ML032790029
| ML032790029 | |
| 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: ML032790029 (128) | |
Text
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 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:
. 5. Brihmadesom 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 -"O" Degree Nozzle, All 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 inchlhr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flow and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle 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" 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 ULSrs.Dist := 1796 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Venried by:
B. C. Gray Developed by:
J. S. Bnhmadesam
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 2 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him = 1500 T := 604 aOc := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 id Rid t:= Ro -Rid t
Rm:=Rid+ -
Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk:
-ur Ibhim 5
Prntblk =
50l L
C0 2
Rm Rt:=-
Co I :=
Trf4.7a 0 c TemperatureCorrectionforCoefficientAlpha Co:= C01 Stress InDut Data 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bdhmadesam Vernlied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data in the table below. The column designations are as follows:
Column "o = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksl)
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 :=
1 I
2 3
4 5
0 0
-25.09
-27.55
-27.79
-25.62
-23.76 1
0.49
-0.56
-0.54
-2.11
-4.85
-6.16 2
0.87 21.52 18.64 17.12 14.84 10.09 3
1.19 32.75 28.49 24.14 19.64 14.45 4
1.44 35.67 29.6 26.17 25.59 28.42 5
1.64 34.24 29.57 28.29 35.41 45.38 6
1.8 29.45 29.81 31.39 43.34 61.71 7
1.93 23.67 26.5 33.26 47.61 64.65 8
2.07 18.93 24.56 33.97 49.07 65.88 9
2.2 16.54 22.85 34.79 49.52 62.8 AXLen := AllData(°)
IDAII AllData()
0DA11 := AData(5)
Stress Distribution 100 cjG t)
I-IDAll ODAll 50 Ii I
I L$44 1.,796 I
I I
I I
I I
I I
l I
0 I 0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
Observina the stress distribution select the reacon in the table above labeled DataAn that represents the Developed by:
Venlfied by:
J. S. Blihmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 4 of 11 Engineering Report M-EP-2003402-O1 region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
Data :=
0 0.485 0.874 1.186 1.436 1.635 1.796 1.932 2.068
-25.088
-0.563 21.515 32.751 35.667 34.244 29.45 23.674 18.928
-27.546
-0.539 18.635 28.494 29.598 29.574 29.814 26.502 24.564
-27.787
-2.111 17.122 24.136 26.166 28.286 31.385 33.261 33.968
-25.624
-4.851 14.843 19.645 25.589 35.408 43.337 47.609 49.071
-23.763 )
-6.157 10.089 14.45 28.417 45.379 61.713 64.65 65.876 )
AxI :
Data(O)
(3)
MD:
Data ID:= Data(l)
TQ :=Data(4)
QT : Data(2)
(5)
OD:= Data RID := regress(Axl,ID,3)
RQT:= regress(Axl,QT,3)
ROD := regress(Axl, OD, 3)
RMD:= regress(Axl, MD, 3)
RTQ := regress(Axl, TQ, 3)
FLcntr RefPo in t -C 0 if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c0 otherwise UTip := FLCntr + C0 IflCstrs.avg ULStrs.Dist - UTip 20 Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point fSat Aug 09 10:21:18AM 2003 Developed by:
J. S. Bnhmadesam Veiffled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 6 of 11 Engineering Report M-EP-2003.002-01 ProLength = 0092 0.6 U
C 0) 0 0.4 t Flaw Growth in Depth Direction I
I I
I I
I I
I I
I I
I I
I 0.2 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model 4
U 0
'5 0
g:
LL 0.8 0.6 1,
1,5 1
.092 1-
=-----------
I I
~~I I I
I 0.4 F 0.2 0 CI 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed by:
J. S. B1hmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 7 of 11 Engineering Report M-EP-2003-00201 Stress Intensity Factors 0
ai, ca vE (n
80 60 -
40 v 0 0.5 1
1.5 2
2.
Operating Time {years}
Depth Point Entergy-CEP Model
- - Surface Point Entergy-CEP model 5
3 3.5 4
Developed by:
J. S. Bnhmadesam Ven'lfed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw I
0.9I 0.8 vn va 0
c E
-0 0
I-0.7 0.6 0.5 0.4 0.3
.... 11.....-......
I -......................
I-.....
I -............
.X
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.2 Verified by:
B. C. Gray COW 0.1 0 I I
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. Brhmadesam
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 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) 18.307 19.315 19.322 19.33 19.337 19.344 19.352 19.359 19.366 19.374 19.381 19.388 19.396 19.403 19.41 19.417 CGRsambi (k, 5) 13.252 13.936 13.941 13.946 13.951 13.956 13.962 13.967 13.972 13.977 13.982 13.988 13.993 13.998 14.003 14.008 Developed by:
J. S. Bnihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs so -
[
40 -
J 20 0 - 04-
- 0 34 -
zE
-5 0 23 -
6
.0 0.3 Appendix "C"; Attachment 2 Page to of 1 Engineering Report M-EP-2003-00201 0.0 0 5 1 0 1 5 2.0 2.5 3.0 Distance from Nozzle Bottom (inches}
0 1
2 3
4 O perating Time (years)
Developedby.-
J. S. Bihmadesam Vedried by.:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.4 0.34 z
0.23
.1 0
-0
, 0.2 i
.0 2
O p eretin g T ime (ye ars 5 0 S u rfa c e P___
___o
__in
__t 50~ ~
~~~~
D e p thce P o v n t (;c
- t ip }l 40 2 0 i0 f
X ~0 1
2 3
4 Ope~~ sti Timne Cy aeAr)
Venfied by B. C. Gray al D
- ~
~~~~~~~~~C?
Developed by.
J. S. Brlhmadesam
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 3 Page of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when R,,,,tjd is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"O"degree Nozzle, All Azimuth, 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).
he throughwall flaw "Upper Tip" is located at the Reference line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the Upper Li mit for the evaluation, which is the bottom of the file t weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist:= 1.796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 3 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :
L :=.794 od := 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 Ilim:= 1500 T:= 604 v := 0.307 ao, := 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 I
g I
L:.103 1
L T+459.67 Tref+459.67)I Timopr := Years-365-24 od 2
id 2
t := Ro - Ri Rm:= R + -
2 CFinhr:= I.417105 Tiflopr Cblk:=
him Pmtblk:= l 50 I
L 2
Developed by:
Verified by:
lIDeveloped by:
Verified by:- I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 3 of 10 Engineenng 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)
DataAII :=
0 1
2 3
4 5
o 0
-25.09
-27.55
-27.79
-25.62
-23.76 1
0.49
-0.56
-0.54
-2.11
-4.85
-6.16
-2 0.87 21.52 18.64 17.12 14.84 10.09 3
1.19 32.75 28.49 24.14 19.64 14.45
.4 1.44 35.67 29.6 26.17 25.59 28.42 5
1.64 34.24 29.57 28.29 35.41 45.38 6
1.8 29.45 29.81 31.39 43.34 61.71 7
1.93 23.67 26.5 33.26 47.61 64.65 8
2.07 18.93 24.56 33.97 49.07 65.88 9
2.2 16.54 22.85 34.79 49.52 62.8 10 2.34 17.56 22.68 33.81 47.49 63.56 AIIAxi:= DataA I a)
AIED DataAIll AIIOD := DataAII 5)
IDeveloped by Venfied by: I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 4 of 10 Engineering Report M-EP-2003-00201 2
0 0.5 1
1.5 2
2.5 3
Axial Distance above Bottom [inch]
ID Distribution
- - OD distribution Observing the stress distribution select the region in the table above labeled DataA, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-25.088 -27.546 -27.787 -25.624 -23.763)
Data:=
0.485 -0.563 0.874 21.515 1.186 32.751 1.436 35.667 1.635 34.244 1.796 29.45 1.932 23.674 2.068 18.928
-0.539
-2.111
-4.851
-6.157 18.635 17.122 14.843 10.089 28.494 24.136 19.645 14.45 29.598 26.166 25.589 28.417 29.574 28.286 35.408 45.379 29.814 31.385 43.337 61.713 26.502 33.261 47.609 64.65 24.564 33.968 49.071 65.876 k2.204 16.541 22.854 34.789 49.525 62.795 )
(: )
AAl:= Data (I)
ID: Data (5:
OD:=Data RID:= regress(Axi, ID,3)
ROD:= regress(Axi, OD,3)
Developed by:
Venfied by:
lIDeveloped by Venfiedby. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr := BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ 1ncStrs.avg :=
20 No User Input required beyond this Point M Sat Aug 09 11:44:49 AM 2003n-Developed by:
Venfied by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 6 of 10 Engineering Report M-EP-2003-00201 PrOPLength = 0.252 Flaw Length vs. Time 1.5
.~ TWCPWSCC a
j,3 0
L-1 0.5 0
-0.5 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWSCC I
I )
Operating Time years)
Entergy Model Increase in Half Length 2
U-e U
C3 1.5 1
0.5 0 0 0.5 1
1.5 2
2.5 3
Operating Time Years}
3.5 4
Developed by:
Verified by:
IDeveloped by:-
Verified by:I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 8
.5 a
200 0
u co LT-
.2 100 C
A P
u 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years}
-- ID SIF - Entergy Model SIF Average 4
Developed by:
Verified by:
lIOeveloped by.,
Verifed by:I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCC(j,6) =
35.366 42.321 42.355 42.39 42.424 42.459 42.494 42.528 42.563 42.598 42.633 42.668 42.702 42.737 42.772 42.807 TWCpWSCC (j7 =
37.917 41.494 41.524 41.555 41.586 41.616 41.647 41.678 41.708 41.739 41.77 41.801 41.832 41.863 41.894 41.925 TWCpwscc(j 8) 38.137 43.512 43.547 43.582 43.617 43.652 43.687 43.723 43.758 43.793 43.828 43.864 43.899 43.934 43.97 4.005 Developed by:
Verified by:
lIDeveloped by:
Venfied by:I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot 60 40 I 20' 0
-20 F
IDHI I-ODF
/
raoopa2<ron
_ ~
of
..,~
\\
.OW 4U 0.0 I
I I
I 0.5 1.0 1.5 2.0 Distance from Nozzle Bottom (inch) 2.5 3.0 300 0
a to i
0 l_____
O D S u rface S IF ID Su rfa ce SI Average S IF 0
1 2
1 3
4 Ope ratingTime T
- e(yea rs) lDeveloped by:
V
Entergy Operations nc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.5
£ F
1.0
° 0 5 0.0 2
3 0 p e ra ling Time years)
Developed by:
Verified by:
IDeveloped by:
Verified by: I
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 4 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. Bnhmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM '8" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius to-Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to 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 the reference point elevation measured upward from the nozzle end.
RefPo int =1544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "C-tfig" located of 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 eg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzk bottom) below.
ULStrs.Dist :=
.786 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Brihmadesam Veified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 2 of 1 1 Engineering Report M-EP-2003-00201 Input Data :-
L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 P Int := 2.235 Years := 4 r
=im 1500 T := 604 aoc := 2.67 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 Rid := id Rid
-Y t := Ro-Rid t
RIM Rid+2 Timopr := Years365-24 CFinhr := 1.417 105 Timopr Cblk.= -
lim
'im Prntblk =
50 L
Co := -
RrM t-t
[
Qg
(
11 1.103 10- 3 T+459.67 Tref+4 59.67 )
T Co I := e
- 0c Temperature Correction for Coefficient Alpha CO:= CO 0
75 th percentile MRP-55 Revision 1 Developed by:
J S. Bnhrmadesam
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 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 "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 o o 1
02 3
4 5
O 0
-27.4
-24.36
-22.21
-20.41
-18.98 1
0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4
1.43 33.62 27.79 24.8 24.32 26.99 5
1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67 9
2.18 14.83 22.26 34.78 49.05 63.38 AXLen := AlIData(0)
IDAII:= AI]Data(')
ODAII:= AllData()
100 (jn U,
50 Stress Distribution I
I I
I I
1.44 1.786
_I, E
,~~~~~
I 0
-4n 0 0.5 1
1.5 2
Axial Elevation above Bottom [inch]
2.5 3
ID Distribution
OD Distribution Developed by:
J. S. Brlhmadesam Velirled by.-
B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 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 0.483 0.87 1.18 1.428 1.627 1.786 1.919 2.051 2.183
-27.404 0.633 17.665 29.798 33.623 32.364 27.394 21.498 16.944 14.834
-24.356
-1.486 16.422 26.049 27.792 28.469 28.918 25.556 23.793 22.263
-22.209
-3.599 14.61 22.723 24.8 27.591 31.388 33.55 34.064 34.779
-20.407
-4.44 12.415 18.95 24.321 34.284 43.882 48.089 49.472 49.055
-18.978 )
-5.268 9.376 14.201 26.989 45.104 63.718 66.365 67.672 63.377 Axl := Data(°)
(3)
MD:
Data
()
ID: Data TQ:= Data4)
QT := Data(2)
OD := Data(5)
RID := regress(Axi,ID,3)
RQT:= regress(AxI,QT,3)
ROD:= regress(AxI,OD,3)
RMD:= regress(Axl, MD, 3)
RTQ := regress(Axl,TQ,3)
Developed by:
J. S. Blihmadesam Vered by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 5 of 1 1 Engineering Report M-EP-2003-00201 FLCntr =
Refpoint - co if Val =
Refpoint if Val = 2 RefPoint + CO otherwise Flaw center Location above Nozzle Bottom ULStrs.Dist - UTip UTip := FLCntr + CO Intrsavg 20 No User Input is required beyond this Point ffi Sat Aug 09 10:59:39 AM 2003 Developed by:
J. S. Brhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 6 of 1 Engineering Report M-EP-2003-002-01 ProPLength = 0.082 0.6 U
C C
V 0
0 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 3
3.5 4
Operating Time {years}
2 0
r-
.rd W
V-L; 0
I I I
I I
I 0.082
-I 0
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developed by:
J S. Bnhmadesam Verifred by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 7 of 11 Engineering Report M-EP-2003-002-01 100 U
I-t!
0 U
C I-80 60 Stress Intensity Factors I
I I
I I
I I
40 20 0
0 0.5 l
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developed by J. S. Brihmadesam Vefied by.
B. C. Gray
Entergy Operations Inc.
CentralI Engineering Programs Appendix "C"; Attachment 4 Page 8 of 1 1 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 1
0.9
~2 C
0 0C V
E 0
0.8 0.7 0.6 0.5 0.4
................-.................... I.-...............................
..................................................................................... I.............................-.... -W"MMW4
...I....
I--- ----------------------- ----------------- i--- -------------------------
0.3 0.2 0.1 0
0
----------------------------------------............................................. I........................................
0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
Il"- Tip -- Uniform "la" - Tip -- Linear Ila - Tip -- Quadratic Via - Tip -- Cubic ti"- Tip -- Uniform llc' -Tip -- Linear ti"- Tip -- Quadratic ti"- Tip -- Cubic Developed by:,
J. S. Brihmadesam Verified by:
B. C. Gray Ccce
Entergy Operations Inc.
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 4 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k, 6) 14.996 14.886 14.89 14.895 14.899 14.903 14.907 14.912 14.916 14.92 14.925 14.929 14.933 14.938 14.942 14.946 CGRsambi 12.571 12.495 12.499 12.504 12.509 12.513 12.518 12.522 12.527 12.531 12.536 12.541 12.545 12.55 12.554 12.559 Developed by:
J. S. Brihmadesam Verfied by:
- 8. C Gray
Entergy Operations Inc.
Central Engineering Programs 6 0 1
[
Appendix "C"; Attachment 4 Page JO of 11 Engineering Report M-EP-2003-00201 i
I 40 20 0
-2 0
-40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance From N ozzle Bottom
{inch) 0.12 -
O.10 -
C 0.08 -
0.06 -
0.0 4 0
1 2
3 4
O perating T ime
{yea rs}
Developed by:V J. S. Bnhmadesam Verified by B. C Gray
Entergy Operations Inc.
Central Engineering Programs 0.1 2 -
.S Oi 0.08-I 0 0.0 0
0.0 0 -
Appendix "C"; Attachment 4 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
3 4
O perating Tim e {years) 1 9 -
5 17 -
E
.5 i 15 -
I A 13 -
11 0
3:
4 O perating T im e {year)s Developed by.
J. S. Brihmadesam Verified by:
B. C Gray Co5
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. 5. Brihmadesom 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 -"8" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmdt" -- between 1.0 and 300.0 Note: Used the Metrc 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 rinch) 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 Ulpper "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 elevation from Nozle Bottom. Enter this value below ULStrs.Dist = 1.786 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Input Data :-
Appendix "C"; Attachment 5 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 aO := 0.661*0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him := 1500 T := 604 XOC := 2.67 10- 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 id Rid := 2 t:= R-Rid i
Rm:Rid+2 Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk:=
m 1lim IJim Prntblk =
50 L
C0 2
Rm RIt. :=
-103 Tref+459.67)
C01 := e
)
0c Temperature Correction for Coefficient Alpha Co:= Co0 Stress Inout Data 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bnihmadesam
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 3 of 1 Engineering Report M-EP-2003-00201 Input all available Nodal stress data in the table below. The column designations are as follows:
Column "on = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "" = ID Stress data at each Elevation (ksi)
Column f2" = Quarter Thickness Stress data at each Elevation (ksi)
Column 3m = 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
-27.4
-24.36
-22.21
-20.41
-18.98 1
0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4
1.43 33.62 27.79 24.8 24.32 26.99 5
1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67 9
2.18 14.83 22.26 34.78 1 49.05 63.38 AXLen:= AllData(°)
IDAII := AData')
0DA11 := AData(5)
Stress Distribution 100 an rla CA IDA))
ODA!!
50 0
-50 0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
Developedby:V J. S. Blihmadesam Verfifed by:-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 4 of 1 1 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataA, that represents the region of interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equalff sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-27.404 -24.356 -22.209 -20.407 -18.978) 0.483 0.633
-1.486
-3.599
-4.44
-5.268 0.87 17.665 16.422 14.61 12.415 9.376 22.723 18.95 14.201 1.18 29.798 26.049 Data :=
1.428 33.623 27.792 24.8 24.321 26.989 1.627 32.364 28.469 27.591 34.284 45.104 1.786 27.394 28.918 31.388 43.882 63.718 1.919 21.498 25.556 33.55 48.089 66.365
~2.051 16.944 23.793 34.064 49.472 67.672 )
Ax := Data(0)
MD := Data)
(I)
ID: Data TQ := Data(4)
QT := Data(2)
OD:= Data(5)
RID := regress(Axi,ID,3)
RQT := regress(AxI, QT, 3)
ROD := regress(Axl,OD,3)
RMD:= regress(Axl, MD,3)
RTQ := regress(AxI, TQ,3)
FLCntr Refpoint - c0 if Val =
Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + c0 otherwise UTip := FLCntr + co SncStrs.avg ULStrs.Dist - UTip 20 De veloped by:
J. S. Brihmadesam Verfed by B. C. Gray
Entergy Operations Inc Central Engineeing Programs Appendix "C"; Attachment 5 Page 5 of I1 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM 2003-Developed by:
J. S. Brlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 6 of 11 Engineering Report M-EP-2003-00241 ProPLength = 0.082 Flaw Growth in Depth Direction 0.6 U
0 0.4 I
I I
I I
I I
I I
I I
I I
0.2 0 0 0.5 I
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model u
0Q-0.81 0.61 I
I II 1.5
~~~~~~~~~~~~~~~~~~~~~~~.092
~ ~ ~~~ ;~-
~~~~I I
I I I 0.4 1 0.2 0a) 0.5 I
1.5 2
2.5 3
Operating Time {years}
3.5 4
Entergy-CEP Model Developed byV e
J. S. Brihmadesam Veried by:-
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 7 of 1 1 Engineering Report M-EP-2003-002-01
.)_
U V) c 0
vw 80 60 Stress Intensity Factors
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I I
I~~~~~~~~~............
40 20 A
u 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 byV e
J. S. Bnifmadesam Venired by:-
B C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw co~
C v
0 c-)
C 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating time {years}
"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 C0(D
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 9 of 1 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) 18.417 19.5 19.507 19.515 19.522 19.53 19.538 19.545 19.553 19.56 19.568 19.575 19.583 19.59 19.598 19.605 CGRsambi(k, 5) 13.271 14.008 14.014 14.019 14.024 14.03 14.035 14.04 14.046 14.051 14.056 14.062 14.067 14.072 14.078 14.083 Developed by.,
J. S. Bnhmadesam Verned by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 5 Page 10 of 1 1 Engineering Report M-EP-2003-002-01 a60 4 0 l
20 0
-20
-40 0 istanc from Nozzle B ottom finches)
_ 0.4 -
E
.2 ii I
g 0.1 C) 0.0-0 1
2 3
4 O pera ting Time (yea rs}
Developed by:
J. S. Blihmadesam Vedifled by:-
B. C Gray
Entergy Operations Inc Central Engineering Programs 0.4-U 0.3 0
C
- 0.2 2
0 0.1 0
0.0 Appendix "C"; Attachment 5 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
3 4
O perating Time (years}
50 l
~~~Surf ace Po intI ""-1iip}
l p th P int ($
jti) 450 0
'f 40
/
- l30
- C
~
~
~
S 2 0 10 0
0 perat:n:2 3
[y4 Operating Time (years)l
\\
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray 007
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw beveloped by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when R,,,td/t is between 2.0 and 5.0 Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, Downhill Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric fon 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 nput 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 Input is the UIpper 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 (measred from nozzle bottom) below.
ULStrs.Dist := 1786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by:
Verified by: I De eo e by eife y
Entergy Operations nc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :
L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years := 4 hjim:= 1500 T := 604 v := 0.307 a0c:= 2.67 10 12 Qg:= 31.0 Tref:= 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio R 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F 0
-Q Tg 5
I 1.103. l 3 T+45g 7 f+45967)2 Co := e ao(XC Timnopr Years 365-24 od 2
Ri:= id 2
t:= Ro -Ri Rm:= Ri + -
2 CFinhr:= 1.417-105 TiITopr Cblk:=
hlim Prntblk:= l 50 L
I: -
2 IDeveloped by:
Venfied by: I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 3 of o Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "
= Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAIl :=
a 0 7 1
2 3
4 5
0 0
-27.4
-24.36
-22.21
-20.41
-18.98 1
0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4
1.43 33.62 27.79 24.8 24.32 26.99 5
1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67
.9 2.18 14.83 22.26 34.78 49.05 63.38 AllAxl:= DataAII MUD:= DataAII AIIOD:= DataAIl 5 Ievelped by:
Verified byI Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 4 of 10 Engineering Report M-EP-2003-002-01 100 75 P
CZ 50 25 0
-25
-50 0 0.5 1
1.5 2
2.5 3
Axial Distance above Bottom [inch]
ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-27.404 -24.356 -22.209 -20.407 -18.978)
Data:=
0.483 0.633 0.87 17.665 1.18 29.798 1.428 33.623 1.627 32.364 1.786 27.394 1.919 21.498 2.051 16.944 12.183 14.834
-1.486
-3.599
-4.44
-5.268 16.422 14.61 12.415 9.376 26.049 22.723 18.95 14.201 27.792 24.8 24.321 26.989 28.469 27.591 34.284 45.104 28.918 31.388 43.882 63.718 25.556 33.55 48.089 66.365 23.793 34.064 49.472 67.672 22.263 34.779 49.055 63.377 )
Axl:= Data (I
ID:
Data (5)
OD:=Data RID := regress(Axl,ID,3)
ROD:= regress(Axi,OD,3)
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr := BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ ncStrs.avg =
20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM VTr[1:
IDeveloped by:-
Verified by:I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.242 Flaw Length vs. Time 1.5
.5 2]T~llsc 0
0.5 0
-n 1;
A.,
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
r-5 mb r_
C2 r) a)
C)C 1.5 0.5 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time Years) 4 IDeveloped by:
Verified by:I
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 z
.)
t:
.M i
0 t.
200 100 0
0 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {Years}
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average Developed by:
Veted b(
lIDeveloped by.,
Verified by I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCPWSCC
- 6) =
34.773 41.861 41.893 41.925 41.958 41.99 42.022 42.054 42.087 42.119 42.152 42.184 42.216 42.249 42.281 42.314 TWCpwscc(j7) =
35.756 39.204 39.232 39.26 39.288 39.316 39.344 39.373 39.401 39.429 39.457 39.485 39.513 39.542 39.57 39.598 TWCpwsc 36.661 42.033 42.065 42.097 42.129 42.162 42.194 42.226 42.259 42.291 42.324 42.356 42.389 42.421 42.454 42.486 Developed by:
Vefied by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 9 of 10 Engineering Report Ra On 'n, nins I%4 IVI-crI-A 60 40 fX I-20 (20 z
-20
-40 300 -
- , 2 5 0 -
6 I
200 -
1 5 0 10 50 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (inch)
I n n If 7ffjb ID Su rfa ce SIF
/
Average SIF A _ _
0 1
2 3
4 Operating Time (years)
Developed by
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 6 Page 10 of 10 Engineering Report M-EP-2003-00201 1.5 I
.0
.3 S
0.5 0.0 2
3 0 p r&ling Time (ye are)
Developed by:
Verified by:~~~~
lIDeveloped by:-
Verified by.:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 7 Page of 11 Engineering Report M-EP-2003-00201 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 -'8" Degree Nozzle, Uphill 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. 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 flow with repsect to the reference point, the flow tips and center can be located as follows:
- 1) Tie 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 "T-tip" located at the reference point (Enter 3).
Val := 2 The Dzput Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld keg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below LJLStrs.Dist := 2386 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:V J. S. Bnhmadesam Vef tried by.-
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 7 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 uim = 1500 T := 604 aOc := 2.67-10 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R. :=od
- 0.
2 Rid :
id Rid T=
t:= Ro - Rid Rm:=Rid+
Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk:= -
P b imn
~~~~~~Ptblk
=
50l L
co:= 2 Rm Rt :=-
~Q g
( _ _ _ _ _ _ I_ _ _
I 1.103-103 T+459.67 Tref+4 5 9.67 C01 C 0 C 0
.a0c Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 7 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 "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
-22.34
-20.02
-18.96
-18.09
-17.15 1
0.64
-0.72
-3.67
-6.82
-8.7
-10.19 2
1.16 17.28 14.91 9.65 3.77
-1.22 3
1.58 29.36 26.5 20.58 13.8 4.75 4
1.91 36.5 30.92 25.41 21.15 18.37 5
2.17 36.54 30.33 27.24 32.61 41.48 6
2.39 33.13 31.54 31.44 42.45 57.26 7
2.53 27.12 28.37 33.43 47.23 63.83 2.67 21.96 26.11 34.41 48.85 63.88 9
2.81 18.99 24.12 35.2 49.9 62.11 AXLen:= AllData()
ID
= AllDatP)
All ODAII := AllData)
Stress Distribution
[U ci) a)
50 13544 2J86 0
-50.A 0
0.5 I
1.5 2
2.5 Axial Elevation above Bottom [inch]
3 3.5 4
ID Distribution OD Distribution Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 7 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.
(
0
-22.34 -20.022 Data :=
0.645 1.162 1.575 1.907 2.173 2.386 2.528 2.67 2.813
-0.722 17.28 29.359 36.503 36.536 33.132 27.116 21.957 18.993
-3.667 14.912 26.501 30.924 30.331 31.54 28.37 26.115 24.124
-18.961
-6.821 9.653 20.582 25.411 27.24 31.442 33.434 34.408 35.202
-18.087
-8.696 3.766 13.796 21.15 32.606 42.452 47.233 48.851 49.904
-17.153)
-10.19
-1.22 4.753 18.374 41.485 57.257 63.826 63.884 62.107 )
Ax := Data(0)
MD:= Data)
ID := Data)
TQ := DataP QT := Data(2)
OD := Data (5)
RID := regress(Axl, ID, 3)
RQT:= regress(Ax1,QT,3)
ROD:= regress(Axl, OD, 3)
RMD:= regress(Axl, MD, 3)
RTO:= regress(Ax1,TQ,3)
Developedby:V J. S. Bnhmnadesam Veiffed by B. C Gray
Entergy Operations Inc.
Appe Central Engineering Programs FLCntr =
Refpi t - co if Val =
Refpoint if Val = 2 Refpoint + co otherwise endix "C"; Attachment 7 Engi Page 5 of 11 ME I
Flaw center Location above Nozzle Bottom neering Report EP-2003-002-01 I
Flaw center LocationaboveNozzle Bofforn UTip := FLCntr + Co InCstrs.avg =
ULStrs.Dist - UTip 20 No User Input is required beyond this Point fSat Aug 09 10:59:39AM 2003 Developed by:
J S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 7 Page 6 of 11 Engineering Report M-EP-2003-00201 ProPLength 0.682 Flaw Growth in Depth Direction 0.6 CL e)1 a
0.4 I
I I
I I
I I
I I
I II 0.2 0
2 0
0.5 1
1.5 2
2.5 3
3.5 A
Operating Time {years}
I c-,
c 3-I I
I I
I I
I I
.682 I
I I
I I
I I
0
-1 0I 0.5 1
1.5 2
2.5 3
Operating Time {years}
3.5 4
Developed by:
J. S. Sifhmadesam Vered by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 7 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors own I U U
r-UL 0) a, U
C I-V)w 80 60 I
I I
I I
I I
I.........
I..
I...
I I
I I
I I
I 40 20 0 _
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developed by:
J. S. Blihmadesam Veried by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 7 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.I 0.9 v:
0 c
C 0
Cn 0
0 C
0 c) c c
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1.5 2
2 Operating time {years}
.5 3
3.5 4
a" - Tip-- Uniform a - Tip -- Linear lai - Tip -- Quadratic "a" - Tip -- Cubic c" - Tip -- Uniform c'- Tip -- Linear
Vic" - Tip -- Quadratic c" - Tip -- Cubic Developed byV J. S. Brihmadesam Verified by.-
Bc.
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 7 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi(k 6) 14.023 14.503 14.507 14.511 14.514 14.518 14.522 14.526 14.53 14.534 14.537 14.541 14.545 14.549 14.553 14.556 CGRsambi 11.685 12.086 12.09 12.094 12.098 12.102 12.105 12.109 12.113 12.117 12.121 12.125 12.129 12.132 12.136 12.14 Developedby:
J S. Bnlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 7 Page 10 of 11 Engineering Report M-EP-2003-00201 6 0 40 -
- p qtBllnd Zn.
20 0
W~~~~~~~~~~~~~~~-
WId SoIto 0.1.
2....
. 0 t~~~~~~.0 o
.s
.0 I..
2.0 2.5 3.0 3.5 AxIsl DIstance From N ozzle Bottom (inch}
AlIData(') )
(All~ata(°) ADIMP~)
0.14 -
0.1 2 0.10 1
~
0.0 4..
a.046 11-I
-.... 1.. -
....... I .
... I... 1. -...
I.....I.............. I.... -. 1-1...
I 1
2 3
4 O perating Tm (years)
Developed by:V J. S. Bnhmadesam Veiffled b.v.-
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 7 Page 11 of 11 Engineering Report M-EP-2003-002-01
' 0.1 2 To 0.048 C)
I 0.
5 20.0 20 004 -_
0 1
2 3
4 O perating Time years}
20 0
1 8 t I
_ 14 1 2 10 f
v l -
s IF Depth Point I
0 S IF Surface Point
r
f J
9 l
__.;--
0 f-
-- R g -- -:
1-f -
V f f I
C J
0; >_Ar I
\\
5 d
y d
0
- E 7
9
\\
C f
X; n
S 0
0 l
0 1
2 3
4 Operating Time (years )
t A
Verifed by.
S. C. Gray CAt Developed by.
J. S. Bnhmadesam
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 Page 1 of 11 Engineering Report M-EP-2003-00241 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby:
. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -8" Degree Nozzle, 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 forn of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input isa location for a point on the tube elevation to define the point of Interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow both for the initial flaw and for a growing flaw. This is defined as the reference point Enter a number (inch) that represnets the reference point eleation 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 "c-tip"1 located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower Xc-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 = 2386 Developed by:
J. S. Blihmadesam Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Verified by:
B. C. Gray
Entergy Operations Inc Central Engineeng Programs Input Data :-
Appendix "C"; Attachment 8 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint = 2.235 Years := 4 him := 1500 T := 604 aOc := 2.67 10- 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R.
od Rid := id t:= Ro -Rid
- t Rm= Rid+ +
Timopr := Years-365-24 CFinhlr := 1.417-105 Timopr Cblk:
-ur
'him Pmtblk =
50 L
co:= 2 Rm Rt :=-
1.103 lo-3(T+4 59.6 7 Tref+459.67)
T Co0 1 e
- 0C Temperature Correction for Coefficient Alpha Co:= Co1 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bffhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 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 "1" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ks)
Column "5" = OD Stress data at each Elevation (ks)
AllData :=
0 1
2 3
4 5
0
-22.34
-20.02
-18.96
-18.09
-17.15 1
0.64
-0.72
-3.67
-6.82
-8.7
-10.19 2
1.16 17.28 14.91 9.65 3.77
-1.22 3
1.58 29.36 26.5 20.58 13.8 4.75 4
1.91 36.5 30.92 25.41 21.15 18.37 5
2.17 36.54 30.33 27.24 32.61 41.48 6
2.39 33.13 31.54 31.44 42.45 57.26 7
2.53 27.12 28.37 33.43 47.23 63.83 8
0 2.67 21.96 26.11 34.41 48.85 63.88 9
2.81 18.99 24.12 35.2 49.9 62.11 AXLen := A1ata(o)
IDAI:= AllData()
0DA11 := AlIData(5)
Stress Distribution 100
-IDAII W
All (n
50 0
-50 _0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
3.5 4
Developed by:V J. S. Bfihmadesam Veiffed by:-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 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 "equalP sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
-22.34 -20.022 -18.961 -18.087 -17.153 0.645 -0.722 -3.667
-6.821
-8.696
-10.19 Data :=
1.162 17.28 1.575 29.359 1.907 36.503 2.173 36.536 2.386 33.132 2.528 27.116 14.912 9.653 26.501 20.582 13.796 4.753 30.924 25.411 21.15 18.374 3.766
-1.22 30.331 27.24 32.606 41.485 31.54 31.442 42.452 57.257 28.37 33.434 47.233 63.826 k 2.67 21.957 26.115 34.408 48.851 63.884 )
AxI := DatP)
MD:= Data3)
ID:= Databl)
TQ := Data(4)
QT := Data(2)
OD: Data~
RID := regress(Axl,ID,3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD:= regress(Axl,MD, 3)
RTQ := regress(Axl, TQ, 3)
FLCntr:
-Co if Val =i Flaw center Location Location above Nozzle Bottom if Val = 2
+ c0 otherwise UTiD FLCntr + cO Developedby J. S. Bdhmadesam Inlcstsav2.
UL~Strs.Dist - UTip ina Velffled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ff Sat Aug 09 10:21:18AM 2003-Developed by:
- 1. S. Bdhmadesam Vendled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 Page 6 of 11 Engineering Report M-EP-2003-002-01 PrOPLength = 0.682 Flaw Growth in Depth Direction I
I I
I I
I I
0.6
- ti 0.4 a) 02 00 U
ib 0.6 a) 0.4 p
I-5 0.6 r
i
'5 0.4 CL 0.
I-0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model 4
t I
I I
I I
I I
1 5
.092 I----
.~~~~~~~~~~
t 0
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed bye J. S. Bndhmadesam Venffed by B. C Gry
Entergy Operations Inc Appendix "C"; Attachment 8 Engineering Report Central Engineering Programs Page 7 of 11 M-EP-2003.002-01 Stress Intensity Factors
.s 80 604 60 C
20 b
400 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
J. S. Bfifmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 C
C 0
.C a
E C
I-
...... I............................I......I.........
0.6 0.5 0.4 0.3 0.2 0.1 0
-. -.. -.- -. --,- -- -- I- -- -- -- -- -.-- -- -- -- -- --- -- -- -- -- -- -- -- -- -- - -- -- -- --- -- -- -- -- -- -- -- -- -- ---- -- --..
I.....................
0 0.5 l
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform la" - Tip -- Linear "a" - Tip -- Quadratic ia" - Tip -- Cubic tic" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verifed by:
B. C. Gray Cl "
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 Page 9 of 11 Engineering Report M-EP.2003-002-01 CGRsambi k 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k 6) 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 5.099 CGRsanbi(k, 5) 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 4.125 Developed by:
1 S. Bnhmadesam Veried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 8 Page 10 of II Engineering Report M-EP-2003-002-O1 S 0 0 D D s t ri b u t cnl 4 -
Tow P f
1 Ze 40 20
-40 0 0 0.5 1 0 1 5 2.0 2.5 Distance rom Nozzle Bottom (Inches) 3.0 3.5 (AXLen(°)
IDAII ()
ODAll(° )
0 5 -
i 0 3 -
1l0.1
-0.1 -
f,
-0 3 -
-0.5 -
Developed by:
J. S. Blhmadesam 0
1 2
O perating Tim e (yoars) 3 4
Verified by:
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs 0.5
_03 21 0.1 I
I i -0.1 i
-0.3 Appendix "C"; Attachment 8 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
Operating Time (years) 3 4
Su rfa ce Po in t {"c"-tip Depth Point {"a-tipj 5.0 6
~4.8 0
uL 4.8
- 4.4 4.2 4.0 IL1 2
3 4
OWPeratingfT1Me { yearsl Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray C),2
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 9 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 RPtd/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, Uphill Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric fon 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 Zput is to locate the Reference Lne (eg. top of the Blind Zone).
The throighwall flaw 'Vpper ip-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 Dnput 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:= 2.386 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by.
Verified by. I Deeoe by eife y
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 9 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :
L := 0.344 od:= 4.05 id:= 2.728 Pnt:= 2.235 Years:= 4 Ilim:= 1500 T := 604 v := 0.307 Initial Flaw Length TW axial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F aoc := 2.67 10 12 Qg:= 31.0 Tref:= 617
[
-Qg
-(
I I
a 1.103. 10- 3 V +459.67 Tfe+459.67)J Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Timopr := Years 365-24 od 2
Ri:= id 2
t:= Ro - Ri Rm:= Ri + -
2 CFinhr:= 1.417-105 TiTmpr Cblk :=im
'Jim PintbIk :=
50 50"m I
L 2
Developed by:
Verified byI
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 9 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 "I" = ID Stress data at each Elevation (ksi)
Column 5" = OD Stress data at each Elevation (ksi)
DataAu :=
0 1
2 3
4 5
0 0
-22.34
-20.02
-18.96
-18.09
-17.15 1
0.64
-0.72
-3.67
-6.82
-8.7
-10.19 2
1.16 17.28 14.91 9.65 3.77
-1.22 3
1.58 29.36 26.5 20.58 13.8 4.75 4
1.91 36.5 30.92 25.41 21.15 18.37 5
2.17 36.54 30.33 27.24 32.61 41.48 6
2.39 33.13 31.54 31.44 42.45 57.26 7
2.53 27.12 28.37 33.43 47.23 63.83 8
2.67 21.96 26.11 34.41 48.85 63.88 9
2.81 18.99 24.12 35.2 49.9 62.11 i0 2.96 19.58 24.12 34.38 48.41 64.46 111 3.1 23.12 24.38 33.3 45.65 61.6 AllAxl:= DataAIl I (I)
MIID= DataAlI (5)
AllOD:=DataAII Developed by:
Verified by:
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 9 Page 4 of 10 Engineering Report M-EP-2003-002-01 80 20
-40 0 0.5 1
1.5 2
2.5 3
3.5 4
Axial Distance above Bottom [inch]
ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled 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).
/
IIC I.-
InQ C\\
U
-L/L.34 0.645 -0.722 1.162 17.28 1.575 29.359 1.907 36.503 2.173 36.536 2.386 33.132 2.528 27.116 2.67 21.957 2.813 18.993 2.955 19.578
-ZU.ULL
-3.667 14.912 26.501 30.924 30.331 31.54 28.37 26.115 24.124 24.12
-15.yo1
-I6.V5
{.133 I Data:=
-6.821
-8.696
-10.19 9.653 3.766
-1.22 20.582 13.796 4.753 25.411 21.15 18.374 27.24 32.606 41.485 31.442 42.452 57.257 33.434 47.233 63.826 34.408 48.851 63.884 35.202 49.904 62.107 34.376 48.405 64.458 33.301 45.647 61.604 J 3.098 23.12 24.375 Axl:= Data (I)
ID:
Data (5)
OD:=Data RID:= regress(Axl, ID, 3)
ROD:= regress(Axl, OD, 3)
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 9 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ Strs.avg :
20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM 2003 jDeveloPed by:
Verified by:
lIDeveloped by Verffed byt
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 9 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 0.842 1.5 Ci TCpwscc
- ~
-Cj,3 0
I 0.5 0
-0.5 L-0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCpwscc(J l)
Operating Time {years}
Entergy Model 2
C)
C-1.5 0
0.5 Increase in Half Length
~~~~~~~~~~~~~~~~~~~~~~~~~~t 0 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {Years}
lIDeveloped by:
Verified by Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 9 Page 7 of 10 Engineering Report M-EP-2003-00201 300 0
a.
V)
FE.
c.
vo 200 100 0
P _....
l-----
0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time (Years)
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average Developed by:
Verified by:
lIDeveloped by.
Verffied by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 9 Page 8 of 10 Engineering Report M-EP-2003-00201 TWCpwscc(j6) =
7.288 9.187 9.189 9.192 9.194 9.197 9.2 9.202 9.205 9.208 9.21 9.213 9.215 9.218 9.221 9.223 TWCPWSCC(j,7) =
19.481 20.457 20.461 20.465 20.469 20A73 20A77 20.481 20.485 20.489 20.493 20.497 20.501 20.505 20.51 20.514 TWCps TWPWSCC(,.8) 13.773 15.225 15.228 15.232 15.235 15.239 15.243 15.246 15.25 15.253 15.257 15.26 15.264 15.267 15.271 15.275 Developed by:
Verified by:
lIDeveloped by-,
Verified by:-
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 9 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t Stress 60 -
40 -
ID H oo l
=
0 D H o A
a roe M:
20 -
0-Top of om prosio Zo.
,S re s I
p S tre s s Top of e I
"'IO, -----------
W,I
-2 0
-40 0 0 0 5 1 0 1.5 2 0 2.5 D ista nce from N ozzle Bottom
{inch}
3.0 3.5 3
30 -
I 2
1 20 -
i 5 15 -
0I o -
D S u r fa c e S I F r
A v e r a g
S I F J 1
eraigf'4jy i)
F i
S A
=
A t
t S
!rified by:
A r 5R
=
lDeveloped by:
Ve
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 9 Page 10 of 10 Engineering Report M-EP-2003-002-01 0.20 -
0.1 5 -
0.10 0 05 -
0.00 -
I 0
1 2
3 4
prating Tim
{years)
Developed by:
Verified by:
I Developed by:-
Verified byI
Entergy Operations Inc.
Central Engineering Programs Appendix "C'; Attachment 10 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, Mid-Plane Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "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 ference point is necessar to evaluate the stress distribution on the flow both for the initial flaw and for a growing flow. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refp0 int = 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "c-tip" located at the rference 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 := 2.087 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:V J. S. Bdhmadesam Verffied by B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C'; Attachment 10 Page 2 of 11 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Pint = 2.235 Years := 4 him := 1500 T := 604 aoc := 2.67 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 Rid :
id Rid t:= Ro-Rid t
Rm :=Rid + -2 Timopr := Years-365-24 CFinhr := 1.417-105 Tirnopr Cblk 11im rhim Pmtblk =
50 L
Co := 2 Rrn Rt :=-
[
Qg r( ll 8
1.103-3 yT.+459.67 Tref+4s9.67 J T
C e -
- ac Temperature Correction for Coefficient Alpha Co Coi 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Brlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C'; Attachment 10 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 "" = 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
-24.18
-21.84
-20.55
-19.44
-18.5 1
0.56
-1.41
-3.32
-4.98
-6.48
-7.75 2
1.02 22.03 16.77 12.53 8.72 4.43 3
1.38 29.96 26.48 21.85 16.05 9.43 4
1.67 34.51 28.44 24.2 22.09 22.08 5
1.9 33.22 28.07 26.32 32.42 42.48 6
2.09 28.22 28.59 29.91 41.71 57.59 7
2.22 22.01 25.06 31.61 45.62 63.12 8
2.36 17.22 23.06 32.35 47.57 64.11 9
2.5 14.68 21.28 33.22 47.8 60.65 AXLen := AlIData(0)
IDA
- = AIData(i)
ODAII := AllData()
100
,j2 50 0
Stress Distribution I I I,
I 1i44 2.i87-----.
I~~~~~~/
i,.
-Itn uo 0.5 I
1.5 2
Axial Elevation above Bottom [inch]
2.5 3
3.5 ID Distribution OD Distribution Developed by:V J. S. Blhmadesam Venffedby SR. C Gray
Entergy Operations Inca Central Engineering Programs Appendix "C; Attachment 10 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entre matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the toot bar to paste the selection.
Data :=
0 0.564 1.016 1.378 1.668 1.9 2.087 2.224 2.361
-1.412 22.032 29.956 34.51 33.218 28.217 22.006 17.219
-3.32 16.773 26.483 28.439 28.069 28.594 25.059 23.064
-24.18 -21.838
-20.55
-4.982 12.529 21.849 24.198 26.319 29.911 31.606 32.349
-19.438
-6.476 8.722 16.053 22.09 32.416 41.713 45.624 47.567
-18.504)
-7.753 4.428 9.428 22.082 42.48 57.592 63.118 64.115 )
AxI := Data(0)
(3)
MD: Data ID:= Data(l)
TQ := Data(4)
QT := Data(2)
OD := Data()
RID := regress(Axl, ID, 3)
RQT := regress(Axl, QT, 3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axl, MD, 3)
- = regress(Axl, TQ, 3)
Developed by J.. Brihmadesam Verifed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C'; Attachment 10 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLCntr =
Refpoint -co if Val =
Refpoint if Val = 2 Refpoint + co otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr+ Co InCstrs.avg :=
ULStrs.Dist - UTip 20 No User Input is required beyond this Point fSat Aug 09 10:59:39AM 2003 Developed by:
1 S. Bnhmadesam Verffied by.
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C'; Attachment 10 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength 0.383 Flaw Growth in Depth Direction 0.6 Us C
Z-a M.
0.4 I
I I
I I
I I
I I
I I
0.2 0
2 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
I Uf_
U 0
.c
}5 3I II I
I I
I I
I I
.383 I
I I
I I
I I
0 I 0I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developedby J. S. Blihmadesam Velffied by B. C Gray
Entergy Operations Inc.
Central Engineering Programs Appendix WC'; Attachment ID Page 7 of 11 Engineering Report M-EP-2003-002-01 100 U
Ci 0
--uM 80 60 Stress Intensity Factors
_____~__
40 20 O 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developed by:
J S. Blihmadesam Verfifed by B. C. Gray
Entergy Operations Inc.
Central Engineering Prograns Appendix "C'; Attachment 10 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw
~0 U
U
.U U
v 1.1 0.9 0.8 0.7 0.6 0.5 0.4
-~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~................... -----
~~~~~~~~~~~~~~~~~~..........................
~~.1
- - --- -- - -- -- - -- - I--
..............................I.........
................I..... "...................... -..
- - -- - -- - -- -- -- - - - -- -I......
0.3 0.2 0.i Ii I 0
0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform "a" - Tip -- Linear
"a" - Tip -- Quadratic I"a" - Tip -- Cubic V"c" - Tip -- Uniform
........ "c' - Tip -- Linear
-"c"
- Tip -- Quadratic
~--. V"c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by.
B. C. Gray CQ1.-
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 10 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k, 6) 15.797 15.981 15.987 15.993 15.998 16.004 16.009 16.015 16.02 16.026 16.031 16.037 16.042 16.048 16.053 16.059 CGRsambi(k, 5) 13.11 13.273 13.279 13.284 13.29 13.296 13.301 13.307 13.313 13.318 13.324 13.33 13.335 13.341 13.347 13.352 Developed by:
J. S. Bn/hmadesam Veried by:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C'; Attachment 10 Page 10 of 11 Engineering Report M-EP-2003-002-01 60 40 G
20
'0
-20
-40 0.0 0.5 1 0 1.5 2.0 2.5 Axial Distance From Nozzle Bottom (Inch) 3.0 3.5 0.6 -
0.14 -
0.1 2 -
0.10 -
I 008 -
0.06 -
0.0 4 -
,~~~~~~~~~~.
0 I
2 0Opering Tme (years) 3 4
Developed by:
J. S. Bnhm.adesam Verified by.
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs 0.1 0 0.10 -
P 0.05 -
0.0 Appendix "C'; Attachment 10 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
3 4
O perating Time (years) 22 -
20 -
C
@ 18-l1 14 S :F D ue p tin P in tr' t S
F S rfa c e P o i I
0 1
2 3
4 O pe ra tingq T ime (y a rs )
Developed by.
J. S. Brihmadesam Verified by.
B. C. Gray 0,
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 1 of 11 Engineering Report M-EP-2003-00201 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Progrms, Entergy Operations Inc bevelopedby: J. S. Brihmadesotn Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, Mid-Plane Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flow and for a growing flow.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpoint :
1.544 To place the flow with repsect to the reference point, the flow tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of he 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 distribation (e.g. Weld bottom ).
This is the elevation from Nole Bottom. Enter this value below ULStrs.Dist :=2.087 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Bnhmadesam Vedried by:
B. C. Gray
Entergy Operations Inc Central Engineerng Programs Input Data :-
Appendix "C"; Attachment 11 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt := 2.235 Years := 4 Iiim := 1500 T := 604 aoc := 2.67-I 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R.
od R0 2
Rid :
id Rid t:= Ro -Rid Rm:= Rid+
Timopr:= Years-365-24 CFinhir := 1.417-105 Timopr Cblk :=-
hlim.
rhim Pmtblk =
50 L
C0 2 Rm Rt :=t p~ -Q
(
l I5.67' 103-.F3(T+459.67 Tref+459.6 7 Co C 0 1
- 0a(C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Blhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 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 sheetsinches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
-24.18
-21.84
-20.55
-19.44
-18.5 1-0.56
-1.41
-3.32
-4.98
-6.48
-7.75 2
1.02 22.03 16.77 12.53 8.72 4.43 3
1.38 29.96 26.48 21.85 16.05 9.43 4
1.67 34.51 28.44 24.2 22.09 22.08 5
1.9 33.22 28.07 26.32 32.42 42.48 6
2.09 28.22 28.59 29.91 41.71 57.59 7
2.22 22.01 25.06 31.61 45.62 63.12 8
2.36 17.22 23.06 32.35 47.57 64.11 9
2.5 14.68 21.28 33.22 47.8 60.65 AXLen:= AllData(o)
IDA11 := AllData(l)
ODAII := AData 5)
Stress Distribution 100 IDAll U ODAH 50 0
-50 _0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
3.5 Developed by:
- 1. S. Bnhmao'esam Venired by:.
B. C Gray
Entergy Operations Inc Central Engneeng Programs Appendix "C"; Attachment 11 Page 4 of 11 Engineering Report M-EP-200300201 Observing the stress distribution select the region in the table above labeled DataAI that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
Data :=
o
-24.18 0.564 -1.412 1.016 22.032 1.378 29.956 1.668 34.51 1.9 33.218 2.087 28.217 2.224 22.006 2.361 17.219
-21.838 -20.55 -19.438
-3.32
-4.982 -6.476 16.773 12.529 8.722 26.483 21.849 16.053 28.439 24.198 22.09 28.069 26.319 32.416 28.594 29.911 41.713 25.059 31.606 45.624 23.064 32.349 47.567
-18.504)
-7.753 4.428 9.428 22.082 42.48 57.592 63.118 64.115 AxI : Data(0)
MD := Data(3)
ID:= Datae )
TQ := Data(4)
QT := Data(2)
OD:= Data(5)
RID := regress(Axl,ID,3)
RQT.= regress(Axl,QT,3)
ROD:= regress(Axl, OD,3)
RMD:= regress(Axl, MD,3)
RTQ := regress(Axl,TQ,3)
FLCntr =
-C 0 if Val =
Flaw center Location Location above Nozzle Bottom if Val = 2
+ c0 otherwise ULStrs.Dist -
Tip In UTiv := FLCntr + CO Developed by:
./ S. Bihmadesam IflcStrsavg.
Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 5 of 11 Engineering Report M-EP-2003-00201 No User Input is required beyond this Point
& Sat Aug 09 10:21:18 AM 2003 Developed by:
J. S. Brihmadesam Verfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 6 of 11 Engineering Report M-EP-2003-002-01 PrOPLength = 0.383 0.6 s
c9 aE C:
n 0.4 Flaw Growth in Depth Direction I
I I
I I
I I
I I
I I
III 0.2 o 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model 4
03 I-C 0.8 0.6.-
I I
I I
I I
I I 5
.383 I
I
~iI I
0.4 0.2 0 0 0.5 1
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model Developed by:
J. S. Bdhmadesam Verlfiedby:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 7 of 11 Engineering Report M-EP-2003-002-01 I-0 C
.-a, In 2
80 60 40 20 0
Stress Intensity Factors I
I I
I I
I I
I I
I I
I I
I 0
0.5 1
1.5 2
2.
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 5
3 3.5 4
Developed by:V J. S. Blhmadesam Vedried by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.9 0.8 vn E
U C0
.on c
c)
U I.
c.)
0C U
C 0.7 0.6 0.5 0.4 0.3 0.2 0.1 1.........I..............I......-...
p..............................................................
I................
0 CI 0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform Ia" - Tip -- Linear
"a" - Tip -- Quadratic I"a" - Tip -- Cubic t ic" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic tic" - Tip -- Cubic Developed by.,
J. S. Brihmadesam Verified by:
B. C. Gray u (n
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 0.839 CGRsambi(k 6) 10.735 11.648 11.65 11.652 11.654 11.656 11.658 11.66 11.662 11.663 11.665 11.667 11.669 11.671 11.673 11.675 CGRsambi 8.046 8.676 8.679 8.681 8.684 8.687 8.689 8.692 8.694 8.697 8.7 8.702 8.705 8.707 8.71 8.713 Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 11 Page 10 of 11 Engineering Report M-EP-2003-00201 80 40 X
20 a
-20
-40 0.08 i
0 04 fi 0.0 4 0.00 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 Distance from Nozzle Bottom
{inches 2
3 4
0 pareting Tim year)
Developed by:
- 1. S. Brlhmadesam Venlfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs 0.068 0.086 2
0.0 0.004 Appendix "C"; Attachment 11 Page 1 of 11 Engineering Report M-EP-2003-002-01 0
1 2
3 4
O p e ra tin g T im e (y e a rs S u r fa c s Por i n t " C"'- i p 16 1 2 0
0 1
2 3
Op e ai
- Ime {years)
Developed by.
Verified by:
J. S. Brihmadesam B. C. Gray C 1--
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 12 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when RQo,tsd&/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8"Degree Nozzle, Mid-Plane Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Input is to locate the Reference Line (eg. top of the Blind Zone).
Te throughwall flaw "Upper Tip"-
is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle boffom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second rhout 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 := 2.087 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Deeopdb:oeiiewy IDeveloped by:
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 12 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :
L := 0.744 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 lim:= 1500 T:= 604 v := 0.307 aoc:= 2.67-10 12 Qg:= 31.0 Tref:= 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth MRP)
Reference Temperature for normalizing Data deg. F
['-Q g 1(
I 1.103-10 T+459.67 TreF459.67)
Co:= e
.a~c Tirnopr:= Years-365-24 od 2
Ri2= id t:= Ro - Ri Rm:= R +
2 CFinhjr:= 1.417-105 Tiflhipr Cblk :=
r h1ir Prntblk:= l-50"m I
L 2
e lIDeveloped by.
Verified by.:
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 12 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 "fV = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAII :=
0 1
2 3
4 5
0 0
-24.18
-21.84
-20.55
-19.44
-18.5 1
0.56
-1.41
-3.32
-4.98
-6.48
-7.75 2
1.02 22.03 16.77 12.53 8.72 4.43 3
1.38 29.96 26.48 21.85 16.05 9.43 4
1.67 34.51 28.44 24.2 22.09 22.08 5
1.9 33.22 28.07 26.32 32.42 42.48 6
2.09 28.22 28.59 29.91 41.71 57.59 7
2.22 22.01 25.06 31.61 45.62 63.12 8
2.36 17.22 23.06 32.35 47.57 64.11 9
2.5 14.68 21.28 33.22 47.8 60.65 AllAxl:= DataAI,(
AllD := DataAIlI (5:
AIIOD= DataAII Developed by:
Verified by:
I~vloped by:-
Verffied by:- I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 12 Page 4 of 10 Engineering Report M-EP-2003-00201 40 0 0.5 1
1.5 2
2.5 3
3.5 Axial Distance above Bottom [inch]
ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataAle that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-24.18 -21.838 -20.55 -19.438 -18.504)
Data:=
0.564 -1.412
-3.32 1.016 22.032 16.773 1.378 29.956 26.483 1.668 34.51 28.439 1.9 33.218 28.069 2.087 28.217 28.594 2.224 22.006 25.059
-4.982 -6.476 12.529 8.722 21.849 16.053 24.198 22.09 26.319 32.416 29.911 41.713 31.606 45.624 32.349 47.567
-7.753 4.428 9.428 22.082 42.48 57.592 63.118
~2.361 17.219 23.064 64.115)
Axl:= Data (1D ID= Data (5)
OD:=Data RID := regress(Axl,ID,3)
ROD:= regress(Axl,OD,3)
Developed by:
Verified by:
lIDeveloped by.,
Veified by. I
Entergy Operatfons Inc.
Central Engineering Programs Appendix "C"; Attachment 12 Page 5 of 10 Engineering Report M-EP-2003-00201 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ IncStrs.avg =
20 No User Input required beyond this Point n Sat Aug 09 11:44:49 Developed by:
Verified by:
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Venifed byI
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 12 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.543 1.5r 4
TWCpWSCC3 o
0 B.
0.5 0
u.J 0
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
Entergy Model TWCPWSC I)
Operating Time years}
Increase in Half Length 2
c 0
c c
1.5 0.5 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years) 4 Developed by:
Verified by:
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 12 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 z
c._
VI 200 I0 100 LA rn vC UC
'I 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time (Years)
OD SIF - Entergy Model ID SEF - Entergy Model SWF Average 4
lIDe veloped by.
Veified by I Developed by:
Verified by:
Entergy Operations Inc.
Cents/ Engineering Programs Appendix "C"; Attachment 12 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC TWC TWCpwsc(j 6) 18.194 23.154 23.166 23.178 23.191 23.203 23.215 23.228 23.24 23.252 23.265 23.277 23.289 23.302 23.314 23.327 TWCPwScC
,7) 29.656 33.394 33.407 33.419 33.432 33.445 33.458 33.471 33.483 33.496 33.509 33.522 33.535 33.548 33.561 33.573 PWSCC(.8) 25.114 29.591 29.605 29.619 29.632 29.646 29.66 29.674 29.687 29.701 29.715 29.729 29.742 29.756 29.77 29.784 Developed by:
Verified by:
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Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 12 Page 9 of 10 Engineering Report M-EP-2003-002-01 H oop Stress P lot 60 4 0 2 0 e
05
-2 0
-4 0 200-s 1 50
-4
.D 1 0
12 410 S
a s
1.0 1.5 2.0 D istance from N ozzle B ottom
{inchl 3.5 f
O D Su rfa ce S IF ID S ura c e S IF A v e rage SIF r w 0
0 1
2 3
4 O p era tin g T im e fy a r IDeveloped by:
Verified by:
u Q1
Entergy Operatfons Inc.
Central Engineering Programs Appendix "C"; Attachment 12 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.2 -
X 0.8 -
I 0.4 -
O.0 0
1 2
3 4
0 pe ra tin T im e (ye a rs)
Developed by:
Verified by:
lIDeveloped by.
Verified by.:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 13 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. Bnhmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM '28" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmit" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distri6bution on the flow both for the initial flow and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that epresnets the reference point elevation measured upward rom the nozzle end.
Refp0 int = 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) 7he Center of the flaw at the reference point (nter 2)
- 3) The lower "c-tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist := 1-704 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Bffhmadesam Verfied by:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 13 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 Plnt := 2.235 Years := 4 imrn := 1500 T :=604 aOC := 2.67-IC 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 R.:= od Rid :
id Rid t:= Ro - Rid Rm Rid + 2 Timopr := Years-36s-24 CFirhr = 1.417-105 Timopr Cblk:=
m
'=im Prntblk :=
50 L
co := 2 Rm Rt :=t 1.103-T+459 6 7
]Tref+4.67 C01 1.e 3
- aC Temperature Correction for Coefficient Alpha Co:= C01 75 th percentile MRP-55 Revision 1 Developed by:
- 1. S. Bnlmadesam Venifed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 13 Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "O = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (kst)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksl)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1y_
F..
2 3
4 5
O 0
-17.41
-13.55
-11.11
-8.88
-8.63 1
0.46
-8.49
-6.31
-4.92
-3.71
-2.54 2
0.83 0.09 0.18 0.11 0.19 0.28 3
1.13 7.03 6.95 6.31 5.21 4.65 4
1.36 8.22 10.95 10.85 9.51 5.65 5
1.55 13.27 16.41 16.06 17.13 25.26 6
1.7 20.63 22.24 25.41 43.58 53.78 7
1.83 29.04 28.83 31.29 53.55 64.08 8
1.95 33.95 30.93 36.41 61.6 71.01 9
2.07 29.59 31.79 40.54 64.61 76.42 AXLen:= AlUData()
IDA11 := AllData(')
ODA11:= AllData)
Stress Distribution cn U) 1oo 50_
0-
-50 0 0.5 ID Distribution
-G------
OD Distribution 1
1.5 2
2.5 3
Axial Elevation above Bottom [inch]
3.5 Developed by:
J. S. Brlhmadesam Veriled by.
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 13 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 button down. Once this is done click the right mouse button and select wCopy Selection"; this will copy the selected area on to the clipboard. Then click on the Matrx" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data:=
0 0.461 0.83 1.126 1.363 1.552 1.704 1.825 1.946 2.066
-17.414
-8.494 0.089 7.025 8.215 13.266 20.627 29.036 33.945 29.591
-13.552
-6.31 0.179 6.953 10.954 16.41 22.237 28.83 30.929 31.788
-11.113
-4.924 0.11 6.314 10.85 16.061 25.413 31.285 36.407 40.536
-8.884
-3.706 0.186 5.208 9.512 17.131 43.58 53.547 61.6 64.612
-6.628)
-2.541 0.284 4.646 5.646 25.256 53.784 64.082 71.01 76.418 )
AA i Data(0)
(3)
MD:
Data ID:= DataP TQ := Data)
QT := Data(2)
OD := Data~
RID := regress(Axl,ID, 3)
RQT := regress(Axi, QT, 3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axl, MD, 3)
RTQ:= regress(Axl,TQ,3)
Developed by:
J. S. Bnhmadesarn Vef tried by.-
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 13 Page 5 of 11 Engineering Report M-EP-2003-0021 FLCntr :=
Refpoint - co if Val =
RefPoint if Val = 2 Refpoint + co otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr + CO InCStrs.avg =
ULStrs.Dist - UTip 20 No User Input is required beyond this Point M Sat Aug 09 10:59:39 AM 2003 Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 13 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 0 Flaw Growth in Depth Direction 0.6 U
I.-
ls cn 0.4 0.2 o -
o 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
4 U
V 53
'u2 2
I I
I I
I I
I 2
fi
-IL o
I I
I I
I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 13 Page 7 of 11 Engineering Report M-EP-2003-00201 100 U
U) u Cn 80 1 60.
Stress Intensity Factors 40 20 o I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 13 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9 A
t) 0
.° E
r-V a.)0 U
C-C-
0.8 0.7 0.6 0.5 0.4
................... 1-I....
0.3 0.2 0.1 0
0 0.5 l
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by:
B. C Gray cl19
Entergy Operations Inc.
Central Engineering Programs CGRmmbi(k 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 13 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi k 6) 8.464 10.317 10.318 10.318 10.318 10.319 10.319 10.32 10.32 10.321 10.321 10.322 10.322 10.323 10.323 10.323 CGRsambi 7.148 8.617 8.618 8.618 8.618 8.618 8.619 8.619 8.619 8.62 8.62 8.62 8.62 8.621 8.621 Developed by.,
- 1. S. Bnhmadesam Veriied by.
B. C. Gray
Entergy Operations Ina.
Central Engineerng Programs Appendix "C'; Attachment 13 Page l0oaf I1 Engineering Report M-EP-2003-002-01 P-40 20
-2 0 0.0 0.5 1.0 I.5 2.0 2.5 3.0 Axial D satance Frown N ozzle ottonm (inch)
. 5 3
.05 0 04 9 0.0 47 0.04 5 Developed by:,
J S. Brihmadesam 1
2 peatin g Time (years) 3 4
Veried by
. C. Gray
Entergy Operations Inc.
Centra I Engineering Programs 0 0 3 -
iE 0.02 0
i-09 0 0 T
§ 30.0 Appendix "C"; Attachment 13 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
3 4
O perating Time
{years}
v_
S--[
I F SIu face oint C 1 0..:
- a.
9 7 -
3t 4
Ti M 8 0
X
°
~~~~~P eattitg T tmn * (yea ra);0;000 ---;04 Developed by:
J. S. BrJhmadesam Verified by:
B. C. Gray C --
,