
~~~Depth Po int
(."a"- tip)l 35-:/
30 J 25 2 0 I 5 0
1 2
_n 4'
a is-u 0
- gd 0
0Operaing Time ('yars)
S A
Verified by:
B. C. Gray GOZ Developed by:
J. S. Brihmadesam
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when R,,,,tde/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -28"Degree Nozzle, Downhill Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Input is to locate the Reference Line (eg. top of the Blind Zone).
The throughwall flaw "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (e.9. 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.
Ul-Strs.Dist = 1.704 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Developed by:
Verified by:
IDeveloped by Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :-
L := 0.25 od:= 4.05 id 2.728 Pint:= 2.235 Years := 4 1jim:= 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 lI 1
L1103 10 3 T+459.67 Tf-+459.67)_
Tifopr := Years 365.24 od 2
id Ri=2 t:= Ro - Ri Rm:= Ri + -
2 CFinhr := 1.417-105 Tifllpr Cblk Ti-1im Ih'im Prntbik:=
50 I
L 2
Developed by:
Verified by:
lIDeveloped by.
Verified by.:
Entergy Operations Inc.
Central Engineeing Programs Appendix "C"; Attachment 15 Page 3 of 10 Engineering Report M-EP-2003-00201 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "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)
DataAll :=
0 1
2 3
4 5
0 0
-17.41
-13.55
-11.11
-8.88
-6.63 1
0.46
-8.49
-6.31
-4.92
-3.71
-2.54 2
0.83 0.09 0.18 0.11 0.19 0.28 3
1.13 7.03 6.95 6.31 5.21 4.65 4
1.36 8.22 10.95 10.85 9.51 5.65 5
1.55 13.27 16.41 16.06 17.13 25.26 1.7 20.63 22.24 25.41 43.58 53.78 7
1.83 29.04 28.83 31.29 53.55 64.08 98 1.95 33.95 30.93 36.41 61.6 71.01 9
2.07 29.59 31.79 40.54 64.61 76.42 10 2.19 23.26 29.74 41.2 64.19 79.63
.11 2.31 18.69 27.73 41.29 61.78 78.12 AllAxl:= DataAIl 0 AIIID:= DataAII)
AIIOD := DataAIl 5 Developed by:
Verified by:
IDeveloped by Verifed by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 4 of 10 Engineering Report M-EP-2003-00201
[UV 75 1 50 ci ut 1.5441.704 10 25 0
25
-50 0.5 I
1.5 2
Axial Distance above Bottom [inch]
2.5 3
3.5 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).
/A 1_7 AIA 1 CC, II 11I l OOA Co\\
Data:=
U
-I
.- j-0.461 -8.494 0.83 0.089 1.126 7.025 1.363 8.215 1.552 13.266 1.704 20.627 1.825 29.036 1.946 33.945 2.066 29.591 2.187 23.26 2.308 18.689 (I)
ID :=Data
-6.31 0.179 6.953 10.954 16.41 22.237 28.83 30.929 31.788 29.738 27.734
-1.1
-4.9 0.1 6.31 101 16.01 25.4 31.2 36.41 40.5.
41.
41.2 I.
-0.O0't
-U.Uoz0 24 -3.706 -2.541 1
0.186 0.284 14 5.208 4.646 15 9.512 5.646 61 17.131 25.256 13 43.58 53.784 85 53.547 64.082 07 61.6 71.01 36 64.612 76.418 2
64.193 79.626 29 61.777 78.117)
(:5 OD:
Data
(: )
Axl:
Data RID:=regress(Axl,ID,3)
ROD:= regress(Axi, OD, 3)
Developed by:
Verified by:
IDeveloped by Veiffied by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr := BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist -BZ lStrs.avg :=
20 No User Input required beyond this Point 3 Sat Aug 09 11:44:49 AM 2003 -
Developed by:
Verified by:
lIDeveloped by:
Verified by. I
Entergy Operatfons Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 6of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.16 1.5 2*U r-F "c TWCp"Scc 3
j,3 0
l 0.5 0
-0.5 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWCsjC I)
Operating Time (years}
Entergy Model Increase in Half Length 2
c c
r-V rU 4>
VU It P
C-1.5 I
-I 0.5 I V0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time Years)
Developed by:
Verified by:
IDeveloped by Verifedby. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 va 0
on 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
Developed by:
Verified by:
lIDeveloped by Veified byI
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 8 of 10 Engineering Report M-EP-2003-00201 TWCPWSCc 6) 19.249 20.707 20.715 20.724 20.732 20.741 20.749 20.758 20.766 20.774 20.783 20.791 20.8 20.808 20.817 20.826 TWCPWSCC 7) 12.744 13.424 13.43 13.436 13.442 13.447 13.453 13.459 13.465 13.471 13.476 13.482 13.488 13.494 13.5 13.506 TWCpwsc 16.124 17.198 17.205 17.212 17.22 17.227 17.234 17.242 17.249 17.257 17.264 17.271 17.279 17.286 17.293 17.301 lDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 9 of 10 Engineering Report M-EP-2003-002-01 80 80 4 0 20 0
-2 0 0.0 0.5 1.0 1 5 2.0 2.5 D is ta n c e fro m N o z z le B o tto m (in c h 3.0 80
?- 6 0 4 0 a
20 D
D Su rfa c e S IF ID S u rfa ce S IF Average SIF 1, I
_~~~~~~~~~
'~
I I
,? 'd'I' I
'1
.1 #
IH H-e e5f
0 1
D I 2
3 4
0 -O p e ra tin g Time f te ar IDeveloped by:Ve
Entergy Operatfons Inc.
Central Engineering Programs Appendix "C"; Attachment 15 Page 10 of 10 Engineering Report M-EP-2003-002-01 0.5 0 4 0.2
.S 0.1 0.0 2
paeatin Time (years)
Developed by:
Verified by:
lIDeveloped by:
Venfied by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 16 Page of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM '28" Degree Nozzle, UPhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Requred 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 nozzk end.
Refpoint 1544 To place the flow with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "C-tip located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter 2)
- 3) The lower "C-tip 1 located at the reference point (Enter 3).
Val := 2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the filet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrsDist := 4.268 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
Verifed by:
J S. SBhmadesam B. C. Gray
Entergy Operations Inc.
Centra I Engineering Programs Appendix "C"; Attachment 16 Page 2 of II Engineering Report M-EP-2003-00201 Input Data :-
L := 0.32 ao := 0.661'0.07 od := 4.05 id := 2.728 PInt := 2.235 Years := 4 him = 1500 T := 604 aoc := 2.67 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2d id Rid:
2Y t:= Ro -Rid t
Rm :Rid+ -2 Timopr := Years365-24 CFinhr := 1.417-105 Timopr Cblk:=
i h=im Pmrtblk :=50 L
co:= 2 Rm Rt
[ -Qg
(
I _ 1 1 10 3 reT+459.67 T.ef+4 9.67 To C0 1 e=
re 00C Temperature Correction for Coefficient Alpha Co:= C0 1 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bnihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 16 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column O" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "I" = ID Stress data at each Elevation (ksi)
Cloumn W2' = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn f3' = Mid Thickness Stress data at each Elevation (ksi)
Column 4f = 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
i 0 0
-9.03
-5.86
-4.25
-2.69
-1.03 1
1.15
-6.76
-6.74
-7.24
-7.66
-7.8 2
2.08 7.97 1.74
-6.23
-11.85
-16.39
'3 2.82 23.85 21.76 8.56
-6.39
-17.65 4
3.41 43.99 38.07 29.83 13.47
-1.63 5
3.89 47.95 41.75 35.45 33.32 35.85 6
4.27 43.76 39.21 38.4 53.02 57.54 7
4.38 40.77 36.24 41.27 61.45 62.19 8
4.49 39.28 35.33 44.86 64.2 63.9 4.6 36.02 35.39 46.84 64.32 62.93 AXLen:= AlData()
IDA11:= MlDatP)
ODAII := AllData()
Stress Distribution 100 I
I I
50 -
0
-50 l
l o
0.5 1
1.
ID Distribution OD Distribution
.5 2
2.5 3
3.5 4
4.5 5
5.5 6
Axial Elevation above Bottom [inch]
Developed by:
J. S. Bnlhmadesam Veiffied by B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 16 Page 4 of 11 Engineering Report M-EP-2003-0021 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. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 1.154 2.078 2.819 3.412 3.888 4.268 4.377 4.486
-9.034
-6.761 7.965 23.851 43.99 47.954 43.756 40.773 39.277
-5.855
-6.739 1.742 21.763 38.072 41.753 39.214 36.237 35.327
-4.246
-7.237
-6.23 8.555 29.826 35.453 38.4 41.27 44.863
-2.689
-7.662
-11.848
-6.39 13.47 33.324 53.023 61.453 64.204
-1.031
-7.803
-16.387
-17.647
-1.632 35.846 57.543 62.189 63.895 AxI := Data(°)
(3)
MD:
Data ID:= Data(])
TQ := Data(4)
QT := Data(2)
OD := Data(5 RID := regress(Axl, ID, 3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axi, MD, 3)
RTQ:= regress(Ax1,TQ,3)
Developed by:e J. S. Brihmadesam Venffed by:-
B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 16 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLCntr =
Refpoint -
if Val =
RefPoint if Val = 2 Refpoint + co otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr+ CO Ilncstrs.avg ULStrs.Dist-UTip 20 No User Input is required beyond this Point MSat Aug 09 10:59:39 AM 2003-Developed by:
J. S. Bnhmadesam Verffed by B. C Gay
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 16 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 2.564 Flaw Growth in Depth Direction I
I I
I III 0.6 U
C-3 3
Cu L(.
0.4 -
0.2 _
l l
l l
0 )
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
2 Q
0.-
Q5 2u I
-i L-0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
4 Developed by:
J. S. Brhmadesam Venired by:
B. C. Gray
Entergy Operations Ic Central Engineering Programs Appendix "C"; Attachment 16 Page 7 of 11 Engineering Report M-EP-2003-00201 8
Q 0
U]
.7 U
V 1..
6 4
Stress Intensity Factors I
I I
I I
I.................................................................................................
0 L0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developed by:V J. S. Blihmadesam Verlfed by:-
B. C. Gray
Entergy Operations Inc.
Centra I Engineering Programs Appendix "C"; Attachment 16 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9 0
CIn v:
(L)
E
-oc
.°2 vw c
I._
s)0 C
(1)
Ca 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 4....
11..
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 Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inca Centra I Engineering Programs CGRsambi(k 8) 1.1031 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 16 Page 9 of II Engineering Report M-EP-2003-002-01 CGRsambi(k 6)
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323
-0.323 CGRsambi
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397
-0.397 Developed by:
J S. Brihmadesam Venffied by:
B. C. Gray
Entergy Operations Inc.
Centra I Engineering Programs Appendix "C"; Attachment 16 Page O of I Engineering Report M-EP-2003-002-01 80 -
so-4 0-1 20 0- I D H
o p 5 ire 5
0 D ~H o
p S re s
.o
_'f0114Zn
/..
_w&
W Id 9 ell..
0 1
2 3
4 Axil D ltance Fom N ozzle Bottom (Inch) a 6
0.07 0 06 SE 0-05 0 0 4-0 03 -
002 -
0 I
2 pratling Tim e a
ye areI 3
4 Developed by:V J S. Bnfhmadesam Verfifed by B. C Gay
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 16 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
0.3 -
I 0.1 -
05 0
1 2
O pe ra tin g T ime eye ars 3
4
-0.32 -
0 S -O 34 -
A
-O0.34-
-0.4 0 -
f.
S IF D epth P oin1 f
S IF S u rfa ce P o in t 0
f:
- 0
0 t:
X u
?St::.
X 0'
S n.
.z.t f X
0
. d;
\\
f 0 0.)
- 0.
._,__.__.7 5
j 0
1 2
pra tin TiOmeo ye0ars )
3 4
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray CoG
Entergy Operations Inc Central Engineering Prograins Appendix "C"; Attachment 17 Page 1 of 11 Engineering Report M-EP-200300201 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28" Degree Nozzle, Uphill 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 nozle end.
RefP o in t := 1-544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The ipper "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 = 4268 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Bnhmadesam Velffied by.-
B. C Gtay
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 17 Page 2 of 1 1 Engineering Report M-EP-200300201 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 Iiim = 1500 T := 604 aOC := 2.67-1 0- 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 t:= Ro-Rid Rm := Rid + 2 Timopr:= Years-36524 CFinhr := 1.417105 Timopr Cblk ur I'irn, Pmtblk =
50 L
c :=-2 Rm Rt :=
-Q g
(
I I
C 1.103-1°- 3 T+459.67 Tref+459.6 7) 01 *- e co:= co
) 00C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Brihmadesam Veried by:
B. C. Gray
Entergy Operations Inc Central Engneeing Programs Appendix "C"; Attachment 17 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = 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
45 0
0
-9.03
-5.86
-4.25
-2.69
-1.03 1
1.15
-6.76
-6.74
-7.24
-7.66
-7.8 2
2.08 7.97 1.74
-6.23
-11.85
-16.39 3
2.82 23.85 21.76 8.56
-6.39
-17.65 4
3.41 43.99 38.07 29.83 13.47
-1.63 5
3.89 47.95 41.75 35.45 33.32 35.85 6
4.27 43.76 39.21 38.4 53.02 57.54 7
4.38 40.77 36.24 41.27 61.45 62.19 8
4.49 39.28 35.33 44.86 64.2 63.9 9
4.6 36.02 35.39 46.84 64.32 62.93 AXLen:= AllData(°)
ID~i := AllData )
0DAll:= AllData(5)
Stress Distribution 100 M
IDAII ODAll 50 0
-50 0 1
2 3
4 5
AXLen Axial Elevation above Bottom [inch]
6 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 4 of 1 Engineering Report M-EP-2003-002-01 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
-9.034 -5.855 -4.246
-2.689
-1.031 1.154 -6.761 -6.739 -7.237 -7.662 2.078 7.965 1.742
-6.23
-11.848 Data :=
2.819 23.851 21.763 8.555 3.412 43.99 38.072 29.826 3.888 47.954 41.753 35.453 4.268 43.756 39.214 38.4 4.377 40.773 36.237 41.27
-6.39 13.47 33.324 53.023 61.453 64.204
-7.803
-16.387
-17.647
-1.632 35.846 57.543 62.189 63.895 )
K4.486 39.277 35.327 44.863 AxI := Data(0)
MD:= Data(3)
ID:= Data 1 TQ := Data(4)
QT := Data(2)
OD:
Data (5)
RID := regress(Axl, ID, 3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Ax,OD, 3)
RMD:= regress(Axl, MD, 3)
RTQ := regress(Axl,TQ,3)
FLCntr RefP o in t -C if Val i
Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c otherwise UTip := FLCntr + co Developed by:
J. S Brihmadesam lncstrs.av2 :=
ULStrs.Dist - UTip hA Venried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 5 of 11 Engineering Report M-EP-2003-00201 v
No User Input is required beyond this Point fSatAug 09 10:21:18AM 2003 Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength - 2564 Flaw Growth in Depth Direction 0.6 Q
0 3
0.4 I
I I
I I
I I
I I
I I
I I
I 0.2 _
0 0.5 I
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model
._u 0
.0 0
0 AL 0.8 0.6 0.4 0.2 o Lo 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed byb J. S. Bnhimadesam Veded by B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 7 of 11 Engineering Report M-EP-2003-00201 Q
(A I-0 U
v:
A o
50 0
-50 Stress Intensity Factors I
I I
I III 0
0.5 1
1.5 2
2.5 Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 3
3.5 4
Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 8 of 11 Engineering Report M-EP-2003-002-01 0.8 0.7 Influence Coefficients - Flaw 0
0 i-d)
U 5) 0.6 0.5 0.4 0.3 0.2 0.I 0
................................................................................................... I............................................
....I...........................-............................................. --.............................................................................................-..........................................................................
...................................... I---------------------------- -I................................. I....................
......................... I............
0 0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
Ia" - Tip -- Uniform Ila - Tip -- Linear Ila - Tip -- Quadratic Ila - Tip -- Cubic ti"- Tip -- Uniform "c-Tip -- Linear ti"- Tip -- Quadratic cip"
- Tip -- Cubic Developed by
. S Bri/imadesam Verified by.-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi k 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k 6)
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284
-5.284 CGRsambi
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812
-3.812 Developed by.
J. S. Bnihmadesam Verif ed by:
B. C. Gray
Entergy Operations Inc Central Engineering Prograns 80 6 0 40 1
20 0
-20 Appendix "C"; Attachment 17 Page 10 of II Engineering Report M-EP-2003-002-01 0
1 2
3 4
5 D istance from N ozzle Bottom (inches) 0.5 c-0 3 0.3 0.1 B.
0 -0.3
-0 5 0
I 2
p era tin g Time (years) 3 4
Developed by:V J. S. Blihmadesam Venired by B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 17 Page 11 of 11 Engineei M-EP-2 0.5
-0
.3
.SZ 0.1 -
2
-0.
'1; rs w
j
-O.I 2
-0.3
-.5 0
1 2
o p e ra tin T im e
{y e a rs 3
4 Iring Report 2003-002-01 Verified by.
B. C. Gray C)
Su rfa ce Po in t {'c-tip}
De pth Po in t ("a tip)
-4.0 06~
g -5. 0 0
00 l
0~~~Opearating Time (yeaers)} 00$00 Developed by:
J. S. Brihmadesam
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when R,,,tj,-/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28"Degree Nozzle, Uphill Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric fonm 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). Te throughwall flaw "Upper Tip" is located at the Reference Line.
Enter the eleation of the Reference Line (eg. Blind Zone) above the nozze botom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the ipper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist:= 4.268 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by.
Verified by I Developed by:
Verited by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :
L := 0.25 od:= 4.05 id := 2.728 Plnt:= 2.235 Years:= 4
,im := 1500 T := 604 v := 0.307 cXoc:= 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
Qg
-(
1 I
.103 16 3 T+459.67 Tre+459.67)I C0 e
to Timopr:= Years-365-24 od 2
R2= id t := Ro - Ri Rm:= Ri + -
2 CFinhr:= 1.417 105 Tir~pr Cblk i
Ilim Pmtblk:=
50 I
L 2
Developed by:
Verified by:
IMeveloped by:
Verified by.: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 3 of 10 Engineering Report M-EP-2003-00201 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "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)
DataAII :=
0 1
2 3
4 5
O 0
-9.03
-5.86
-4.25
-2.69
-1.03 1
1.15
-6.76
-6.74
-7.24
-7.66
-7.8 2
2.08 7.97 1.74
-6.23
-11.85
-16.39 3
2.82 23.85 21.76 8.56
-6.39
-17.65 4
3.41 43.99 38.07 29.83 13.47
-1.63 5
3.89 47.95 41.75 35.45 33.32 35.85 6
4.27 43.76 39.21 38.4 53.02 57.54 7
4.38 40.77 36.24 41.27 61.45 62.19 8
4.49 39.28 35.33 44.86 64.2 63.9 9
4.6 36.02 35.39 46.84 64.32 62.93 10 4.7 33.54 36.17 48.06 64.48 66.03 11 4.81 32.63 36.62 47.78 67.61 70.36 AIIAxl:= DataAII(
AIIID DataAl1 AIIOD:= DataAI (5 Developed by:
Verified by:
lIDeveloped by:-
Verified by:-
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 18 Page 4 of 10 Engineering Report M-EP-2003-00201 100 25 1=
0:
2550 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).
K A afAA C
-r A
AK taQ I
A N U
-Y.U4 63
-'+..I0 OOY
-I.U.)I 1.154 -6.761
-6.739 -7.237 -7.662
-7.803 2.078 7.965 1.742
-6.23 -11.848 -16.387 2.819 23.851 21.763 8.555
-6.39
-17.647 Data.=
3.412 43.99 38.072 29.826 13.47 3.888 47.954 41.753 35.453 33.324 4.268 43.756 39.214 38.4 53.023 4.377 40.773 36.237 41.27 61.453 4.486 39.277 35.327 44.863 64.204 4.595 36.022 35.389 46.842 64.323 4.704 33.54 36.173 48.06 64.483
-1.632 35.846 57.543 62.189 63.895 62.934 66.03
~4.813 32.631 36.616 47.779 67.612 70.356 (o)
Axi:
Data ID:= Data (5:
OD: Data RID:= regress(Axl,ID,3)
ROD:= regress(Axl, OD,3)
Developed by:
Verified by:
Ieeloped by Venifed by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr : BZ - I Flaw Center above Nozzle Bottom Inc ULStrs.Dist - BZ IncStrs.avg 20 No Urn qrbo20 No User Input required beyond this Point A. Sat Aug 09 11:44:49 AM Inn ZuuZ Q
I AQA-I.-'
uI veupeoU [j'y Verified by:
I~~~~~~~~~~~~~
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProkPength = 2.724 Flaw Length vs. Time 1.5 1 U
TWCPWscc j,3 I
I 1-5
.15
.543 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 2
U-CZ on C-W C-1.5 0.5 Increase in Half Length f
I~
I i~~~~~~~~~~~~~~
- f~~~~~~~~~~~~~~~~
o -0 0.5 I
1.5 2
2.5 Operating Time (Years}
3 3.5 4
Developed by:
Venfied by:
lIDeveloped by.
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 7 of 10 Engineering Report M-EP-2003-00201 300 z
v 200 rn0 100 r-v) 0 I.........
0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {Years}
OD SE - Entergy Model ID SF - Entergy Model SIF Average Developed by:
Verified by:
lIDeveloped by Verified by.:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 8 of 10 Engineering Report M-EP-2003-00201 TWCPW
(, 6)
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322
-10.322 TWCpWSCCj 7) =
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923
-2.923 TWCpwsccj s)
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63
-6.63 Developed by:
Verified by:
lIDeveloped by:
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 9 of O Engineering Report M-EP-2003-002-01 Ho op S tress P lot 0 -
0 -
4 40 -
o 2 0 -
X 0 -
-2 0 -
el-
-P.,
aC. ap,...
O..
a H00 Z...
,O,,
ID H o op S tre 0OD Hoo P S s
Top f Blind Zne ",41
T.p f C S 1mmo Wl 0
1 2
3 4
D is tan c from No zz le Bo tto m (in c h]
5 B
-30 D S ur fa ce S F1 ID S urfa c S IF veara ge S IF 0
1 2
~~~~~~~~~~~~~~~~3 4
JOperatingj Tme, (yaltrej Developed by:.V
Entergy Operahtons Inc.
Central Engineering Programs Appendix "C"; Attachment 18 Page 10 of 10 Engineering Report M-EP-2003-00201 0.5 0.3 -
0.1 -
-0.3 -
-0.5 0
I 2
O peara tin a Time a
{ye a r) 3 4
lIDeveloped by.,
Verifed by. I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaur; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28" Degree Nozzle, Mid-Plane Azimuth, 1.644" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev..
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Reuired 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 filet weld etc.). This referencepoint is necessar to evaluate the stress distribution on the flaw both for the initial flow and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpoint = 1544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The U~pper "c-tip located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter 2)
- 3) The lower fl-tip" located ot the reference point (Enter 3).
Val := 2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist = 2.999 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 2 of 1 Engineering Report M-EP-2003-00201 Input Data :-
L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Pint := 2.235 Years := 4 him = 1500 T := 604 aOc := 2.67-10 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TVW Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 id Rid T
t = Ro - Rid t
Rm:id+ 2 Timopr := Years-365-24 CFinahr= 1.417 105 Timopr Cblk.
him
'=im Pmtblk :=
50 L
co T=
Rm Rt:=-
eL l03-o- 3 (e+459.67 Tf45967)]
C0 1 :e
- a10C Temperature Correction for Coefficient Alpha Co:= Coi 75 th percentile MRP-55 Revision 1 Developed by:e J. S. Brihmadesam Venffed by B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 3 of 1 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "o" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column 4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
2.08
-0.87
-2.96
-4.82
-6.75 1
0.81 0.09
-2.37
-4.27
-6
-7.55 2
1.46 5.28 1.69
-0.79
-2.49
-3.47 3
1.98 16.88 12.42 9.56 6.91 4.32 4
2.4 24.14 20.89 18.11 16.59 14.51 5
2.73 26.96 22.67 20.69 24.84 33.52 6
3 23.28 20.9 21.71 37.11 47.4 7
3.11 17.16 17.1 20.74 41.09 51.76 8
3.23 11.72 14.42 21.34 43.54 53.69 9
3.34 6
11.11 20.91 43.83 54.15 10 3.46 1.44 8.09 20.38 43.02 57.02 11 3.57
-2.17 5.89 19.93 42.41 56.41 1E 2
3.69
-4.72 4.86 19.99 40.42 58.85 AXLen:= AlIData(0)
IDA11:= A11Data(')
ODAIl := AllData()
100 r='n
-W4 Cn 0
t-C6 50 0
Stress Distribution J44 2 99
,_----~~~~~~~~~~~~'~~~~~~-~~~
A~~NN
-50 0 0.5 I
1.5 2
2.5 3
Axial Elevation above Bottom [inch]
3.5 4
4.5 ID Distribution OD Distribution Developed by:
J. S. Bdhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the rght mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 2.079 0.811 0.091 1.46 5.283 1.98 16.881 2.397 24.144 2.731 26.962 2.999 23.279 3.113 17.161 3.228 11.722 3.343 6.004 3.457 1.439 3.572 -2.175 3.687 -4.725 12.419 20.894 22.672 20.902 17.101 14.424 11.108 8.085 5.891 4.858 9.564 18.115 20.686 21.706 20.743 21.34 20.912 20.38 19.929 19.994 6.907 16.59 24.842 37.111 41.091 43.543 43.833 43.021 42.405 40.425 4.319 14.513 33.523 47.395 51.762 53.688 54.154 57.025 56.415 58.85
-0.875
-2.96
-4.82
-6.75 )
-2.37
-4.267 -6.004 -7.552 1.686
-0.786
-2.49
-3.469
)
Ax := Data(°)
MD:= Data(3)
ID:= Data()
TQ := Data(4)
QT := Data(2)
OD:= Data(5)
RID := regress(AxI, ID,3)
RQT:= regress(Axl,QT,3)
ROD:= regress(AxI, OD, 3)
RMD := regress(AxJ, MD, 3)
RTO := regress(Axi, TQ, 3)
Developed by.
J. S. Bn7imadesam Venided by:-
. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 5 of 11 Engineering Report M-EP-2003-00201 FLCntr =
Refpoint - CO if Val =
Refpoint if Val = 2 Refp0 int + co otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr + CO InCStrs.avg =
ULStrS.Dist - UTip 20 No User Input is required beyond this Point f Sat Aug 09 10:59:39 AM 2003 Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 6 of 11 Engineering Report M-EP-2003.002-01 PrOPLength = 1.295 Flaw Growth in Depth Direction I
I I
I I
I I
0.6 u
- L 03 0.4 _
0.2 -
l l
0 I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years) 2 Q
4)-
0 2
3 0
I I
I I
i I
1 1.295 I
I I
I I
I I
-1 )I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years)
Developedby:
J. S. Blihmadesam Velr/led by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 100 I
I I
I I
I I
0 a.-
00 rV I-17 80 -
60 _
40 -
20 _
I I
I I
I I
I 0 0 0.5 I
1.5 2
Operating Time 2.5
{years}
3 3.5 4
Depth Point Surface Point Developed by:e J. S. Bdhmnadesam Venffed by:-
B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 1
0.9
.E C) 0 E
c)
,~-
........................................................I.......... -_..
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
S F
A i
S F
A Verged by:
B. C. Gray i
COR 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
Entergy Operations Inc.
Central Engineering Programs CGRsambi(k 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 19 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi(k, 6) 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 5.43 CGRsambi 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 4.419 Developed by:
J. S. Brlhmadesam Verifiedby:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 19 Page l0 of 1 1 Engineering Report M-EP-2003-002-01 j
-~~~~~----
ID Hoop Stress TT~~-1.-
.~.-
.. 1 0 ID Hoo 0
Sress I I
5 0 T
C.
i tM 3 0 10a
-1I0 0
1 2
3 AxIsl IDIisan co rom N ozzles BotIto m finch) 4 0.0 7 0.06 10.0 5 I0 04 0.0 3 0.0 2 De veloped by:
. S. Bnihmadesam 1
2 0 peato nI TIm (y a rs 3
4 Verffied by:
B. C. Gr-ay
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 19 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 c
0.3 I
IT 0.1
-0.1 (2
) -0.3 -
-0.5 T
0 1
2 O perating Time (years) 3 4
5.4-i 5.2 5.0 f 4.8 -
J 4.A -
4.4 IF Dep th P o in t
_____ s IF S u rfa c e P o in t 0
1 2
3 4
O0 perating Tlme years)
Developed by.
Venfied by J. S. Br/hmadesam B. C. Gray B.C. Gra f
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesonm Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"'28" Degree Nozzle, Mid-Plane Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represnets the reference point ekvation measured upward from the nozzle end.
Refpoint = 1544 To place the flaw with repsect to the reference point, the flow tips and center can be located as folloms:
- 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 "-
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 eevation from Nozzle Bottom. Enter this value below ULStrs.Dist = 2999 Developed by:
J S. Biihmadesam Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Verified by:
B. C Gray
Entegy Operations Inc Central Engineerng Programs Input Data :-
Appendix "C"; Attachment 20 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
'urm = 1500 T := 604 aOC := 2.67 lo-12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R
_ od 0
2 Rid := id t = Ro - Rid Rm := Rid +
Timopr := Years-365-24 CFihr := 1.417-105 Timopr Cblk:=
-u rlim Pmtblk:
50 L
2 Rm Rt :=-
J 1Q
(
l l
Tf Co] :=
103-16-3 r
Temperature Correction for Coefficient Alpha co-C01 75 th percentile MRP-55 Revision 1 Developed by:
.1 S. BSnmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "" = Axial distance from minumum to maximum recorded on data sheet(inches)
Column 1W = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column A3d" = Mid Thickness Stress data at each Elevation (kst7 Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksl)
AllData :=
0 1
2 3
4 5
0 0
2.08
-0.87
-2.96
-4.82
-6.75 1
0.81 0.09
-2.37
-4.27
-6
-7.55 2
1.46 5.28 1.69
-0.79
-2.49
-3.47 3
1.98 16.88 12.42 9.56 6.91 4.32 4
2.4 24.14 20.89 18.11 16.59 14.51 5
2.73 26.96 22.67 20.69 24.84 33.52 6
3 23.28 20.9 21.71 37.11 47.4 7
3.11 17.16 17.1 20.74 41.09 51.76 8
3.23 11.72 14.42 21.34 43.54 53.69 9
3.34 6
11.11 20.91 43.83 54.15
- 10 3.46 1.44 8.09 20.38 43.02 57.02
'11 3.57
-2.17 5.89 19.93 42.41 56.41 11^2-3.69
-4.72 4.86 19.99 40.42 58.85 1
3.8
-4.92 4.88 20.34 38.45 57.62 AXLen := AlIData()
IDAl:= AllDatP~)
ODAII := AData(5)
Stress Distribution 60
,IDAII A
ID EO 40 20 0
-20 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
3.5 4
4.5 Developed by:
J. S. Bnhmadesam verffled by:-
B. C. Grayt
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataA, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then Insert the same to the right of the Mathcad Equals sign below (paste symbol).
Data :=
0 2.079 0.811 0.091 1.46 5.283 1.98 16.881 2.397 24.144 2.731 26.962 2.999 23.279 3.113 17.161 3.228 11.722 3.343 6.004 3.457 1.439 3.572 -2.175 3.687 -4.725
-0.875
-2.37 1.686 12.419 20.894 22.672 20.902 17.101 14.424 11.108 8.085 5.891 4.858
-2.96
-4.82
-6.75
-4.267 -6.004 -7.552
-0.786 -2.49 -3.469 9.564 6.907 4.319 18.115 16.59 14.513 20.686 24.842 33.523 21.706 37.111 47.395 20.743 41.091 51.762 21.34 43.543 53.688 20.912 43.833 54.154 20.38 43.021 57.025 19.929 42.405 56.415 19.994 40.425 58.85 Ax] : Data(0)
(3)
MD: Data ID:= Data)
TQ := Data(4)
QT := Data(2)
OD:= DatP)
RID := regress(Axl, ID, 3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axl, MD, 3)
RTQ:= regress(Axl,TQ,3)
FLcntr
- C0 if Val = I Flaw center Location Location above Nozzle Bottom if Val = 2
+ c0 otherwise UT
- FLCntr + CO Developed by:
J. S. Bihmadesam Incstrs.ave :=
ULStrs.Dist - UTip
-'n Vernfied by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 5 of 11 Engineering Report M-EP-2003-002-01
v No User Input is required beyond this Point 6f Sat Aug 09 10:21:18 AM 2003-Developedby.
J. 5. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProLength 1.295 0.6 U
r-0.4 Flaw Growth in Depth Direction I
I I
I I
I I
I I
III 0.2 -
CI 0.5 1
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model I
U-0
.V3.
0.5 0
-0.5 I
I I
I I
I l l5 0
I I
I I
I I
I
-1 0
0.5 I
1.5 2
Operating Time 2.5
{years}
3 3.5 4
Entergy-CEP Model Developed by:
J. S. Blhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 7 of 11 Engineering Report M-EP-2003-002-01 C=
t!
U~T-4.
C u:
9 80 60 40 20 0
-n Stress Intensity Factors I
I I
I III Mu, 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. Bnhmadesam Verf ied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 C
Ln 0
.°A a
E r-C 0
U r-C)
C-0.6 0.5 0.4 0.3 I..................................................
0.2 0.1 0
I..........................----------...
0 0.5 I
I.5 2
2 Operating time {years}
.5 3
3.5 4
"a" - Tip -- Uniform Via" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray C
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi (k, 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k, 6)
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017
-0.017 CGRsambi(k,5) 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 0.133 Developed by:
J. S. Bdlhmadesam Verified by:
S. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 10 of 11 Engineering Report M-EP-2003-002-01 50 a3 0 10
-1 0
1 2
3 4
D stane from N ozzle B ottom (inches) 0.5 0.3 -
I 0.1 -
X -0.1
.0.5 0
I 2
prating Tim e (years) 3 4
Developed by:V J. S. Bnhmadesam Veded by:-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 20 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 0.3 3
I t
.1 Sy -o.1 e
-0.3
-O S
0 I
2 O pe ra tin g ime
{y e ars}
3 4
0.1 3 -
I 0.0 8 -
ir sG 0.03 -
-O.02 -
l_____
Surface Point {"c`-tip}
I Depth Point "a`- tip) f0 I
Operattin g T0 (m eirs)
A 3 4
Developed by:
J. S. Brnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineefing Programs Appendix "C"; Attachment 21 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesom Verified by: B. C. Gray Note : Only for use when Restdt is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28"Degree Nozzle, Mid-Plane Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Dapt is to locate the Reference Line (eg. top of the Blind Zone).
The throughwall flaw pper Tip" is located at the Reference Line.
Enter the elevation of the Reference line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Dryut 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:= 2.999 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by:
Verified by:I
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 21 Page 2 of 10 Engineering Report M-EP-2003-002-01 InDut Data :-
L := 0.25 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 him:= 1500 T := 604 v := 0.307 cxOc:= 2.67-10 Qg := 31.0 Ttef:= 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 -600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F
- Og
(
ll L.103 10-3 3T+45967 Tr+45967)I co:
ae Tinlopr:= Years-365 24 od Ro:= -2 R; = id 2
t:= Ro - Ri Rm:= Ri +
CFinhr:= 1.417-105 Tilfopr Cblk:=
him Prntblk:= l-l 2
Developed by:
Verified by:
lIDeveloped by.,
Verifed by.: I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 21 Page 3 of 10 Engineering Report M-EP-2003-00201 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "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)
DataAl:=
0 b
1 2
3 4
5 0
0 2.08
-0.87
-2.96
-4.82
-6.75 0.81 0.09
-2.37
-4.27
-6
-7.55 2
1.46 5.28 1.69
-0.79
-2.49
-3.47 3
1.98 16.88 12.42 9.56 6.91 4.32 4
2.4 24.14 20.89 18.11 16.59 14.51 5
2.73 26.96 22.67 20.69 24.84 33.52 6
3 23.28 20.9 21.71 37.11 47.4 7
3.11 17.16 17.1 20.74 41.09 51.76 8
3.23 11.72 14.42 21.34 43.54 53.69 9
3.34 6
11.11 20.91 43.83 54.15 10 0 3.46 1.44 8.09 20.38 43.02 57.02 1
d 3.57
-2.17 5.89 19.93 42.41 56.41 AllAxl:= DataAII AIIID:= DataAl1 (5)
AIIOD= DataAll Developed by:
Verified by:
lIDeveloped by:-
Vefified by. I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 21 Page 4 of 10 Engineering Report M-EP-2003-002-01
-20 0 0.5 1
1.5 2
2.5 3
3.5 4
Axial Distance above Bottom [inch]
4.5 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).
2.079 -0.875 -2.96
-4.82
-6.75 1.46 1.98 2.397 Data := 2.731 0.091
-2.37 5.283 1.686 16.881 12.419 24.144 20.894 26.962 22.672 23.279 20.902 17.161 17.101 11.722 14.424 6.004 11.108 1.439 8.085
-4.267 -6.004 -7.552
-0.786 -2.49 -3.469 9.564 6.907 4.319 18.115 16.59 14.513 20.686 24.842 33.523 21.706 37.111 47.395 2.999 3.113 3.228 3.343 20.743 41.091 51.762 21.34 43.543 53.688 20.912 43.833 54.154 L3.457 20.38 43.021 57.025)
(0)
AAx= Data (I)
ID: Data (5)
OD:=Data RID:= regress(Axl,ID,3)
ROD:= regress(Axl,OD,3)
Developed by:
Verified by:
lIDeveloped by:
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 21 Page 5 of 10 Engineering Report M-EP-2003-00201 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ Strs.avg :=
20 No User Input required beyond this Point f Sat Aug 09 11:44:49 AM 2003 lIDeveloped by.,
Verffied by I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 21 Page 6 of 10 Engineering Report M-EP-2003-002-O01 ProPLength = 1.455 1.5 C.)
." TWCPI-cc I-s aE is 0
0.5 Flaw Length vs. Time 1.455 0
-A t
M., 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
C C
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:
IDeveloped by:
Verified by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 21 Page 7 of 10 Engineering Report M-EP-2003-002-01 a-,
3uu 200 1 A A_
Iuu 0
I.
6:;' :
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 Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 21 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCj,6)
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027
-1.027 TWCpwscc(j7) =
5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 5.625 TWCPWSCC(J 8) 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 2.389 Developed by:
Verified by:
lIDeveloped by.,
Vedfied by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 21 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre ss P lo t 50
" 30O I
10
-1 0 2
3 D is ta n c f fro m N o z z le ttom
{in c h 6
0 e 4-2 k
2-2 ODSurface SIF ID Surface SIT Average SIF 0
1 2
Opraibrtg Time (1 3
4 Developed by:
Verified by:
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 21 Page 10 of 10 Engineering Report M-EP-2003-00201 0.5 -
0.3 -
I
.1
-0.1 -1
-0.3
-0.5 0
I 2
O perealing Time ye re 3
4 Developed by:
Verified by:
lIDeveloped by.,
Verified by.: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-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, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of filet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flow and for a growing flow. This is defined as the reference point. Enter a number (inch) that represnets he reference point elevation measured upward from the nozzle end.
Refpoint = 1544 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 (Eater 3).
Val := 2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist = 1.889 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developedby:e J. S. Bnhmadesam Velffied by B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 2 of 11 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.32 ao := 0.661 0.07 od := 4.05 id := 2.728 P Int := 2.235 Years := 4 irm = 1500 T := 604 aoc := 2.67 lo 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od R._:
o 2
id Rid t:= Ro - Rid i
Rm :
i+-
Timopr := Years-365*24 CFihr = 1.417 105 Timopr Cblk.=
Pmtblk 0=
0 L
co:= 2 Rm Rt t
[
Q
_g Qg03-tT+459.67 Tref+459.67j C,
- = e3-o 3 a0 Temperature Correction for Coefficient Alpha Co:= C0 1 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bnhmadesam VedrIed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3N = Mid Thickness Stress data at each Elevation (ks,)
Column 4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "" = OD Stress data at each Elevation (ksi)
AllData :=
0 ° 1
2 3
4 5
o 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 91.74 16 22.02 39.19 62.95 75 10 1.89 15.86 23.14 40.23 64.33 74.87 AXLen := AllData()
IDAII:= AllData(l)
ODAI := AllData()
Stress Distribution 100 I-50 0
-50 _0 0.5 1
1.5 2
2.5 3
Axial Elevation above Bottom [inch]
3.5 ID Distribution G---
OD Distribution Developed by:e J. S. Bn'hmadesam Venffed by:-
B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 4 of 11 Engineering Report M-EP-2003-00201 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection";; this will copy the selected area on to the clipboard. Then click on the "Matrix below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 0.35 0.63 0.854 1.034 1.178 1.293 1.442 1.591 1.74 1.889
-28.324
-18.794
-17.838
-20.517
-19.663
-17.203
-8.023 4.778 13.252 16.001 15.857
-18.299
-12.495
-10.518
-12.968
-11.831
-10.587
-2.205 9.557 18.569 22.017 23.14
-12.16
-6.607
-4.407
-5.902
-5.288
-0.515 10.461 24.903 35.278 39.194 40.235
-6.201
-1.366
-0.477
-0.874 0.227 16.326 32.658 38.177 52.808 62.945 64.335
-0.021 3.655 2.08
-1.536 1.46 21.019 37.289 54.089 66.517 75.001 74.874)
Ax := Data(0)
(3)
MD: Data ID:= Data)
TQ := Data(4)
QT := Dat(2)
OD := Data(5)
RID:= regress(Axl, ID,3)
RQT := regress(Axl, QT, 3)
ROD:= regress(Axl, OD,3)
RMD := regress(Axl, MD, 3)
RTO:= regress(Axl,TQ,3)
Developed by:
J. S. Blhmadesam Velred by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 5 of 11 Engineering Report M-EP-2003-00201 FLCntr =
- co if Val = 1 Flaw center Location above Nozzle Bottom if Val = 2
+ co otherwise UTip = FLCntr + co InCstrs.avg =
ULStrs.Dist - UTip 20 No User Input is required beyond this Point
& Sat Aug 09 10:59:39 AM 2003V Developed by J. S. Bnhmadesam Vended by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 6 of I1 Engineering Report M-EP-2003-00201 ProLength = 0.185 Flaw Growth in Depth Direction I
I I
I I
I I
0.6 U
0 V-0.4 _
0.2 -
0 LI l
l l
l l
l l
4 0.5 l
1.5 2
2.5 3
3.5 Operating Time {years}
2 u
I 5
0 I
I i
I I
I I
I I
I I
I I
I
-I' I
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developed by:
J. S. Bnihmadesam Verified by.
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 7of 11 Engineering Report M-EP-2003-00201 Stress Intensity Factors I
I I
I I
I I
8 0
0 a,
W Cu r-)
7 6
5 _
4 3
l l
l l
l 2 0 0.5 I
1.5 2
Operating Time 2.5
{years}
3 3.5 4
Depth Point
-.. -Surface Point Developed by:V J. S. Bdhmadesam Veded by B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9 v
c) 0 U
HE
.U I='-
fr D
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0 0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
la" - Tip -- Uniform "a" - Tip -- Linear ia" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs CGRsambi(k 8) 1H103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 22 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRO-mbi(k 6) 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 2.778 CGRsambi(k 5) 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 2.34 Developedby:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 22 Page 10 of 11 Engineering Report M-EP-2003-00201 XI I
0.07-0.06 0.05 I
I 0 04 0.03 0 02 0
a60 40 20 0
-2 0
-4 0 0.0 0.5 1 0 1
2 0 2.5 3.0 A xiaI stanco Fro N ozzle 8 ottom finch
... 1.. - 1..
.
...
.1.
I I.-
-.1.1
- 1.
.1-I... 1-1-.-,.
.1...
-...I -
.11.
-
- 1.. I I
-.1-l-..
...
.1.
-.1-
..-. 1.
... 1. -
--- 1.
0 1
2 0 perating T ime (years 3
Developed by:
J. S. Bnhmadesam Vedfied by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Progrnms Appendix "C"; Attachment 22 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 2'
0.3 I
U 0.1 i5
! -0.1
( -0.3
-0.5 0
1 2
p e ra tin g T im e (y ea rs )
3 4
2.8 SFSu rfa ce P oin t 21 p2.4 2.3 0
- 1.
...,.S. r... f f.:. X,,:....
2 3
4 40 0
f t
0
~~Operating Time (years)000 Developed by.
J. S. Bihmadesam Verified byi B. C. Gray CI.-
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49" Degree Nozzle, Uphill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmit" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpoint = 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "-
tip" located at the reference point (Enter 3).
Val := 2 The Xhput Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist := 6.628 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Bnhmadesam Vendledby:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 2 of 11 Engineering Report M-EP-2003-00201 Input Data :-
L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Pint := 2.235 Years := 4 im = 1500 T := 604 aOc := 2.67 10 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TWN)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2d id Rid:2 t = Ro -Rid Rm id+ 2 Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk= -1lim Pmtblk =
50 L
co:= 2 Rm Rt:=t
_ L (4
I T
t C
t Co
= e 1*a3 r
Temperature Correction for Coefficient Alpha Co:= Coi 75 h percentile MRP-55 Revision 1 Developed by:
J. S. Blihmadesam Verfiled by:
B. C. Gray
Entergy Operations Inc.
Centra I Engineering Programs Appendix "C"; Attachment 23 Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn '2' = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
-20.18
-11.45
-5.94
-1.16 3.7 1
1.79
-3.02
-4.38
-5.44
-5.51
-5.34 2
3.23 9.4 12.13
-0.26
-12.62
-20.23 3
4.38 25.65 24.71 14.58
-15.3
-25.69 4
5.3 36.18 33.79 26.29
-5.92
-24.31 5
6.04 38.11 35.03 31.43 21.21 8.83 6
6.63 42.19 38.1 36.25 40.68 36.41 7
6.76 45.07 42.22 42.74 47.55 44.23 8
6.9 44.97 43.61 46.01 49.99 48.8 9
7.03 44.7 44.12 47.02 51.04 54.11 AXLen:= AllData(O)
IDA11 := A1IDatP~)
ODAIl := AllData()
Stress Distribution 100 I
I 1.44 50 -
0---
-50 1
I 0
1 2
ID Distribution OD Distribution 3
4 5
6 7
8 9
Axial Elevation above Bottom [inch]
Developed by:
J. S. Bldhmadesam Venffed by B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 23 Page 4 of 11 Engineering Report M-EP-2003-00201 Observing the stress distribution select the region In the table above labeled DataAle that represents the region of Interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region In the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue buffon down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 1.792 3.228 4.378 5.299 6.037 6.628 6.764 6.899
-20.175
-3.024 9.398 25.65 36.179 38.106 42.186 45.067 44.968
-11.45
-4.378 12.134 24.71 33.787 35.028 38.102 42.217 43.606
-5.94
-5.443
-0.258 14.577 26.287 31.43 36.248 42.736 46.007
-1.163
-5.5 11
-12.622
-15.299
-5.925 21.215 40.684 47.553 49.995 3.704
-5.341
-20.232
-25.689
-24.306 8.834 36.405 44.235 48.803 )
AxI := Data(0)
(3)
MD: Data ID:= Datal)
TQ :=Data(4)
QT:= Data2)
OD := Data~'
RID := regress(Axl,ID, 3)
RQT := regress(Axl, QT, 3)
ROD:= regress(Ax, OD,3)
RMD:= regress(Axl, MD, 3)
RTO:= regress(Axl,TQ,3)
Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 5 of 11 Engineering Report M-EP-2003-00201 FLCntr := Refpi t - co if Val =
Refpoint if Val = 2 Refp0 int + co otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr + Co InCstrs.avg := ULStrs.Dist - UTip 20 No User Input is required beyond this Point ISat Aug 09 10:59:39AM 2003 Developed by J. S. f hmadesam Velifled by:-
. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 6 of 11 Engineering Report M-EP-2003-00201 ProPLength = 4.924 Flaw Growth in Depth Direction I
I
-I I
I I
0.6
-c u
0.4 _
0.2 _
l l
1 1
o LI 0.5 l
1.5 2
2.5 3
3.5 4
Operating Time {years}
U
'5 2
A I
I I
I I
-1 I so 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developed by:
J. S. Bn'hmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors I
I I
I I
I I
8 0
or rA c
I-0
[U U,
I-4 0 -
1 I
-2 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point
- -- Surface Point Developed by:
J. S. Bflhmadesam Ventled by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9
'A V
0
._A 0
S 0.8 0.7 0.6 0.5 0.4 I..........................................
0.3 0.2 0.1 0 D 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
Entergy Operations Inc.
Central Engineering Programs CGRsambi(k 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 23 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi(k 6)
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99
-1.99 CGRsambi(k 5)
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612
-1.612 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 10 of II Engineering Report M-EP-2003-002-01 6 0 -
l
=
ID H o
oS tre l--s 4~~~~O Hoop Stress 40
- t. 2to a
t lid&o....
2 0 as
-20
-40
..... I
... - 1.
W aid tt..
1 3
5 AxIal Distance From N zzle Bottom finch) 7 9
0.07 0 06 0
O.0 5 X 0 04 0.03 0.02 0
1 2
0 perating Tm
- ayearn) 3 Developed by:
J. S. Stihmadesam Verified by:
. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 23 Page 11 of 11 Engineeri M-EP-2C 0.5 -
0 3 -
I 0
.1 C5 E
.0.3 -
-0.5 0
I O perating Time
{years) 3 4
ing Report 303-002-01 i
A serif ed by:
B. C. Gray C
-1.6 0
o~~~~~~r L~~~
eD P th,I r inIf I
-1.8
-2.0
~~~
O p e r a ti n g iin a (y e rs )l Developed by; J. S. Bnhmadesam
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 1 of 11 Engineering Report M.EP-2003-00201 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49" Degree Nozzle, Uphill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inchhr.
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 evalute the stress distribution on the flaw both for the initial flaw and for a growing flow.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpoint = 1544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper Tc-tip" located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter Z)
- 3) The lower ti-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 = 6628 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developedby:
J. S. Bnhmadesam Verfied by:
B. C. Gray
Entergy Operations Inc Central Engineering ProSrams Input Data :-
Appendix "C"; Attachment 24 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID P~nt = 2.235 Years := 4 im = 500 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 id Rid:
2 t:= Ro - Rid Rm:= Rid +
Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk -r lim Pmtblk =
50 L
co:= 2 Rr
(
Qg (i 1 1.103-10-3 T+45967 Tref+459.67)
T C01 e=.
reX
- C Temperature Correction for Coefficient Apha CO:= Co]
75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bn'hmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "
= ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (kst)
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
O 0
-20.18
-11.45
-5.94
-1.16 3.7 1
1.79
-3.02
-4.38
-5.44
-5.51
-5.34 2
3.23 9.4 12.13
-0.26
-12.62
-20.23 3
4.38 25.65 24.71 14.58
-15.3
-25.69 4
5.3 36.18 33.79 26.29
-5.92
-24.31 5
6.04 38.11 35.03 31.43 21.21 8.83 6
6.63 42.19 38.1 36.25 40.68 36.41 7
6.76 45.07 42.22 42.74 47.55 44.23 8
6.9 44.97 43.61 46.01 49.99 48.8 9
7.03 44.7 44.12 47.02 51.04 54.11 10 7.17 43.72 43.97 47.64 50.17 54.17 AXLen:= AllData(°)
IDA11:= AllData(1)
ODAII := AData()
Stress Distribution 100 U,
V)
IDAll ODAII 50 0
-50 0 1
2 3
4 5
6 7
8 9
AXLen Axial Elevation above Bottom [inch]
Developed by:
J. S. Bnhmadesam Verdfed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 4 of 11 Engineering Report M-EP-2003-00201 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).
/
17C 11 AC C
A I IZ1-I "fkA I
U
-ZU.IIJ I I.)
- j.
- 1. I UJ 1.792 -3.024
-4.378 -5.443
-5.511 3.228 9.398 12.134 -0.258 -12.622 4.378 25.65 24.71 14.577 -15.299 Data :=
5.299 36.179 33.787 26.287 6.037 38.106 35.028 31.43 6.628 42.186 38.102 36.248 6.764 45.067 42.217 42.736
-5.925 21.215 40.684 47.553
-5.341
-20.232
-25.689
-24.306 8.834 36.405 44.235 48.803 54.113 54.17 )
6.899 44.968 43.606 46.007 49.995 7.035 44.695 44.12 47.021 51.043 k 7.17 43.723 43.973 47.639 50.172 AxI : Data(O)
MD:= Data(
ID:= Data(i)
TQ :=DatP)~ 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 =
-co if Val=i Flaw center Location Location above Nozzle Bottom if Val = 2
+ c otherwise UTiD := FLCntr + C0 Developed by:
J. S. Bdhmadesam Ilcstrsav2. :
ULStrsDist - UTip IA Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 5 of 11 Engineering Report M-EP-2003-002-01
,V No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM 20013 Developed by:
J. S. Bnhmadesam Venired by:
B. C. Gray
Entergy Operations Inc Central Engineeing Programs Appendix "C"; Attachment 24 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 4.924 Flaw Growth in Depth Direction I
I I
I I
I I
0.6 I,-
C 0.4 -
0.2 _
U I-C 0.
0 I
1 1
1 1
1 1
0 0.5 1
1.5 2
2.5 3
3.5 9
Operating Time {years}
Entergy-CEP Model I
I I
I I
I 15 8
6 4-2-
0 n
I 0.
0.
0.
0 0.5 1
1.5 2
Operating Time 2.5
{years}
3 3.5 4
Entergy-CEP Model Developed by:
J. S. Bnhmadesam Verlffedby B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 7 of 11 Engineering Report M-EP-2003-002-01 U,
0 0!
a-m) 4)
80 60 40 20 0
Stress Intensity Factors I
I I
I I
I I
II I
I I
I_
I Zu 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. Blihmadesam Verledby:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 C
~0
.C_._
0 a
V I-4-
0 U
U U
U C.
0.6 0.5 0.4 0.3 0.2
-.1.....
-.................. I...................
I..... -...-
1................................................................
0.1 O )I 0.5 l
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform la" - Tip -- Linear "a" - Tip -- Quadratic la" - 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)%Y
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k, 6)
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776
-0.776 CGRsambi k 5)
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013
-1.013 Developed by:
J. S. Bdhmadesam Verfied by:
B. C Gray
Entergy Operations Inc Central Engineerng Programs Appendix "C"; Attachment 24 Page 10 of II Engineering Report M-EP-2003-002-01 60 40 20 I
0
-20
-40 1
3 5
7 9
Distance from Nozzle Bottom
{inch a) 0.5 I
03 j5 0.
5
-0.3
-0 5 0
I 2
OpVorafin g T me (ye ars )
3 4
Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 24 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 0
O.3 -
I z
0.1 e
rD i6
!-0.1 -
0
-0.5 -
0 1
2 p e ra tin g T im e
{y e ars 3
4 Su rfa ce Po int {'c -tip}
De pth Po int
~a-tip)
-0.80
-0
-1.00 g o s:S.
0 1:q:
000 C
0 00 jr'
- $0 0
0200 00002;0040 ;
- <0 iOpor4tg Time rears)5-i00;t 000 0; c Developed by.,
J S. Brihmadesam Verified by:
B. C. Gray CI