ML032790032
| ML032790032 | |
| 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: ML032790032 (127) | |
Text
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 25 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 Developedby: J. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when Rt 5 dj/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49"Degree Nozzle, Uphill Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized 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 nch/hr.
Through Wall Axial Flaw The first XZut is to locate the Reference Une (eg. top of the Blind Zone). 7he throughwall flow "1pper rp-is located at the Reference ine.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ := 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld eg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist:= 6-628 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Developed by:
Verified by:~~~
IDeveloped by.,
Verified by.- I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 25 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :
L := 0.25 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 Ilim:= 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 Themal activation Energy for Crack Growth MRP)
Reference Temperature for normalizing Data deg. F
- Qg I 1 L I
.103-10 TT+459-67 Tf459.67) co: e 0o Tinlopr:= Years365-24 Ro:= od 2
Ri:= id 2
t := Ro - Ri Rm:= Ri + -
2 CFi,lhr:= 1.417-105 Tiflopr Cblk :=
r Ilim Prmtblk:=
I L
2 lDeveloped by:
Verfied by.
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 25 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 Woo = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAll :=
_1 i-2 l 3 4_ l 5l 0
1 2
3 4
5 O
0
-20.18
-11.45
-5.94
-1.16 3.7 1
1.79
-3.02
-4.38
-5.44
-5.51
-5.34 2
3.23 9.4 12.13
-0.26
-12.62
-20.23 3
4.38 25.65 24.71 14.58
-15.3
-25.69 4
5.3 36.18 33.79 26.29
-5.92
-24.31 5
6.04 38.11 35.03 31.43 21.21 8.83 6
6.63 42.19 38.1 36.25 40.68 36.41 7
6.76 45.07 42.22 42.74 47.55 44.23 8-6.9 44.97 43.61 46.01 49.99 48.8 9
7.03 44.7 44.12 47.02 51.04 54.11 10 7.17 43.72 43.97 47.64 50.17 54.17 11 7.31 42.93 43.82 47.52 52.33 56.55 AllAxl:= DataAI1 0)
AlID:= DataAIl (5)
All0D= DataAII I
lDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 25 Page4of 10 Engineering Report M-EP-2003-00201 100 75 -
50 _
25 0...
-25
-50 I
I 1.19l&44 l
I I
I I
I I
I I
I I
AS ___
10 1
2 3
4 5
6 7
8 Axial Distance above Bottom [inch]
9 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
-20.175 -11.45 -5.94
-1.163 3.704 Data:=
1.792 -3.024 3.228 9.398 4.378 25.65 5.299 36.179 6.037 38.106 6.628 42.186 6.764 45.067 6.899 44.968 7.035 44.695 7.17 43.723 7.305 42.926
-4.378 -5.443
-5.511
-5.341 12.134 -0.258 -12.622
-20.232 24.71 14.577 -15.299 -25.689 33.787 26.287 -5.925
-24.306 35.028 31.43 21.215 8.834 38.102 36.248 40.684 36.405 42.217 42.736 47.553 44.235 43.606 46.007 49.995 48.803 44.12 47.021 51.043 54.113 43.973 47.639 50.172 54.17 43.816 47.515 52.325 56.546)
Axl:= Data (1)
ID: Data (5>
OD:=Data RID:= regress(Axl,ID,3)
ROD:= regress(Axl,OD,3)
Developed by:
Verified by:
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 25 Page 5 of 10 Engineering Report M-EP-2003-00201 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist -BZ fCStrs.avg:=
20 No User Input required beyond this Point M Sat Aug 09 11:44:49 AM 2003 Developed by:
Verified by:
ILvoped by Verified by. I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 25 Page 6 of 10 Engineering Report M-EP-2003-00201 PropLength = 5.084 Flaw Length vs. Time 1.
6" TWCpNscc 0
4)
.16 0~ ~
~ ~ ~~~~~~---------
0.
-0.5 0I 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCpwscc 1)
Operating Time years)
Entergy Model Increase in Half Length 2
4.)
4 1.5 1
0.5
.t.
I I...
=~~~~~~
nI
.1.
u 0 0.5 I
1..5 2
Z Operating Time {Years}
2.5 3
3.5 4
lIDeveloped by.
VefibI jDeveloPed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 25 Page 7 of 10 Engineering Report M-EP-2003-002-01 300
.)_
.t a,
.)
S
.)
200 100 i-0 0.5 I
1.5 2
Operating Time Years}
2.5 3
3.5 4
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 001 IDeveloped by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 25 Page 8 of 10 Engineering Report M-EP-2003-00201 TWC TWC TWC wcpwsc(j,6)
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672
-1.672 TWCPWSCC(j,7)
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119
-4.119 4.119 4.119 4.119 4.119 WCpwSCC(j 8)=
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952
-2.952 jDeveloPed by:
Verified by:
I Developed by.
Verified by:-
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 25 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot 60 40
-2 0
-4 0
-1.7 -
A. -2.2 -
E 2.7 i -3.2 -
c i
-3.7 -
-4 2 -
3 5
7 9
Distance from Nozzle Bottom (inch)
D S u rfa c e S IF ID ra e
S IF I
A v erae SFI 0
1 2
o p ra tin g T m a years) 3 4
Developed by:
Verified by:
lIDeveloped by Verified by: I
Entergy Operatfons Inc.
Central Engineenng Programs Appendix "C"; Attachment 25 Page 10 of 10 Engineering Report M-EP-2003-002-Oi
.6 0.3 I
0.1 V -O.1
-0.3
-0.5 0
I 2
0 peratin g T me (ye are) 3 4
IDeveloped by.,
Veted by. I Developed by:
Verified by:
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 26 Page of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -'49" Degree Nozzle, Mid-Plane Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius o-Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric fonn of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube levation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow both for the initial flaw and for a growing flow. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpoint = 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "-
tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "C-tip" located at the reference point (Enter 3).
Val := 2 The Xnput 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 nozzle bottom) below.
ULStrs.Dist := 4034 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developedby:
J. S. Bnihmadesam Verfled by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 26 Page 2 of 11 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.32 ao := 0.661.0.07 od := 4.05 id := 2.728 Pint := 2.235 Years := 4 him = 500 T := 604 ao, := 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 R._ od O.2 Rid :
id Rid T=
t:= Ro - Rid Rm:= Rid +
Timopr= Years-365-24 CFih :=1.417-105 Timopr Cblk =-
11im
'=im Prntblk :=50 L
co := 2 Rm t
F -Qg
(
l 1
1.103. i-3 T+459.67 Tref+459.67 J Co :e.r aOc Temperature Correction for Coefficient Alpha Co C 0 1 75 m percentile MRP-55 Revision 1 Developedby:
J. S. Btihmadesam Verffied by:
B. C. Gray
Entergy Operations Ina Central Engineering Programs Appendix "C"; Attachment 26 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data In the table below. The column designations are as follows:
Column "0 = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksl)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ks)
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 (kso AllData :=
0 1
2 4
5 o0 17.35 8.19 2.28
-3.06
-8.64
¶ 1.09 6.89 1.47
-2.22
-5.44
-7.2 2-1.96 5.78 2.36 0.75
-0.95
-3.23 3
~
2.66 10.29 7.15 5.32 3.43 0.49 4
3.23 12.24 7.03 6.83 7.24 5.95 5
3.67 6.58 4.66 5.87 12.45 16.38 6
4.03
-5.62
-1.3 4.18 17.86 24.28 7
4.18
-12.25
-6.01 2.74 20.52 31.88 8-4.32
-15.64
-9.13 2.2 21.5 30.45 9
4.46
-18.61
-11.79 1.32 20.22 30.79 AXLen :=A1lData(0)
IDAlI := AllData(1)
ODAll:= AllData5)
Stress Distribution 40 20 C
0)Ca V
Cn 01 I
I I
I I
I I
II I
I I
1344 4d I
I I!I I
I I
I!I I
I
-20 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
5.5 6
Axial Elevation above Bottom [inch]
ID Distribution OD Distribution Developed by:
J. S. Bnhmadesam Verified by.
. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 26 Page 4 of 11 Engineering Report M-EP-2003-00201 Observing the stress distribution select the region in the table above labeled DataAl that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 1.091 1.964 2.664 3.225 3.674 4.034 4.176 4.317 17.354 6.892 5.781 10.289 12.243 6.579
-5.621
-12.251
-15.641 8.186 1.47 2.359 7.148 7.028 4.659
-1.296
-6.006
-9.131 2.284
-2.224 0.754 5.324 6.829 5.865 4.184 2.741 2.2
-3.064
-5.444
-0.955 3.428 7.244 12.453 17.859 20.517 21.496
-8.637)
-7.199
-3.232 0.494 5.952 16.377 24.278 31.88 30.446 )
AxI := Data(°)
MD := Data)
ID := Data(i)
TQ := Data(4)
QT := Data(2)
OD := Data(5)
RID := regress(Axl, ID, 3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axl, MD, 3)
RTO:= regress(Axl,TQ,3)
Developed by:
J. S. Bn'hmadesam Venried by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 26 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLCntr =
-Co if Val =
Flaw center Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + o otherwise UTip = FLCntr + CO InCstrs.avg =
ULStrs.Dist - UTip 20 No User Input is required beyond this Point ffi Sat Aug 09 10:59:39 AM 2003 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 26 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 2.33 Flaw Growth in Depth Direction I
I I
I I
I I
0.6 u
c t
0.4 a0-2 Y
0.2 0*0 I
1 I
1 I
I I
0.5 I
1.5 2
2.5 Operating Time {years}
3 1
1 3.5 4
2
-c uC 0
I-J a
Er I
0 I
I I
I I
I i
I I
I I
I I
I
-1 0 0.5 I
1.5 2
Operating Time 2.5
{years}
3 3.5 4
Developed by:
- 1. S. Bn'hmadesam Venied by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 26 Page 7 of 11 Engineering Report M-EP-2003-00201 Stress Intensity Factors 0
of U
C)
C
- 6-
.2 9
2-1!
VA Uv 71 6
5 4
3 I
I I
I I
I I
II I
I I
I 2 0 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years)
Depth Point
-...Surface Point Developed by:
J. S. Buihmadesam Veried by:
. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 26 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9
'A 0
._n E
.Q c)0 C) c 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1...
0-0 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 ic" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray cO3;,
Entergy Operations Inc.
Central Engineering Programs CGRsambi(k8 k,8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 26 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi k 6) 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 3.484 CGRsambi(k 5) 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 2.72 Developed by:
J. S. Bflhmadesam Veirifed by:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment 26 Page 10 of 11 Engineering Report M-EP-2003-00201 I
e 0 ~D H o S tfe 3 ~~~~~0, 0 0 P ID re i J 3 0
....... T. V t..
........X--
- 10 0
-30 0
i 2
3 4
Axinl D tznce F rem N ezzle Bottom (inch}
6 6
0.07 0.o I
0.05 I
0.04 0.03 0.02 0
I I
1 2
0 perating Tim lyears) 3 4
Developed by:
J.
S. Bihmadesam Veifed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 26 Page 11 of 11 Engineering Report M-EP-2003-002-01 o.
(3
-0.1 -
! -O..3
-O.
0 1
2 O pera tin g Time (years) 3 4
3.4
.2 -
3.-
9 2.8 -
2.6 Il S F D e pth P o int S IF S a rta e P in tI 0
1 2
jop era tin g T ime (yea;rn )
3 4
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw beveloped by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesom Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49" Degree Nozzle, 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.
OD Surface Flaw The first Required input s a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flow.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpoint = 1.544 To place the flow with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "-
tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "c-tip" located at the reference point (Enter 3).
Val := 2 Ulpper imit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below LULStrs.Dist := 4.034 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 27 Page 2 of 11 Engineering Report M-EP-2003-00201 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him = 1500 T := 604 aXO, := 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 0o:
2 Rid :
id Rid T=
t:= Ro - Rid
- t R:=Rid+-
Timopr := Years-365-24 CFindhr := 1.417-105 Timopr Cblk:
im him Pmtblk :=
50 L
co:= 2 Rm Rt :=t 1103-103 (T+4s9.67 Tref+459.67)
C0 1 e
.X0C Temperature Correction for Coefficient Alpha Co:= C 0 1 75 t percentile MRP-55 Revision 1 Developed by:
J. S. Bahmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column 0' = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "" = ID Stress data at each Elevation (ksi)
Column 2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column 4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column f5f = OD Stress data at each Elevation (ksi)
AllData :=
'0 u
-1 2
3 4
5
.0 0
17.35 8.19 2.28
-3.06
-8.64 1
1.09 6.89 1.47
-2.22
-5.44
-7.2 2
1.96 5.78 2.36 0.75
-0.95
-3.23
,3 2.66 10.29 7.15 5.32 3.43 0.49 4;
3.23 12.24 7.03 6.83 7.24 5.95 5
3.67 6.58 4.66 5.87 12.45 16.38 6
4.03
-5.62
-1.3 4.18 17.86 24.28
.7 4.18
-12.25
-6.01 2.74 20.52 31.88
.8 4.32
-15.64
-9.13 2.2 21.5 30.45 9
4.46
-18.61
-11.79 1.32 20.22 30.79 10 4.6
-21.26
-13.55 0.57 19.39 32.09 AXLen := AData(o)
IDA11 := AlIDatael) 0DA11 := ADatP<)
Stress Distribution 40 20 IDAII ODARI 0
-20
-40 0 1
2 3
4 5
AXLen Axial Elevation above Bottom [inch]
6 Developed by:
J. S. BSlhmadesam Veried by:
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAf 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).
/
17 CA Q 1C
)' OA
_-2 nfS ZA I.J.PV O.1OU
£..dot
-fJ.UU*
O.UVJ 1.091 6.892 1.47
-2.224 -5.444 1.964 5.781 2.359 0.754
-0.955 2.664 10.289 7.148 5.324 3.428 3.225 12.243 7.028 6.829 7.244 3.674 6.579 4.659 5.865 12.453 4.034
-5.621
-1.296 4.184 17.859 Data :=
-7.199
-3.232 0.494 5.952 16.377 24.278 31.88 30.446 30.786 32.088) 4.176 -12.251 4.317 -15.641
-6.006 2.741 20.517
-9.131 2.2 21.496 4.459 -18.614 -11.785 1.319 20.216 0.574 19.393 V4.601 -21.257 -13.548 Axl := Data(°)
3)
MD: Data" ID:= Datai)
TQ :=Data(4)
QT := Data(2)
GD : 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 RefPo in t -C if Val =
Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise ULStrs.Dist - UTip UTip := FLCntr + C0 Developed by:
J. S. Bihmadesam IflcStrsavg.
Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 5 of 11 Engineering Report M-EP-200300201 No User Input is required beyond this Point
& Sat Aug 09 10:21:18 AM 2003 Developed by:
J. S. Bdlhmadesam Venied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 2.33 Flaw Growth in Depth Direction I
I I
I I
0.6 u
I,-
v C
tb C-Vu 3a 0.4 _
0.2 _
0 0'
I I
IIIII 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model I
IIIIII
.8 1
.6
.4 I
.2-it I
I I
I I
I 0
I 0
0 0
00 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed by:
J. S. Bnhmadesam Venfled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 7 of 11 Engineering Report M-EP-2003-002-01
-C U
vt Cr U)
C U2 80 60 40 20 0
-on Stress Intensity Factors I
I I
I I
I I
I I
I I
I III Zu 0
0.5 1
1.5 2
2.5 Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model 3
3.5 4
Developed by:
J. S. Bnhmadesam Verified by' B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 (A
(L) c
._0 0
0 0
0.6 I............................................
a................
0.5 0.4 0.3 0.2 0.1 0
... 1...
1.........
1.....................
0 0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform Via" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Brihmadesam Verified by.
B. C. Gray co r~~
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi (k, 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k, 6)
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939
-1.939 CGRsambi (k,5)
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233
-1.233 Developed by:
- 1. S. Bdhmadesam Venried by.
. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 10 of 11 Engineering Report M-EP-2003-00201 30 10
-I
-30 0.5 i0.3 I0.1 t
I
-0.5 l
ID D istrib u tiO l
I I
l ^
O D D is trib u tir n
- o.
. 1 01 6
T.p of BlInd Zo.
0 1
2 3
4 5
6 DIstonce from Nozzle ottom finches)
I 0
I 2
0 p etingI T meI ye ra) 3 4
Developed by:
J. S. Brhmadesam Veliffed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 27 Page 11 of 11 Engineering Report M-EP-2003-002-01 0 5 -
° 3 -
I e-0 1 -
c -0 o.1 i-tos 0
1 2
pra tin g T ime
{ years) 3 4
-1.2 -
0 -1.4 -
-1.6 -
i f
-I 1.8 -
-2O
.0-Su rfa ce Po int "c"-tip} l Depth Point ("a"- tip} l 0
I 1 O peratintg Time yars) 3 4
Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray C(G
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihrnadesam Verified by: B. C. Gray Note: Only for use when Rw5 ld/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49"Degree Nozzle, Mid-Plane Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Inpt is to locate the Reference Line (eg. top of the Blind Zone).
The throsghwall flaw 'Vpper Tip" is located at the Reference Line.
Enter the elevafion of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist:= 4.034 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by:
Verified by:
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.25 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 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 C [
1 (T
l l96 1
C= 1.103-10-3 tT+459.67 Tf-45967)J Tirnopr:= Years-365-24 od 2
Ri:= id t:= Ro - Ri Rm:= Ri +
2 CFinhr := 1.417-105 Timopr Cblk :=
rn Prntblk:= l-rn 150 I
L 2
lDeveloped by:
Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 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)
DataAII
.=
4 5
0 I
2 3
4 5
O 0
17.35 8.19 2.28
-3.06
-8.64 1
1.09 6.89 1.47
-2.22
-5.44
-7.2 2
1.96 5.78 2.36 0.75
-0.95
-3.23 3
2.66 10.29 7.15 5.32 3.43 0.49 4
3.23 12.24 7.03 6.83 7.24 5.95 5
3.67 6.58 4.66 5.87 12.45 16.38 6
4.03
-5.62
-1.3 4.18 17.86 24.28 7
4.18
-12.25
-6.01 2.74 20.52 31.88 8
4.32
-15.64
-9.13 2.2 21.5 30.45 9
4.46
-18.61
-11.79 1.32 20.22 30.79 10 4.6
-21.26
-13.55 0.57 19.39 32.09 AllAxl:= DataAIl(0)
(I)
MIiD= DataAlI (5)
AIIOD= DataAlI lIDeveloped by:-
Verified by. I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 4 of 10 Engineering Report M-EP-2003-002-01 40 26.67 13.33 130
-13.33 1.2?4 1544, a_
I.
'""it'..-..
\\/
N
-26.67
-40 0 0.5 1
1.5 2
2.5 3
3.5 Axial Distance above Bottom [inch]
4 4.5 5
5.5 6
ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataAle that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
Data:=
0 1.091 1.964 2.664 3.225 3.674 4.034 4.176 4.317 4.459 4.601 17.354 6.892 5.781 10.289 12.243 6.579
-5.621
-12.251
-15.641
-18.614
-21.257 8.186 1.47 2.359 7.148 7.028 4.659
-1.296
-6.006
-9.131
-11.785
-13.548 2.284
-2.224 0.754 5.324 6.829 5.865 4.184 2.741 2.2 1.319 0.574
-3.064
-5.444
-0.955 3.428 7.244 12.453 17.859 20.517 21.496 20.216 19.393
-8.637)
-7.199
-3.232 0.494 5.952 16.377 24.278 31.88 30.446 30.786 32.088)
Axi:= Data ID:= Data (5)
OD: Data RID:= regress(Axl, ID, 3)
ROD := regress(Axl, OD, 3)
Developed by:
Verified by:
lIDeveloped by.
Verified by. I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ IStrs.avg :=
20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM 2003 IDeveloped by:
Verified by: I
Entergy Operatfons Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 6 of 10 Engineering Report M-EP-2003-00201 PropLength = 2.49 Flaw Length vs. Time 15 1.5 z
C TWCpWSCC C:j,3 2i 0
4)
I 0.5
.16 0 _
-0.5 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWscc 1)
Operating Time {years)
Entergy Model 2
U C
rh 4-G 4)
Ee 1.5 0.5 Increase in Half Length ii f
iti i
. - -. .... I..... I I
i iiiiii iiiti i
0 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time (Years)
Developed by:
Verified by:
IDeveloped by.,
Veified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 7 of 10 Engineering Report M-EP-2003-00201 300 zrz 0
CT 0
4
.E U,
U, 4) t 200
........................................................... I................................. I.................
.............................................................I......................[.....................,.................... I.......... -........
I.........
100 0
I 0
0.5 I
- 1. i 2
Operating Time {Years}
2.5 3
3.5 4
OD SF - Entergy Model ID SIF - Entergy Model SIF Average IDeveloped by Verified by. I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 28 Page 8of 10 Engineering Report M-EP-2003-00201 TWC TWC TWC WCpwsCJ,6)
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817
-2.817 TWCpwscc(j 7) 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 4.929 TWCpwscc(j 8) 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 1.141 Developed by:
Verified by:
lIDeveloped by Venfied by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 9 of 10 Engineering M-EP-2003-H o o p S tre s s P lo t 30 -
(0
-1 0 -
-3 0 I
ID H o o p S trf I
oD Ho o p St No Co m pressio n Z one s71
- 10 tensioo)
Bo.tt m 01 old I Top f B nd Z ono 0
I 2
3 4
5 6
D istance from N ozzle Bottom (inch)
Report
-002-01 S
t S
51 S
C,S:7 0 D S u rfa ce S IF ID S u rfa c e S IF 4
A v e ra g e S IF 2
fo
-2
-4
- ~ ~ ~ C 1
2 3
4 0
O~~~~~
peretieg Tim *,fye a r)
Developed by:
Verij lIDeveloped by Veril
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 28 Page 10 of 10 Engineering Report M-EP-2003-002-01 0.5 -
0.3 I
0.1 -
I H.
So 5 -
0 I
2 pra ting9 Time
{ ye art) 3 4
IDeveloped by Verified by. I Developed by:
Verified by:
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw beveloped by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. 5. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM '49" Degree Nozzle, Downhill Azimuth, Augmented Analysis 1.043" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "RmIt" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inchhr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow 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 no2zle end.
Refpoint = 1.043 This allows a 0.25 inch freespan below bottom of weld To place the flow with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The pper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "c-tip " located at the reference point (Enter 3).
Val := 2 Upper imit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist = 1293 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Bnhmadesam Verffled by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 29 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him = 1500 T := 604 aoc := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R.
od id Rid t:= Ro - Rid Rm := Rid +
Timop:=Years-365-24 CFinhr = 1417-105 Timopr Cblk
'Jim Pmtblk =
50 L
C0 2 Rm Rt:=t J l.I 0 3( 3T+459.67 Tref+ 4 59.6 7 CO:= C0 1
)]-0c Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bn'hmadesam Ven~ied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "" = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3' = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (kst)
AllData :=
0 o 3 : _1= a 2
13 4
5 0-0
-28.32
-18.3
-12.16
-6.2
-0.02 1
0.35
-18.79
-12.49
-6.61
-1.37 3.65 2
0.63
-17.84
-10.52
-4.41
-0.48 2.08 3
0.85
-20.52
-12.97
-5.9
-0.87
-1.54 4
1.03
-19.66
-11.83
-5.29 0.23 1.46 5
1.18
-17.2
-10.59
-0.52 16.33 21.02 6
1.29
-8.02
-2.2 10.46 32.66 37.29 7
1.44 4.78 9.56 24.9 38.18 54.09 8--
1.59 13.25 18.57 35.28 52.81 66.52 9
1.74 16 22.02 39.19 62.95 75 AXLen := AloatP)
IDA11:= AlMata(')
ODAIJ = AlIData()
Stress Distribution 100 r-IDAII A
QD-50 0
-50 _
0 0.5 1
1.5 2
2.5 3
3.5 AXLen Axial Elevation above Bottom [inch]
Developed by:V J. S. Buihmadesam VenTied by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete It from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
o
-28.324 -18.299 -12.16 -6.201 0.35
-18.794
-12.495
-6.607 -1.366 0.63
-17.838 -10.518 -4.407 -0.477 0.854 -20.517 -12.968 -5.902 -0.874 1.034 -19.663 -11.831 -5.288 0.227 1.178 -17.203 -10.587 -0.515 16.326
-0.021')
3.655 2.08
-1.536 1.46 21.019 37.289 54.089 Data :=
1.293
-8.023 1.442 4.778
-2.205 10.461 32.658 9.557 24.903 38.177 (1.591 13.252 18.569 35.278 52.808 66.517 )
AxI : Data(0)
MD:= Data(3)
ID:= Data)
TQ := Data(4)
QT := Data(2)
(5)
OD = Data RID := regress(Axl, ID, 3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl,OD, 3)
RMD := regress(Axl,MD, 3)
RTQ:= regress(Axl,TQ,3)
FLCntr Refpoint -c if Val = i Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + c otherwise ULStrs.Dist - UTip UTip := FLCntr + Co Developed by:
- 1. S. Blhmadesam Inlcstsava :
Veried by:
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 5 of 11 Engineering Report M-EP-2003-002-01 u
No User Input is required beyond this Point M Sat Aug 09 10:21:18 AM 2003-Developed by:
J. S. Bdhmadesam Venred by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength 0.09 Flaw Growth in Depth Direction 0.6 0-0a
'5 L
0.4 _
I I
I I
I I
I I
I I
I I
I I
0.2 _
0 l
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model I
0
.=0 r
3 0
0.5 0
-0.5 I
I I
I I
I
- r 1'5 0
I I
I I
I I
I
-I I
0.5 I
1.5 2
2.5 3
Operating Time {years}
3.5 4
Entergy-CEP Model Developed by J. S. Blnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix "C"; Attachment 29 Engineering Report CentralEngineeringPrograms Page 7 of 11 M-EP-2003-002-01 Stress Intensity Factors 80 60 400 LT.
40_
c 20 0~~~~~~~~~~~~~~~~~~~~~~
0 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
J. S. BiihmadesamC velinied by:-
B. C. Gray
Entergy Operations Inc CentralI Engineering Programs Appendix "C"; Attachment 29 Page 8 of 1 Engineering Report M-EP-2003-002-01 influence Coefficients - Flaw 0.8 0.7 to) 0 C
0 0C ta.)
C 0.6 0.5 0.4 0.3
-............. -- ---------- -.- I............................................-...................... I---------------------------------------.....................
0.2.
0.1 0-0 0.5 I
1.5 2
2.5 Operating time years}
3 3.5 4
"la" - Tip -- Uniform ita" - Tip -- Linear ti"- Tip -- Quadratic Ila - Tip -- Cubic tic" - Tip -- Uniform
'e-Tip -- Linear it'c
- Tip -- Quadratic "ic"
- Tip -- Cubic Developed by:,
J. S. Brihmadesam Verified by.-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k, 6) 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 6.514 CGRsambi(k,5) 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 4.851 Developed by:
J. S. Biihmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 10 of II Engineering Report M-EP-2003-00201 60-so -
-40 20 0
-2 0 0.0 0.5 1.0 1 5 2.0 2.5 3.0 Distance from Nozzle Bottom (inches)
.5 0.3 -
I 0.1 X -O.1 X0 3 -
-0.5 -
0 I
2 O pereating9 Time yasr )
3 4
Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 29 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5 0.3 S -0.
-0 5
1 I
-o.
0 1
2 o p e ra tin g T im e (ye a rs )
3 4
6.5 -
.; 6.0 -
.5 I
5.0 -
4.5 -
Il Su rfa ce Po in t {"c'-tip }
Depth Point "a"- tip}
0 I0 O perin g Tme, {years) 3 4
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray C09
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw beveloped by Central Engineering Programs, Entergy Operations Inc Developedby:
. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when Rat,,dlt is between 2.0 and 5.0 (Thickwcll Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49"Degree Nozzle, Downhill Azimuth, Augmented Analysis 1.043 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Input is to locate the Reference Line eg. top of the Blind Zone).
The trouphwoall flaw "Upper Tip" Is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle boftom in inches.
BZ:= 1.043 Location of Blind Zone above nozzle bottom (inch)
This allows a 0.25 inch freespan below bottom of weld The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist := 1.293 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by-Verified by.- I Deeoe by eife y
Entergy Operations Inc.
CentWr Engineering Programs Appendix "C"; Attachment 30 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.25 od := 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 Ihim:= 1500 T := 604 v := 0.307 aoc := 2.67 10 12 Qg:= 31.0 Tref:= 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F
-Qg (r
1 I
[ 1.103-10-3 tT+459.67 T+459.67JJ Co:
e
- .aoc Tiflopr:= Years 365-24 od 2
Ri2= id t:= Ro - Ri Rm:= Ri + 2 CFinhr := 1.417 105 Tifllopr Cblk :=
im
,Jim Prntblk:=
s o I
L2 IDeveloped by.
Verffied by:- I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 3 of 10 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn 'o = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAll :=
0 1
2 3
4 5
o o
-28.32
-18.3
-12.16
-6.2
-0.02 1
0.35
-18.79
-12.49
-6.61
-1.37 3.65 2
0.63
-17.84
-10.52
-4.41
-0.48 2.08 3
0.85
-20.52
-12.97
-5.9
-0.87
-1.54 4
1.03
-19.66
-11.83
-5.29 0.23 1.46 5
1.18
-17.2
-10.59
-0.52 16.33 21.02 6
1.29
-8.02
-2.2 10.46 32.66 37.29 7
1.44 4.78 9.56 24.9 38.18 54.09 8
1.59 13.25 18.57 35.28 52.81 66.52 9
1.74 16 22.02 39.19 62.95 75 AIlAxl:= DataAll(0 AIIID DataAIl (5:)
A11OD= DataAlI Developed by:
Verified by:
lIDeveloped by:-
Vernfed by:-
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 4 of 10 Engineering Report M-EP-2003-002-01 100 75 I
I I.P43 1.94 I
I 70 U
.IU I
I f
,~~~~~~~~~~~~~~~~~~~~~~~~~JI~~~~~~~~~~~~~~~~~~~~~~~~
I I
25 1 I---------------
I I
~~.........
10 u
III
-25
-50 0.5 l
1.5 2
Axial Distance above Bottom [inch]
2.5 3
3.5 ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection In the above table, click on the Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0 0.35
-28.324
-18.794 0.63
-17.838 0.854 -20.517 Data :=
1.034 -19.663
-18.299
-12.495
-10.518
-12.968
-11.831
-10.587
-2.205 9.557 18.569
-12.16
-6.607
-4.407 -0.477 2.08
-5.902 -0.874 -1.536
-5.288 0.227 1.46
-0.515 16.326 21.019 10.461 32.658 37.289 24.903 38.177 54.089
-6.201 -0.021)
-1.366 3.655 1.178 -17.203 1.293 -8.023 1.442 4.778 (1.591 13.252 35.278 52.808 66.517)
(0)
Ax]:
Data ID:= Data (5)
OD:=Data RID:= regress(Axl, ID, 3)
ROD:= regress(Axl, OD, 3)
I IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ Strs.avg :=
20 No User Input required beyond this Point M Sat Aug 09 11:44:49 AM 2003 Developed by:
Ve-ed by:
lIDeveloped by.,
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0.25 65 TWCpVscc 0
0 2
Flaw Length vs. Time 1.5
'3 0.5
.16 0
0.5 1
1.5 2
2.5 3
3.5 4
4.5 TWCPWSCC (il)
Operating Time (years)
IEntergy Model Increase in Half Length I
_ L _
5 c.)
_ )
.)
u
-E 1.5 0
0.5 A
U0 0.5 l
1.5 2
2.5 3
3.5 4
Operating Time (Years)
IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 7 of 10 Engineering Report M-EP-2003-002-01 7anh~ I I.*1 0- 200 0
4~ 100 C-C)
CE I
I M,
4.....
- f.
.. 4...............
0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time (Years)
OD SIF - Entergy Model ID SfW - Entergy Model SEW Average IDeveloped by.
Verified by. I Developed by:
Verified by:
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCpwscc TWCpwsc,(j6) =
4.175 4.175 4.175 4.175 4.175 4.175 4175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 4.175 TWCpwsc(j,7) =
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1
-10.1 TWCpwsc,(j, s)
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3.132
-3132 IDeveloped by Verified by:
I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 80 60 3
40 2
i 20 I
0
-20
-40 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (inchI 4
0 D S u rfa c e S IF ID S u rface S IF A v e re g e S IF Io 3
-1
-11 0
I 2
Op 0erati li T imei~ J Sye re) 3 4
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 30 Page 10 of 10 Engineering Report M-EP-2003-00201 0.5 -
0.3 -
0.1 -
I
- 03 0 0.1
-0.3
-0.5 0
I 2
0 peraing Tim e (years) 3 4
Developed by:
Verified by:
lIDeveloped by.,
Verified by. I
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby:
. S. Brihmadesom Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28.8" Degree Nozzle, 22.5 degress rotated from Downhill, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" - between 1.0 and 300.0 Note: Used the Metric forn of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube eevation 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 Normal blind zone To place the flow with repsect to the reference point, the flow tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower
- tip " located at the reference point (Enter 3).
Val := 2 tipper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.8317 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
Verified by:
J S. Bnhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 31 Page 2 of 11 Engineering Report M-EP-2003-002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt := 2.235 Years := 4 Ilim = 1500 T := 604 aoc := 2.67 10- 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F
_od R := 2 id Rid T=
t:= Ro-Rid t
Rm :=Rid+ j2 Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk =-
Ihim lim Prntblk :=50 L
0.
2 Rm Rt :=-t
[
Qg(i l'
1.103.lo-3 T+459.67 Tref+45967)
T Co1 1: e0aOC Temperature Correction for Coefficient Alpha Co:= C0 1 Stress InDut Data 75 th percentile MRP-55 Revision 1 Developedby:
J. S. Bnhmadesam Veified by:
B. C. Gray
Entergy Operations Inc Central Engineerng Programs Appendix "C"; Attachment 31 Page 3 of 11 Engineering Report M-EP-2003-00201 Input all available Nodal stress data In the table below. The column designations are as follows:
Column Wo = 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 (ksl)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
AXLen 0
23 4
5 o
0
-14.21
-11.51
-9.79
-8.24
-6.72 fV 0.5
-6.49
-5.19
-4.42
-3.8
-3.18 2
0.89 1.55 1.02 0.56 0.26
-0.08 3
1.21 8A3 7.98 7.2 6.19 5.29 4
1.46 10.25 12.71 12.22 11.35 8.36 5
1.67 15.66 18.34 18.7 20.84 29.7 6
1.83 24.32 24.53 26.71 44.52 57.73 7
1.95 31.5 28.7 31.23 53.02 63.55 8
2.07 31.98 30.11 35.63 59.45 69.03 9-2.19 26.83 29.95 38.37 61.12 72.69 10 2.31 20.84 27.29 38.5 59.95 75.04 1
2.43 15.99 24.67 38.16 58.17 73.85
- =AllData(°)
ID A
AllDatali)
OD A
AlIData (5)
Stress Distribution IfAn.
1V U)
U)
IDAII ODAll 50 1 I
I 1
I I
I 1.544 1786 1 I r
"a~~~~~~~~~~~
1.
~~~~~~~~~~~~-> -' "
0 l
l l I
I I
-50 0 0.5 I
1.5 2
2.5 3
3.5 AXLen Axial Elevation above Bottom [inch]
Developed by:
J S. Bn7madesam Verfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAle that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
/
A IA 1
CAI A0 nf 0
-'%A 7£O%
(
U
-I'*.Z.
-iI.jUU Y
0.L't3 UIL 0.495
-6.493
-5.188
-4.425 -3.796 Data :=
0.892 1.555 1.021 0.565 0.257 1.21 8.43 7.98 7.199 6.186 1.464 10.247 12.709 12.22 11.35 1.668 15.665 18.335 18.703 20.835 1.832 24.321 24.532 26.71 44.525 1.951 31.496 28.696 31.228 53.015 2.071 31.975 30.109 35.633 59.449 2.19 26.833 29.946 38.369 61.124
-3.176
-0.076 5.292 8.364 29.697 57.729 63.555 69.026 72.691 75.043) 2.31 20.84 27.287 38.5 59.952 AxI := Data(0)
MD:= Data ID:= Data)
TQ :=DataP)
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)
FLCntr := Refpint - c if Val =
RTQ:= regress(Axl,TQ,3)
- I Flaw center Location Location above Nozzle Bottom Refp0 int if Val = 2 Refp0 int + c0 otherwise UTip := FLCntr + Co lnStrs.avg -
ULStrs.Dist -
Tip 20 Develooped by:e J. S. Bnhmadesam Verffled by.-
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point M Sat Aug 09 10:21:18 AM 2003-Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 6 of 11 Engineering Report M-EP-2003002-01 ProLength = 0.128 Flaw Growth in Depth Direction 0.6 (U
S.
0.4 I
I I
I I
I I
I I
I I
I I
I 0.2 0 AI 0.5 I
1.5 2
2.'
Operating Time (years) 5 3
3.5 4
Entergy-CEP Model p0.8
._~
m 0.6 5
0.4 V
0.2 I
I I
I I
I I
I 1'5 I
.376 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1~~I I
I 1
I u -0 0.5 I
1.5 2
2.5 3
Operating Time (years) 3.5 4
Entergy-CEP Model Developed by:
J. S. Blihmadesam Verffied by:
B. C. Gray
Entergy Operations Inc Central Engeerng Programs Appendix "C"; Attachment 31 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors C.)
0 0
c:
4-.
0 1) 4.c c
80 60 40 I
I I
I I
I I
~~~~~.....
I I
I I
I I
I 20 0
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw
'A V
CQ
(-
U
._)
C 0U I,-
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
I......................... ----------------..........----------....-------..........--------------------
I....
0 0.5 I
I.5 2
2 Operating time {years}
.5 3
3.5 4
Ila" - Tip -- Uniform "a" - Tip -- Linear Ia" - Tip -- Quadratic ta" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear
-"c"
- Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verifed by; B. C. Gray C"
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 CGRsambi(k, 6) 13.267 14.419 14.423 14.427 14.43 14.434 14.437 14.441 14.445 14.448 14.452 14.455 14.459 14.462 14.466 14.47 CGRsambi 9.64 10.474 10.478 10.482 10.485 10.489 10.493 10.497 10.5 10.504 10.508 10.512 10.516 10.519 10.523 10.527 Developed by:
J. S. Bnhmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 10 of 11 Engineering Report M-EP-2003-00201 40 20 0.5 1.0
- 1.
2.0 2.5 30 3.5 sane from Noze Botton (hes) 10.20 1 0.15 5
8f,.
0.10I I
1 0.05 0.00 0
1 2
3 4
OperatngTime (yea-)
Developedby J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 31 Page 11 of 11 Engineering Report M-EP-2003-002-01 20 2 15 i@ 0.1 0 0 010 0
0 0 0 0
1 2
0 p e ra tin T im e (y e a rs 30 5? 25 t 20
_ 15 i
10 Surface Pint ("':ip)
Depth Pint ("a:ip)
IQ 1t.$:C 2
3 4
i perating ra (y
- A Developed by
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 32 Page 1 of 1 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmodesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49" Degree Nozzle, Downhill Azimuth, Augmented Analysis 1.043" 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.
OD Surface Flaw The correction is applied in the determination of the crack extension to obtain the value in inchhr.
This Attachment is Intentionally Blank nSatAug09 10:21:18AM 2003-Developed by:
J. S. Brihmadesam Verifed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page of 10 Engineering Report M-EP-2003-00241 Stress Corrosion Crack Growth Analysis Throughwall flaw beveloped by Central Engineering Programs, Entergy Operations Inc Developedby: T. S. Brihmadesom Verified by: B. C. Gray Note : Only for use when R,,tSjdC/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"O"degree Nozzle, All Azimuth, Augmented Analysis 1.25 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Dzput is to locate the Reference Line (eg. top of the Blind Zone). The throughwali flow 'pper ip" is located at the Reference Line.
Enter the elevation of the Reference ine (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.25 Location of Blind Zone above nozzle bottom (inch)
Note: Lowered BZ This allows a Freespan of 0.546 inch to bottom of weld The Second Dhput Is the pper 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 nozzk bottom) below.
ULStrsDist := 1.796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Developed by:
Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :-
L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 lim:= 1500 T := 604 v := 0.307 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 L
-Qg
(
I I
Co =
1.-003-17 tT+459.67 T+459.67)J-aoc Timopr:= Years-365-24 od 2
R; = id 2
t:= Ro - Ri Rm:= Ri +
2 CFinhr := 1.417 105 Tim0 pr Cblk rn Ilim Pmtblk:= lliml 1= L 2
Developed by:
Verified by:
lIDeveloped by.,
Verifedby. I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 33 Page3of10 Engineeing 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)
DataAIl :=
0 1
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 10 2.34 17.56 22.68 33.81 47.49 63.56 AIIAxl:= DataAIl AID := DataAl(j>
AIIOD DataAII lIDeveloped by.
Verified by:- I Developed by:
Verified by:
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 4 of 10 Engineering Report M-EP-2003-002-01 100
.75 1.544 75 50 U; 25
~~~~~~~~~~~10 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 wData" 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
-25.088 -27.546 -27.787 -25.624 -23.763) 0.485 -0.563
-0.539
-2.111
-4.851
-6.157 0.874 21.515 18.635 17.122 14.843 10.089 1.186 32.751 28.494 24.136 19.645 14.45 1.436 35.667 29.598 26.166 25.589 28.417 1.635 34.244 29.574 28.286 35.408 45.379 1.796 29.45 29.814 31.385 43.337 61.713 1.932 23.674 26.502 33.261 47.609 64.65 2.068 18.928 24.564 33.968 49.071 65.876 2.204 16.541 22.854 34.789 49.525 62.795)
Axl:= Data(
ID:= Datael)
(5)
OD: Data RID:= regress(Axl,ID,3)
ROD:= regress(Axl, OD, 3)
Deeoe y
Vrfe y
IDeveloped by Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom UI-Strs.Dist BZ IncStrs.avg :
20 No User Input required beyond this Point n Sat Aug 09 11:44:49 AM 2003 Developed by:
Venfled by:
lIDeveloped by.,
Verified by.:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 0.546 1.5 z
0 TWCpwxc i-J I
0.5 0
-0.5 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCpwsC(Jc j)
Operating Time {years}
Entergy Model Increase in Half Length 2
z U
U-1.5 0.5 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years}
4 Developed by:
Verified by:
IDeveloped by.,
Verified by
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 7 of 10 Engineering Report M-EP-2003-002-01 5
r-U) a, 0
W) 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years}
-. ID SIF - Entergy Model STF Average 4
IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 8 of 10 Engineering Report M-EP-2003-00201 TWC TWC TWC TwcpwSCCj( 6 )
15.871 23.129 23.139 23.149 23.159 23.169 23.179 23.189 23.199 23.21 23.22 23.23 23.24 23.25 23.26 23.271 TWCPWSCC(j 7) 24.273 29.738 29.748 29.758 29.768 29.777 29.787 29.797 29.807 29.817 29.827 29.837 29.847 29.857 29.867 29.878 Twcpwscc(,g) 21.089 27.647 27.658 27.669 27.68 27.691 27.702 27.713 27.723 27.734 27.745 27.756 27.767 27.778 27.789 27.8 Developed by:
Verified by:
lIDeveloped by.
Verified by: I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 33 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot I
60 -
40 -
j 20 -
I 0 - 1=pres
%I--
Of Weld
-40
, § 0.0 0.5 1.0 1.5 2.0 Dstance from Nozzle Bottom inhl 2.5 3.0 I
D Surface SIF 200 -
' 150-
_f 100I 50-
- 1 I
I\\
T.1 S
. I 1
\\
Ae 0
1 2
3 4
Opertingtirme ar Developed by:
Verified by:
- Iv3,
Entergy Operatfons Inc.
Cental Engineenng Programs Appendix "C"; Attachment 33 Page 10 of 10 Engineering Report M-EP-2003-002-01 1 2
.0 0
2 O perating Time (year,)
4 Developed by:
Verified by:
lIDeveloped by Vefified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 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 Developedby: J. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when R,,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, Augmented Analysis 1.25 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 Input is to locate the Reference Line (eg. top of the Blind Zone).
The throughwall flaw 'Vpper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.25 Location of Blind Zone above nozzle bottom (inch)
Note - BZ lowered; This increases the freespan length to 0.536 inch The Second 2hput is the Upper Limit for the evalwution, 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.
ULStDist:= 1.786 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 34 Page 2 of 10 Engineering Report M-EP-2003-002-01 InDut Data :
L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 llim:= 1500 T := 604 v := 0.307 aoc:= 2.67-10 12 Qg := 31.0 Tref := 617 Initial Flaw Length TW axial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F g
(
I 1
Ll 103-10-3 tT+459.67 TrF459.67)_
Tilmopr:= Years.365-24 od2 Ri= i2 t:= Ro - Ri Rm:= Ri + 2 CFinhr:= 1.417-105 Tifllpr Cblk:=
lim It*-
Prntblk:= I-I 1= L 2
IDeveloped by Verified by.:
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 34 Page 3 of 10 Engineering Report M-EP-2003-00201 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "0 = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAIl :=
-- 1
° l
-- 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:= DataAIl AIIID DataAI(1)
(5:
MlOD= DataAlI Developed by:
Verified by:
lIDeveloped by.
Verified by.:
Entergy Operatfons Inc.
Central Engineenng Programs Appendix "C"; Attachment 34 Page 4 of 10 Engineering Report M-EP-2003-00201 100 05 0.5 11.544 75
~~~.
... ~ ~
50
.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........
25 1
0
-50 0
0.5 1
1.5 2
2.5 3
Axial Distance above Bottom [inch]
ID Distribution
-OD distribution Observing the stress distribution select the region in the table above labeled DataAl, that represents the region of Interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
Data:=
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 1.18 29.798 26.049 22.723 18.95 14.201 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 2.183 14.834 22.263 34.779 49.055 63.377)
Axl:= Data ID:= Data OD:= Data RID:= regress(Axl, ID, 3)
ROD:= regress(AxlOD,3)
Developed by:
Verified by:
INveloped by Verffied b I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr := BZ-I Flaw Center above Nozzle Bottom IncStrs.avg :=
20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM Zuu;1 I -.
Ieveloped by:
Veified by:
_ _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 34 Page 6 of 10 Engineering Report M-EP-2003-002-01 PropLength = 0.536 1.5 PWCj,3 0
U.
1 0.5 0
-n C U..) 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWSCC(J 1)
Operating Time {years}
Entergy Model Increase in Half Length 2
z fU 1.5 0
0.5 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years}
4 IDeveloped by:
Verified by.
Entergy Operatons Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 7 of 10 Engineering Report M-EP-2003-00201 S
r-r-
0 VI 12 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years}
OD SEF - Entergy Model ID SIF - Entergy Model SIF Average 4
Developed by:
Verified by:
lIDeveloped by.,
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 8 of 10 Engineering Report M-EP-2003-002-01 Twc TWCPWSCj,6) =
15.478 22.634 22.643 22.652 22.661 22.67 22.679 22.688 22.697 22.706 22.715 22.724 22.733 22.742 22.751 22.76 TWCpwSCC(j 7) 22.524 27.819 27.828 27.836 27.845 27.854 27.863 27.871 27.88 27.889 27.897 27.906 27.915 27.924 27.932 27.941 TWCPW'c 8) 19.938 26.353 26.363 26.372 26.382 26.392 26.401 26.411 26.42 26.43 26.44 26.449 26.459 26.469 26.478 26.488 Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 9 of 10 Engineering Report M-EP-2003-002-01 H o o p S tre s s P lo t 60 40 2
i 20 8
0
-2 0
-40 200 -
V
° 1
0 9
5 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istlan ce fromr N oz zle B ottomr
( in ch )
D S u rfa c e S IF ID S u face S IF II-A v e ra e S IF 0 -
0 1
g 1
3 4
1 1 ~
QpePre ting9 T i e
ty eaitrs)
Developed by:
Verified by:
lIDeveloped by Verified by: I
Entergy Operatfons Inc.
Central Engineering Programs Appendix "C"; Attachment 34 Page 10 of 10 Engineering Report M-EP-2003-00201 1.2 I
0.4
.0 2
prmatin g Time l ye ar )
Developed by:
Verified bj lIDeveloped by Verified byI
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 1 of 11 Engineering Report M-EP-2003-00201 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49" Degree Nozzle, 22.5 degree from Downhill Azimuth, Augmented Analysis; 1.30" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmdt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inchAhr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow both for the initial flaw and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refpint= 1.3 This is the reduced Blind zone for augmented analysis; permits a 0.2504 inch free span & 0.09 inch Propogation Length To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "-
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" ocated at the reference point (Enter 3).
Val := 2 lipper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozle Bottom. Enter this value below ULStrsDist := 1.5504 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by-J. S. Blihmadesam Vedied by:
B. C. Gray
Entergy Operations Inc Central Engineeing Programs Input Data :-
Appendix "C"; Attachment 35 Page 2 of 11 Engineering Report M-EP-2003-00201 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt = 2.235 Years := 4 Ilim := 1500 T := 604 a0C := 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:= Ro - Rid Rm := Rid +
Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk hlim
'=im Pmtblk :=
50 L
C0 2 Rm Rt:=t
-TQg eI o
f C 1 103-lo-3 T+s.7T.ef+-45.67_
C0
= e r
o aC Temperature Correction for Coefficient Alpha Co:= C01 75 th percentile MRP-55 Revision 1 Developed by:
- 1. S. Bflhmadesam Veniried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data In the table below. The column designations are as follows:
Column "O" = 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:=
1 2
or rF s T...
3 4
5
'o 0
19.3
-12.52
-8.3
-4.31
-0.29 1
0.42
-13.15
-8.57
-4.68
-1.25 1.83 2
0.75
-11.83
-6.96
-2.68 0.03 1.46 3
1.02
-14.15
-8.31
-3.17 1.1 1.22 4
1.24
-12.13
-6.55 0
5.78 7.86 5
1.41
-5.38
-2.41 7.5 23.29 28.72 6
1.55 4.33 6.48 17.84 35.67 42.75 7
1.7 13.64 15.67 27.16 40.65 53.56 8
1.85 18.3 21.2 32.42 50.34 61.38 9
2 18.32 22.29 34.21 53.26 63.46 10 2.14 14.52 21.82 35.09 51.48 61.5 11 2.29 9.62 20.82 34.51 47.88 53.88 12 2.44 6.18 19.92 32.26 40.25 44.06 AXLen:= AllData()
IDA11:= AllData(1)
WAR:= A11Data()
Stress Distribution 80 60
-. ID~l
- 0) OD 0) 40 20
-20 0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
3.5 Developed by:
J. S. Bdhmadesam Veried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 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 wDataf statement below and delete it from the edit menu. Type "Data and the Mathcad equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0
-19.301 -12.523 0.419 -13.153
-8.572 0.755 -11.834
-6.958 1.024 -14.146
-8.315
-8.304
-4.314 -0.289)
-4.68
-1.255 1.834
-2.685 0.028 1.463
-3.168 1.103 1.221 1.239 -12.132
-6.552 3.002X Io-3 5.78 7.858 Data :=
1.412
-5.38
-2.413 1.55 4.331 6.478 7.498 23.29 28.718 17.842 35.67 42.747 1.699 13.644 15.667 27.164 40.65 53.563 1.847 18.304 21.201 32.424 50.345 61.379 k 1.996 18.316 22.292 34.208 53.258 63.464 )
Axl := Data(°)
(3)
MD: Data ID:= Data(i)
TQ := Data(4)
QT : Data(2)
OD := Data~
RID := regress(Axl, ID,3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl,OD, 3)
RMD := regress(Axl,MD, 3)
RTQ:= regress(Axl,TQ,3)
FLcntr RefPoint - c0 if Val=
Flaw center Location Location above Nozzle Bottom Refpoit if Val = 2 Refpoint + co otherwise UTiD := FLCntr + c0 Developed by:
- 1. S. Brihmadesam Inlcstsav2 ULStrs.Dist - UTip Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM 2003 Developed by:
- 1. S Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 009 Flaw Growth in Depth Direction 0.6 U
I,-
c c
[.
0.4 _
I I
I I
I I
I I
I I
0.2 -
0 1
0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model 4
c 0
A V
L 0.5 0
I I
-~~~1~~
I I
I I
1'5 0.09 I
I I
I I
I I
-0.5 -
-I 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating Time (years)
Entergy-CEP Model Developed by:
J. S. Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 7 of 11 Engineering Report M-EP-2003-00201 U
01 LT.
0 rA to 80 60 Stress Intensity Factors I
I I
I I
I I
1 40 20 0* I 0.5 I
'.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
- 1. S. Bnhmadesam Veried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 c')
c0
.C/_
E
.U C)0 U
V-0.6 0.5 0.4 0.3 0.2 0.1 0
A A
f A
VenSiedby:
B. C. Gray t f
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
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi 8) 0.827 0.827 0.827 0.827 0.827 0.828 0.828 0.828 0.828 0.828 0.829 0.829 0.829 0.829 0.829 0.83 CGRsambi(k, 6) 10.711 11.761 11.763 11.766 11.768 11.77 11.772 11.774 11.776 11.778 11.78 11.782 11.784 11.786 11.788 11.79 CGRsambi k,5) 7.9 8.672 8.674 8.677 8.68 8.683 8.685 8.688 8.691 8.693 8.696 8.699 8.702 8.704 8.707 8.71 Developed by:
J. S. Bdhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 35 Page 10 of 11 Engineering Report M-EP-2003-002-01 1=+
ID Dsi--Il eW.
40
&20~
i j 0-
-20 L
0.12 -
0.00 -
0.0 0.5 1.0 1.5 2.0 25 3.0 35 Distance 1oom Nozze Motom inchesl 0
1 2
3 4
Operating Time bears)
Developed by:
J. S. Buihmadesam Verfied by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs 0.12-
° 0.0 8 -
rz
.0 I
I 3 0 00 20 E
0 16
- r 10 zi, Appendix "C"; Attachment 35 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
pra tin g T imte (ye ars})
=
Surface Point ("-tip}
Depth Point {"a"- tip) 0, 1
2 3
111~ A 4
Opa tt
- k*c ~6 0* ;~
rs) 1;;
Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 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 bevelopedby: J. S. Brihmadesam Verified by: B. C. 6ray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49" Degree Nozzle, 45 degree from Downhill Azimuth, Augmented Analysis; 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "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 inchhr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw. This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozle end.
Refpoint = 1544 This is the as-biult Blind Zone To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Uapper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "c-tip" located at the reference point (Enter 3).
Val := 2 Ipper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 2.1632 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Bdhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineerng Programs Input Data :-
Appendix "C"; Attachment 36 Page 2 of 11 Engineering Report M-EP-2003.002-01 L := 0.32 ao := 0.661-0.12 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 Ilim := 1500 T := 604 czOC := 2.67*lo-12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od R 0.
2 Rid :
id Rid t:= Ro - Rid Rm :=Rid +
Timopr:= Years-365-24 CFinhr := 1.417-105 Timopr Cblk:= -
him Pmtblk =
50 L
C0 2 Rm t
[
Qg
(
l' 8
1.103-I13 T+4 9.6 7 Tref+459.67J T
C01 =
.re
-ac Temperature Correction for Coefficient Alpha Co:= C0 1 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bdhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "" = 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 R
1 2
3 4
5 0
0
-0.41
-1.36
-1.84
-2.37
-3.16 1
0.58
-1.26
-1.49
-1.71
-1.95
-2.07 2
1.05
-1.02
-0.22 0.35 0.52
-0.5 3
1.43
-1.56 0.62 2.58 4.9 4.26 4
1.73 4.17 4.31 8.86 13.38 15.25 5
1.97 16.26 12.54 16.93 28.26 32.67 6
2.16 21.13 17.13 20.09 34.28 36.98 7
2.31 21.59 19.09 21.93 34.05 41.72
-8 2.46 17.7 17.82 22.18 34.47 41.21 9
2.6 10.69 14.25 21.11 33.32 39.55 10 2.75 3.59 10.95 19.96 31.01 38.94 11 2.9
-0.98 8.74 18.34 28.35 33.45 12 3.04
-2.94 7.02 18.06 26 29.85 AXLen:= A(oData<°)
IDAll:= AI1DatP)
ODAII = AlIDatP)
Stress Distribution 60
-IDAII En ODAII 40 20
- 2 0.5 1
1.5 2
2.5 AXLen Axial Elevation above Bottom [inch]
3 3.5 4
Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAli that represents the region of Interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0
-0.414 -1.359
-1.842
-2.369 -3.157) 0.585 -1.256 -1.488 -1.714 -1.95 -2.073 1.053 -1.023 -0.223 0.347 0.516 1.429 -1.559 0.622 2.583 4.895 Data :=
1.729 4.165 1.97 16.258 2.163 21.131 2.31 21.593 4.315 8.86 13.38 12.541 16.926 28.26 17.131 20.087 34.279 19.093 21.933 34.049 17.82 22.18 34.468
-0.495 4.258 15.252 32.667 36.98 41.718 41.213)
V2.457 17.702 AxI := Data(°)
MD:= Data(3 (1)
ID :=Data TQ := Data(4)
QT := Data(2)
OD := Data(5)
RID := regress(Axl,ID,3)
RQT:= regress(Axl,QT,3)
ROD := regress(Axl,OD, 3)
RMD := regress(Axi, MD, 3)
RTQ:= regress(Axl, TQ,3)
FLCntr Refpoint c0 if Val = i Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise ULStrsDist - UTip UTi, := FLCntr+ C0 Developed by:
J. S. Bihmadesam IflCStrs av2 :
Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 5 of 11 Engineering Report M-EP-2003.002-01 Mu No User Input is required beyond this Point 8 Sat Aug 09 10:21:18 AM 2003 Developed by:
J. S. Bdihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 6 of 11 Engineering Report M-EP-2003-00201 PrOPLength = 0.459 0.6
'5.
0.4 Flaw Growth in Depth Direction I
I I
I I
I I
I I
III 0.2 CI 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model I
U a
IC0 0.5 0
I I
I I
I I
I ;5 1'5 0.459 I
I I
~
~
~~
~~
~~
~~~~~~~~~~~~~~iI
-0.5
-1I II 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed by:
J. S. Bnhmadesam Veriledby B. C. Gray
Entergy Operations Inc Appendix "C"; Attachment 36 Engineering Report Central Engineering Programs Page 7of 11 M-EP-2003-00201 Stress Intensity Factors 80 0
60
[
40 1
20 f l l0 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
J. S. Brihmadesam Veffed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix '"C"; Attachment 36 Page 8 of 1I Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 0.8 0.7 0
E.
0 CV)
.U 0.6 0.5 0.4 0.3
I..............................................-.................... --------------------------------------------------------------.....................
0.2 0.1 0
0 0.5 I
1.5 2
2.5 Operating time years}
3 3.5 4
"la" -Tip -- Uniform Ila" - Tip -- Linear Ila
- Tip -- Quadratic Ila - Tip -- Cubic ti"- Tip -- Uniform tic' - Tip -- Linear "ic"
- Tip -- Quadratic Ti"- Tip -- Cubic Developed by J. S. Bihmadesam Verified by B.. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k 6)
- 6.
(k 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 6.82 CGRsambi 5) 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 5.201 Developed by:
J. S. Blihmadesam Verlfied by B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page l0oaf 1 1 Engineering Report M-EP-2003-002-01 F
~- -- - --,
4 0 3 0 I
I 2 0 10
-10 0
1 2
3 4
DIs tancea from Noazzle Bto m
line hea) 0.5 i
0.3 f~.1 I-0 3 -
-0.5-0 I
2 pra tin imea (ya rs) 3 4
Developed by:,
J1. S. Bnihmadesam Velred by:
B. C. Gr-ay
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 36 Page 11 of 11 Engineering Report M-EP-2003-002-01 0.5
.3 03 is 0.1 e
0 3
-0 15
-0.3
-0.5 I
I e
2 0 pe ra tin g Tim e (years) 3 4
Su rface Point {"-tipi Depth Point {"a"- tip}
Ga 6.5 -
P i 5
,. 6.0 -
I, 1
5.5 -
5.0 -
0 1
O peratrng Tm e (yearts)I 4
Developed by:
J. 5. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 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. 5. Brihmadesom Verified by: B. C. Gray Note: Only for use when Rs,id/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"49"Degree Nozzle, 22.5 degree from Downhill Azimuth, Augmented Analysis 1.3 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Input is to locate the Reference Une (eg. top of the Blind Zone).
The throughwall flaw "pper Tip" is located at the Reference Une.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.3 This is the reduced blind zone location for augmented analysis; allows a propagation length of 0.25 inch an a freespan length of 0.0.25 The Second.Zput 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:= 1.5504 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
IDeveloped by:
Verified by: j
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :-
L := 0.25 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 Iim:= 1500 T := 604 v := 0.307 aoc:= 2.67 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
.(
I I
8
.103* 10 T+459.67 Tf+459.67)-
Co: e Tra+5.6)
Tinlopr:= Years-365-24 od Ri:= id 2
t:= Ro - Ri Rm:= Ri + -
2 CFinhr:= 1.417-1 05 Tifflopr Cblk =
lim Ih im 1= L 2
lDeveloped by:
Verified by.
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 37 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 "" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAll :=
-l 0° l 1
m 2
]
3 4
5 o
0
-19.3
-12.52
-8.3
-4.31
-0.29 1
0.42
-13.15
-8.57
-4.68
-1.25 1.83 2
0.75
-11.83
-6.96
-2.68 0.03 1.46 3
1.02
-14.15
-8.31
-3.17 1.1 1.22 4
1.24
-12.13
-6.55 0
5.78 7.86 5
1.41
-5.38
-2.41 7.5 23.29 28.72 6
1.55 4.33 6.48 17.84 35.67 42.75 7
1.7 13.64 15.67 27.16 40.65 53.56 8
1.85 18.3 21.2 32.42 50.34 61.38 9
2 18.32 22.29 34.21 53.26 63.46 10 2.14 14.52 21.82 35.09 51.48 61.5 11 2.29 9.62 20.82 34.51 47.88 53.88 AIIAxl:= DataAIlI AIIID := DataAIlI (5)
AIMOD DataAII Developed by:
Verified by:
lIDeveloped by.
Venried by.:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 4 of 10 Engineering Report M-EP-2003-00201 U.
uW
-20 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 DataA,, that represents the region of interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the Data' statement below and delete it from the edit menu. Type Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
( 0
-19.301 -12.523
-8.304
-4.314 -0.289) 0.419 -13.153
-8.572 0.755 -11.834 -6.958 1.024 -14.146 -8.315 1.239 -12.132 -6.552 Data:=
-4.68
-1.255 1.834
-2.685 0.028 1.463
-3.168 1.103 1.221 3.002x 10 3 5.78 7.858 7.498 23.29 28.718 17.842 35.67 42.747 27.164 40.65 53.563 32.424 50.345 61.379 1.412
-5.38 1.55 4.331 1.699 13.644 1.847 18.304
-2.413 6.478 15.667 21.201 22.292 1.996 18.316 34.208 53.258 63.464)
Axl:= Data ID:= Data (5)
OD:=Data RID:= regress(Axi, ID, 3)
ROD:= regress(Axl,OD,3) lIDeveloped by.,
Verified by I Developed by:
Verified by:
Entergy Operatfons Inc.
Cenral Engineering Programs Appendix "C"; Attachment 37 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrsDist -
3Z Strs.avg :
20 No User Input required beyond this Point ffi Sat Aug 09 11:44:49 AM 2003 lIDeveloped by:
Verified by Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 6 of 10 Engineering Report M-EP-2003-00201 PropLength = 0.25 Flaw Length vs. Time
______ 1 15
[
______ I
______ [
______ I 1.5
.' TWCpwscc V5 j,3 0
I i
iT 0.5
.25 0
I l
l l
-0.5 _
0.5 1
1.5 2
2.5 3
3.5 TWCPWSCC 1)
Operating Time {years}
4 4.5 5
Entergy Model Increase in Half Length U
C
,c c
4)
.S U
iG 1.5 I.
5 n~~~~~~~~~~~~~~~~~~~~~
0.
0 0.5 I
1..5 2
2 Operating Time {Years}
2.5 3
3.5 4
Developed by:
Verified by:
IDeveloped by:
Verified by. I
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 37 Page 7 of 10 Engineering Report M-EP-2003-002-01 inf -
0 0
'a, ri, 200 100 F-
+
-I
+
I
-f A --:-:- :-:-- -- :----
.........t...
v 0
0.5 1
1.5 2
Operating Time {Years) 2.5 3
3.5 4
OD SIF - Entergy Model ID SI - Entergy Model SIF Average Developed by:
Verified by:
Ieeloped by Verifiedby.I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 8 of 10 Engineering Report M-EP-2003-002-01 Twc TWCpwscC.
6) 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 10.656 wCpwSCC (j 7)
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835
-2.835 TWCpwsc~j 8) 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 3.829 Developed by:
Verified by:
lIDeveloped by.,
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 37 Page 9 of 10 Engineering R.
M-EP-2003-0(
Ho o p S tre s s P lot a60 ID H o o p S tre s s 0 D H o o p S tre s s S
.0 X
40 20 -
R.t ren.. L ine
& To pel Coom presSlo Zoo.
ar COinocident I
Bottom elm old 0-
-2 0 0.0 0.5 1.0 1.5 2.0 2.5 Distance from Nozzle Bottom (inch) 3.0 3.5 D
eport 02-01 T
D_
D I
D=
D A
D D
D t
D_
D S
D L
D D
A D
D
!d by:
D 0 D S u rfa c e S IF 1 0 ID S u rfac e S IF A v e ra g e S IF
_ -5 0
2 0 erating Time (yars lDeveloped by:
Verifie
Entergy Operatfons Inc.
Central Engineenng Programs Appendix "C"; Attachment 37 Page 10 of 10 Engineering Report M-EP-2003-00201 0.5 -
0.3 I
0.1 -
I I
o.1 -
.3 0.5 -
0 I
2 p era tin g Time a ye rs) 3 4
lDeveloped by:
Verified by: