CNRO-2003-00033, Rev. 1 to Engineering Report M-EP-2003-002, Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack Growth Un-Inspected Regions of the Control Element..., Appendix C, Attachment 47 Thr
| ML032790036 | |
| 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: ML032790036 (91) | |
Text
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page l of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw lDeveloped by Central Engineering Programs, Entergy Operations Inc Developedby: 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 -'28.8" Degree Nozzle, Downhill azimuth, 1.384" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flow both for the initial flw and for a growing flow.
This is defined as the reference point. Enter a number (inch) that represnets the reference point ekvation measured upward from the nozzle end.
Refpoint = 1.384 Reduced Blind Zone; Free span is 0.16 inch 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 XC-tip" located at the reference point (Enter 3).
Val := 2 Upper Limit to be selected for stress distribution (e.g. Weld bottom ).
This is the elevation from Nozzle Bottom. Enter this value below ULStrs.Dist := 1.704 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
- 1. S. Blhmadesam Venried by:
B. C. Gray
Entergy Operations Inc Central Engineenng Programs Input Data :-
Appendix "C"; Attachment 47 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 uirn := 1500 T := 604 aOC := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F
__od Ro := 2d R
id id:= 2 t:= Ro -Rid Rm:Rid +2 Timopr := Years-36s-24 CFinhr := 1.417-105 Timopr Cblk 1im Pmtblk :=
50 L
co := 2 Rm Rt :=-R 1J103-1o-3 T+459.67 T. f+c459.67 C0l := e r
,*ac Temperature Correction for Coefficient Alpha Co:= Coi Stress InDUt Data 75 t percentile MRP-55 Revision 1 Developedby J. S. Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 3 of 11 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data In the table below. The column designations are as follows:
Column "0m = 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 (ks,1 AllData :=
0 d
1 2.........3 4
5 0
0
-17.41
-13.55
-11.11
-8.88
-6.63 1-0.46
-8.49
-6.31
-4.92
-3.71
-2.54
-2 0.83 0.09 0.18 0.11 0.19 0.28 3
1.13 7.03 6.95 6.31 5.21 4.65 4
1.36 8.22 10.95 10.85 9.51 5.65 5
1.55 13.27 16.41 16.06 17.13 25.26 6 -
1.7 20.63 22.24 25.41 43.58 53.78 7
1.83 29.04 28.83 31.29 53.55 64.08 8 -
1.95 33.95 30.93 36.41 61.6 71.01 9
2.07 29.59 31.79 40.54 64.61 76.42 10 2.19 23.26 29.74 41.2 64.19 79.63 11 2.31 18.69 27.73 41.29 61.78 78.12 1-2 2.43 15.39 26.1 40.67 58.6 72.78 AXLen := AllData(P)
IDAll:= A11Data(')
ODA11
- =Al1Data. 5 100 IDAII 0
ODAII 50 1 Stress Distribution I
I I ;I I
1 I.$44 1 ;786 I
I i
I
_~
~ IH I
I I
I.
0
-50 0 0.5 I
1.5 2
2.5 3
3.5 AXLen Axial Elevation above Bottom [inch]
Developedby:
J. S. Bihmadesam Venlfed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled Datable 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
_ 17 AI A
_11 CC) 1 1 1 l' OOA
-O O OA O
U
-I1.1
-1I3.JJZ.
-I1.1J 1
-0.00t
-U.U0o 1
0.461
-8.494
-6.31
-4.924
-3.706 -2.541 0.83 0.089 0.179 0.11 0.186 0.284 1.126 7.025 6.953 6.314 5.208 4.646 1.363 8.215 10.954 10.85 9.512 5.646 Data :=
1.552 13.266 16.41 16.061 17.131 25.256 1.704 20.627 22.237 25.413 43.58 53.784 1.825 29.036 28.83 31.285 53.547 64.082 1.946 33.945 30.929 36.407 61.6 71.01 2.066 29.591 31.788 40.536 64.612 76.418 K2.187 23.26 29.738 41.2 64.193 79.626 )
AxI := Data(0)
MD:= Data(3)
ID:= Datael)
TQ := Data(4)
QT := Data(2)
OD: Data(5)
RID := regress(Axl, ID,3)
RQT:= regress(AxI,QT,3)
ROD:= regress(Axl,OD,3)
RMD:= regress(Axl,MD, 3)
RTQ:= regress(Axl,TQ,3)
FLCntr =
Refpoint - CO if Val = 1 Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 Refp0 int + c0 otherwise UTi:= FLCntr + c0 IncULStrs.Dist
- UTip U~p CStrs+aCO20 Developed by:
.1 S. Bn'imadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point 8 SatAug 09 10:21:18AM
'Inn-4 Developed by:
J. S. Brhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix "C"; Attachment 47 Engineering Report Entergy Operations Inc Appendix "C"; Attachment 47 Engineering Report Central Engineering Programs Page 6 of 11 M-EP-2003-002-01 PropLength 0.16 Flaw Growth in Depth Direction I
I I
i III 0.6 -
0.4 0.2 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model III I
I I
s 0.8 T
0.6 0.4 v
-2 _,.
16-r-----------------------T-----------------
0 0
0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {years}
-Entergy-CEP Model Developed by:
Verifed by J. S. Bdhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 7 of 11 Engineering Report M-EP-2003-002-01
-C Cr en U
CA en 80 60 1 Stress Intensity Factors I
I I
I I
I I
I..
I-40 1 20 1 0 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Developed by:
J. S. Bdhmadesam Verified by B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw I
0.9 0.8 0
(dn E
-o V
0 Q)
Q1 U
0.7 0.6 0.5 0.4 0.3 I- - -- - -- -- - - -- -- -- - -- -- --.- - -- -
0.2 O.l 0
U 0.5 l
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic la" - Tip -- Cubic "c" - Tip -- Uniform
" c' - Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 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 0.829 0.829 0.829 0.829 0.829 0.83 0.83 CGRsambi(k, 6) 10.823 12.011 12.014 12.016 12.018 12.02 12.022 12.024 12.027 12.029 12.031 12.033 12.035 12.038 12.04 12.042 CGRsambi(k, 5) 7.907 8.77 8.773 8.776 8.778 8.781 8.784 8.787 8.79 8.793 8.796 8.799 8.802 8.805 8.807
-8.81 Developed by:
J. S. Blihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 47 Page 10 of 11 Engineering Report M-EP-2003-002-01 I
I 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance *cm Nozzle BoSom (inches) 0.12-I i 0.08I i 0.04 0.00 -
0 1
2 operating Thim {years) 3 4
Developed by:
J S. Bnhmadesam Velffied by.-
B. C. Gray
Entergy Operations Inc Central Engineering Programs 0.12 r
I o
2 0.0 8 -
2 c
2 0.04 0
0.0 0 Appendix "C"; Attachment 47 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
3 4
0 p e ra tin g T im e
{y e a rs )
- g20' 6
I:
4-* 15 I Z
I en i -
5 o
7 2
0, it ~
~
1
- 1 12n. ' I 0 7:
tamTi
- y af 3
4, Developed by:V J. S. Brihmadesam Verified by:-
B. C. Gray cvl
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 48 Page 1 of 10 Engineering Report M-EP-2003-002-01 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note: Only for use when Rtszd/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"28.8"Degree Nozzle, 22.5 degree from Downhill Azimuth, Augmented Analysis 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first rnput is to locate the Reference Line (e~g. top of the Blind Zone). The throughwall flaw "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 This is the normal blind zone The Second Dput 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 nozze bottom) 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:
IDeveWed by.
Verified by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 48 Page 2 of 10 Engineering Report M-EP-2003-002-01 Input Data :
L :=.794 od := 4.05 id := 2.728 Plt := 2.235 Years:= 4 Ihim:= 1500 T := 604 v := 0.307 Initial Flaw Length TW axial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F aoc:= 2.67-10 12 Qg := 31.0 Tref := 617
- Q g 6(
II 1
[1.103.10-3 I~T+459.67 T~,,+459.67)j Co:=
e
.a~~3 Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Timopr:= Years-365-24 ad Ro:= -2 R := id t:= Ro-Ri Rm Ri + 2 2
CFinhr:= 1.417-105 Cbk=Tiniopr C bl' u r Pmntbik:=
5 I
L jDeveloPed by:
Verified by:
IDeveloped by.
Vefified by.- I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 48 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 "o0 = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "I" = ID Stress data at each Elevation (ksi9 Column "5" = OD Stress data at each Elevaton (ksi)
DataAII :=-
0 1
2 3
4 5
0 0
-14.21
-11.51
-9.79
-8.24
-6.72 1
0.5
-6.49
-5.19
-4.42
-3.8
-3.18 2
0.89 1.55 1.02 0.56 0.26
-0.08 3
1.21 8.43 7.98 7.2 6.19 5.29 4
1.46 10.25 12.71 12.22 11.35 8.36 5
1.67 15.66 18.34 18.7 20.84 29.7 6
1.83 24.32 24.53 26.71 44.52 57.73
- 7 1.95 31.5 28.7 31.23 53.02 63.55 8
2.07 31.98 30.11 35.63 59.45 69.03 9
2.19 26.83 29.95 38.37 61.12 72.69 10 2.31 20.84 27.29 38.5 59.95 75.04 11 2.43 15.99 24.67 38.16 58.17 73.85 AllAxl:= DataAIl I A1ID := DataAIl (5)
AIIOD= DataA~l lIDeveloped by.,
Verified y Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 48 Page 4 of 10 Engineering Report M-EP-2003-002-01 80
.75 1.$
.4.
63.33 46.67 W
30 13.33
-3.33.
-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 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 0.495 0.892 1.21 1.464 1.668 1.832 1.951 2.071 2.19 2.31
-14.205
-6.493 1.555 8.43 10.247 15.665 24.321 31.496 31.975 26.833 20.84
-11.506
-5.188 1.021 7.98 12.709 18.335 24.532 28.696 30.109 29.946 27.287
-9.79
-4.425 0.565 7.199 12.22 18.703 26.71 31.228 35.633 38.369 38.5
-8.243
-3.796 0.257 6.186 11.35 20.835 44.525 53.015 59.449 61.124 59.952
-6.722)
-3.176
-0.076 5.292 8.364 29.697 57.729 63.555 69.026 72.691 75.043)
Ax]:= Data ID:
Data~l (D5 OD: Data RID:= regress(Axi, ID, 3)
ROD:= regress(Axl, OD,3) lDeveloped by:
Verified by:.
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 48 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 20nn3 I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 48 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProlL~ength = 0.288 1.5 C
XX
.~TWCpsc, g
~~~~0.5...
0 0.5 1
-Entergy Model 1.5 2
2.5 3
3.5 4
4.5 5
TWCPwscjC l)
Operating Time {years}
Increase in Half Length 2
- a t
r-Q 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 Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 48 Page 7 of 10 Engineering Report M-EP-2003-002-01 300 z
Q r-r.VI 0
r-luc
.E
'A V
200 100 0
0 0.5 1
1.5 2
2.5 3
3.5 Operating Time (Years}
OD SIF - Entergy Model ID SIF - Entergy Model SEF Average 4
IDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 48 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWCpwSCC(j 16.053 22.574 22.579 22.585 22.59 22.595 22.6 22.605 22.611 22.616 22.621 22.626 22.631 22.637 22.642 22.647 TWCpwscc
=
13.281 17.602 17.606 17.61 17.615 17.619 17.623 17.627 17.631 17.636 17.64 17.644 17.648 17.652 17.657 17.661 TWCpWC 8) 15.158 20.728 20.733 20.738 20.743 20.748 20.753 20.758 20.763 20.768 20.773 20.778 20.783 20.788 20.793 20.798 Developed by:
Verified by:~~~~
IDeveloped by.,
Vedfied by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 48 Page 9 of 10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot a
I
£ WI?
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Distance from Nozzle Bottom (inch) 150 -
6 j 100-a 5
50~
50 -
A:
Io
=-
OD Surface SIF ID Surface SIF I-Average SIF 0
i 2
3 4
oparating mi ooara Developed by:
Verified by:
1 {
c)9~
Entergy Operations Inc.
Central Engineenng Programs Appendix "C"; Attachment 48 Page 10 of 10 Engineering Report M-EP-2003-002-01 1.2 1.0 a
Os I
0.4 0.2 0.0 2
3 4
O perating Time *years)
IDeveloped by.
Vedfied by-I Developed by:
Verified by:
Appendix D Contains Mathcad worksheets for;
- 1) Evaluations of Curve Fitting method.
- 2) Demonstration of the validity of the Moving Average method.
- 3) Comparison of SICF for the Edge Crack Formulation and Current model.
- 4) Comparison of Conventional and Current model for OD Surface Crack.
- 5) Comparison of Current model with Conventional model and edge Crack.
model for Through-wall Crack.
This Appendix has five (5) Attachments.
Entergy Operations Inc.
Central Enginenng Programs Appendix D; Attachment I Page 1 of 7 Enginering Report M-EP-2003-002-01 Evaluation of Curve fit for Stress Profile Generation along the Tube Axis In this worksheet the effect of data set selection for curve fitting, using a third order polynomial is evaluated. The data table below is form a data set used in the CEDM analyses. This data set is imported directly from the Excel spreadsheet provided by Dominion Engineering for the CEDM. The evaluation considers the full data set and a limited data set spanning the region of interest.
The purpose of this evaluation is to demonstrate the need for the proper selection of a subset of nodal stress data (in the region of interest) to ensure the accuracy of the analysis.
Data set imported from Excel spreadsheet.
AllData :=
-0
-1.
1 2
3 0
0.0000
-28.3240
-12.1600
-21.0000 1
0.3500
-18.7940
-6.6070 3.6550 2
0.6300
-17.8380
-4.4070 2.0800 3
0.8540
-20.5170
-5.9020
-1.5360 4
1.0340
-19.6630
-5.2880 1.4600 5
1.1780
-17.2030
-0.5150 21.0190 6
1.2930
-8.0230 10.4610 37.2890 7
1.4420 4.7780 24.9030 54.0890 8
1.5910 13.2520 35.2780 66.5170 9
1.7400 16.0010 39.1940 75.0010 10 1.8890 15.8570 40.2350 74.8740 11 2.0380 12.6290 41.2630 66.7770 12 2.1870 10.0610 39.6280 55.0120 1-3 2.3360 11.1610 35.6460 37.5700 14 2.4850 17.2630 31.3090 24.6930 15 2.6340 27.2640 26.5110 17.4680 1-6 2.7830 35.4650 27.1090 16.3050 17 0 2.9930 39.9490 31.3960 12.4040 18 3.0820 39.5470 37.1560 1.4480 AxlLen:= AllData IDAII:= AllData MidWall:= AllData (3) 0DAllI AllData
Entergy Operations Inc.
Central Enginering Programs Appendix D; Attachment I Page 2 of 7 Enginering Report M-EP-2003-002-01 Data:=
0 0.35 0.63 0.854 1.034 1.178 1.293 1.442 1.591 1.74
-28.324
-18.794
-17.838
-20.517
-19.663
-17.203
-8.023 4.778 13.252 16.001
-12.16
-6.607
-4.407
-5.902
-5.288
-0.515 10.461 24.903 35.278 39.194
-21 )
3.655 2.08
-1.536 1.46 21.019 37.289 54.089 66.517 75.001)
Selected subset from the data table above ALen:= Data (I)
IDiim= Data (2)
MWiim= Data (3)
ODlim= Data Regression for the full data set RIDAII:= regress(AxILen,IDA11,3)
RMWAII:= regress(AxlLen, MidWall,3)
RODAII:= regress(AxIlLen,ODA11,3)
Regression for selected data set RiDdata:= regress(ALen, lDlim, 3)
RMWdata:= regress(ALen,MWijm,3)
RODdata:= regress(ALen,0Dlim,3)
WB:= 1.74 Bottom:= 0 Top:= 3.2 Dist:= Top - Bottom Dist Incr :=
20 D := WB - Bottom Incrl :=-
20
Entergy Operations Inc.
Central Enginenng Programs Appendix D; Attachment I Page 3 of 7 Enginering Report M-EP-2003-002-01 L := 0 - Incr i:= 1.. 20 L. := L.
+ Incr i*
i-I LenO := 0 - IncrI Len. := Len i-I + IncrI Determination of Stresses at three locations across wall thickness, using the full data set IDall := RIDAII + RIDAlI L + RIDA1l (L;) + RIDAII *(Li)
MWall := RMWAII + RMWAll 4 L + RMWA115 (L.) + RMWAII -(Li)
ODall := RODAII + RODAII L; + RODAI.(Li) 2+ RODAII -(Li)3 Determination of Stresses at three locations across wall thickness, using the selected data set IDdata := RIDdata + RIDdata Len + RIDdata (Len.)2+ RIDdata 2(Len.)3 MWdatai= RMWdata3 + RMWdata4 Len. + RMWdata5 Len;) +(RMWdata6) (Lnj)3 ODdata = RODdata + RODdata4 Len; + ROD ta5-(Len ) + RODdata (Len )3
Entergy Operations Inc.
Central Enginening Programs Appendix D; Attachment I Page 4 of 7 Enginering Report M-EP-2003-002-01 Graphical Display of Results Distribution Full Nodal Stress Data 100 50 S I
I I
I I
I I
I I
I I
I Nodal stress data plotted for the ID and the OD distribution. This plot is based on the full data set.
0
-50 0 0.5 1
1.5 2
2.5 3
3.5 Axial Length {inch}
ID Distribution Mid-Wall distribution Full Data: @ ID Location 40 20 0
ID Stress Distribution:-
Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.
12
'A 9En 0.
8
-20
-40 0 0.5 1
1.5 2
2.5 Axial Eleveation from Bottom {inch}
ID Regression using All Data
- ID All Nodal Data 3
3.5
Entergy Operations Inc.
Central Enginenng Programs Appendix D; Attachment I Page 5 of 7 Enginering Report M-EP-2003-002-01 OD - Regression vs Nodal Data 100 _
50 _
0
-50 OD Stress Distribution:-
Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.
0 0.5 1
1.5 2
2.5 Axial Elevation from Bottom {inch}
OD Regression Using All data
... OD All Nodal Data 3
3.5 12 B
&n M
8 0
1 2
3 Axial elevation from Bottom {ksi)
Mid-Wall Regression using All data
.Mid-Wall All Nodal Data Mid-Wall Stress Distribution:-
Comparison of regression fit versus the full data set. The third-order polynomial does not provide an accurate fit. The trend in the data is captured.
-10
-20 4
Entergy Operations Inc.
Central Engineting Programs Appendix D; Attachment I Page 6 of 7 Enginering Report M-EP-2003-002-01 ID - Selected Data Set 20 10 ID Stress Distribution (Selected Data Set):-
Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.
A W
'9 Cn 8X 0
-10
-20
-30 I_
0 0.5 1
1.5 Axial Elevation from Bottom (inch)
ID Regression using Selected Data
..ID Selected Nodal Data Mid-Wall - Selected Data Set 2
Mid-Wall Stress Distribution (Selected Data Set):-
Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.
.Q w
8
-10
-"A TV 0 0.5 1
1.5 Elevation from Bottom (inch)
Mid-Wall Regression Selected Data Set Mid-Wall Selected Data Set 2
Entergy Operations Inc.
Central Enginenng Programs Appendix 0; Attachment I Page 7 of 7 Enginering Report M-EP-2003-002-01 OD - Selected Data Set 80 60 40 20 0
-20
-A4 OD Stress Distribution (Selected Data Set):-
Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.
_v 0 0.5 1
1.5 Elevation from Bottom {inch)
OD Regression using selected data Set OD Selected Data Set 2
Conclusion :- By selecting the data judiciously, in the region of interest, facilitates an accurate regression fit of the data.
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 1 of 8 Engineering Report M-EP-2003-002-01 Example Worksheet Developed by Central Engineering Programs, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Example to Evaluate Moving Stress Averaging Technique Basis :- In this worksheet the moving average method is exercised to demonstrate that no numerical errors exist. In this example a linear through-wall stress distribution that remains constant over the length of the nozzle is used. Thus the moving average method, if working properly should provide the same linear through-wall distribution at all segments considered.
This worksheet is developed using the stress distribution analysis portion from the working worksheets used in the analyses. The data table in the worksheet was modified with the entry of a linear throughwall stress distribution at all axial height locations. The result of the moving average technique was output as a table.
The first Required input i 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 necessary 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 represents the reference point elevation measured upward from the nozzle end.
Refpoint = 1.544 To place the flow with respect to the reference point, the flow tips and center can be located as follows:
- 1) The ipper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter 2)
- 3) The lower "C-tip" located at the reference point (Enter 3).
Val := 1 The Input Below is the Upper Limit for the evaluation, which is the bottom of the filet weld leg. Ths is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzk bottom) below.
ULStrs.Dist = 2.75 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Bdhmadesam Venried by:
B. C. Gray
Entergy Operations Ina Central Engineermng Programs Apendix D; Attachment 2 Page 2 of 8 Engineering Report M-EP-2003-002-01 Only input data pertinent to this worksheet are provided. The internal pressure and the information for the PWSCC crack growth, which are not essential to the example problem, have been removed.
Input Data :-
L :=.35 ao := 0.035 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID od Ro := od L
Co := 2 id Rid T=
t:= Ro-Rid Rm :=Rid +
Timopr= YearS*365-24 Rm Rt:=-
Developed by:
J. S. Brdmadesam VerdIed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 3 of 8 Engineering Report M-EP-2003-002-01 The stress input table that is used to import the nodal stress data was modified. The stress input was manually entered as a linear through-wall distribution at all axial height locations. The table entries below shows the entries used.
Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
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 :=
is "1-0 1 -
2 3
4 5
l 0
8 10 12 14 16 0.35 8
10 12 14 16 2
0.63 8
10 12 14 16 3
0.85 8
10 12 14 16 4
1.03 8
10 12 14 16 5
1.18 8
10 12 14 16 6
1.29 8
10 12 14 16 7
1.44 8
10 12 14 16
.8 1.59 8
10 12 14 16 9
1.74 8
10 12 14 16 0
1.89 8
10 12 14 16 E1 2.04 8
10 12 14 16 AXLen:=A11DatP)O IDAII:= AllData(1)
ODAII := AlIData()
Developed by:
J. S. Blihmadesam Verified by-S. C Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 4 of 8 Engineering Report M-EP-2003-002-01 The graph below is a plot of the table data in the previous page. Note the horizontal lines for the ID and OD stress distribution along the nozzle length. Therefore, the input data shows that there is a constant distribution along the nozzle length 20 A.
En ri ri:
(A 15 10 Stress Distribution I
I I
I I
I I
I I
III 5 0 0.5 I
1.5 2
Axial Elevation above Bottom [inch]
2.5 3
3.5 ID Distribution OD Distribution Data :=
0 0.35 0.63 0.854 1.034 1.178 1.293 1.442 1.591 1.74 1.889 2.038 2.187 2.336 2.485 2.634 2.783 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 16) 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16)
The data matrix to the left is the selection of data from the data table used to input the data. All entries have been selected. The matrix is exactly the same as the input data table Developed by:
J. S. Bn'hmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineerng Programs Apendix D; Attachment 2 Page 5 of 8 Engineering Report M-EP-2003-002-01 The statements below are the assignment statements defining the column arrays for the axial height followed by the five locations across the tube wall thickness.
AxI := Data(°)
(3)
MD: Data ID:= Data)
TQ :=Data~4)
(2)
QT :=Data OD:
Data~~
RID := regress(AxI, ID, 3)
RQT := regress(Axl, QT, 3)
ROD:= regress(Axl, OD, 3)
RMD := regress(AxI, MD, 3)
RTQ:= regress(Axl,TQ, 3)
The statement below defines the flaw location to be used in the analysis, based on the entry for the variable 'Val" entered on the first page.
FLcntr :=
Refpoint - C0 if Val = I Refpoint if Val = 2 Refpoint + c0 otherwise Flaw center Location above Nozzle Bottom The two statements below are as follows:
- 1) The statement on the left defines the upper crack tip based on the flaw location determined above.
- 2) The statement on the right computes the segment height for the segments above the upper crack tip based on twenty equal segments.
UTip := FLCntr+ cO UL'-Strs.Dist - U~ip IflcStrs.avg :-20 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 6 of 8 Engineering Report M-EP-2003-002-01 The statements below develops the through-wall stress profiles at the twenty-three segments (three segments for the initial flaw length and twenty segments above the upper tip of the flaw.
Calculation to develop Stress Profiles for Analysis N := 20 Number of locations for stress profiles Loco : FLcntr - L i:= 1..N+3 Incr; :=
c0 if i < 4 InCstrs.avg otherwise Loci := Loci-, + Incr; SIDi := RID3 + RID 4Loci + RID.(Loci)2 + RID *(Loc;)3 SQT RQT3 + RQT4-Loci + RQT.(Loci)2 + RQT6.(Loc;) 3 SMDi= RMD3 + RMD 4Loci + RMD '(Loci) 2 + RMD
- 1 (Loc;)3 STQ:
RTQ + RTQ4-Loci + RTQ.(Loci)2 + RTQ (Loc;) 3 SODi ROD + ROD 4LoCi + ROD.(Loci)2 + ROD *(Loc;)3 Developed by:
J. S. Bdhmadesam Vernfied by:
B. C. Gray
Entergy Operations Inc.
Central Engineeing Programs Apendix D; Attachment 2 Page 7 of 8 Engineering Report M-EP-2003-002-01 The statements below perform the moving average stress profile calculations. The first profile, at location 1, is the average profile for the initial crack. The remaining profiles are the average profiles for the twenty segments above the upper tip of the crack.
j := i..N Sij =
SIDj + SIDj+j + SIDj+2 3
sid
- (j + I) + SIDj+2 j+2 if j = I Sqtj =
SQTJ + SQTj+l + SQTj+2 3
sqt(
)(j + 1) + SQTj+2 j+2 if j = 1 otherwise otherwise 5 md.
J SMDj + SMDj+l + SMDj+2 if j = 1 3
Stqj =
Smd
- (j + 1) + SMDj+2 j+2 STQj + STQj+1 + STQj+2 if j =
3 Stq.
(j + 1) + STQj+2 1
otherwise j+2 otherwise sod =
SODj + SODj+ + SODj+2 if j =
J
~~~~~3 Sodj (j + 1) + SODj+2 i-I otherwise j+2 Developed by.
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 8 of 8 Engineering Report M-EP-2003-002-01 Presented below is the output at each location defined for the moving average stress profile. The first element in each array is for the average stress profile for the initial crack. The subsequent elements in each column array are for the equal segments above the upper tip of the flaw. Each column array represents one of the five locations across the wall thickness (marked).
ID Sidj 8
8 8
8 8
8 8
8 8
8 8
8 8
8 88 Quarter Thickness Sqt. =
i 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Mid-Wall Thickness Smd. =
12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 Three -Quarter Wall Thickness OD Stqj 14
-14 1i4 14 14 14 14 14 14 14 14 14 14 14 14 14 Sod.
16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 The output of the moving average evaluation is the same as the input data. This ensures that the moving average technique is functioning properly.
Developed by:
J. S. Bnhmadesam Vendfed by:
B. C. Gray
Entergy Operations Z.c.
Central Engineenng Programs Appendix D; Attachment 3 Page 1 of 4 Engineering Report M-EP-2003-002-01 Comparison of Edge Crack Model With Through-wall Model (SICF)
Developed by Central Engineering Programs, Entergy Operations Inc Developed by: J. S. Brihmadesam Verified by: B. C. G'ay
References:
- 1) Murakami; "Stress Intensity factors handbook"; 1.3 Single Edge Cracked Plate; page 771.
Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"O"degree Nozzle, All Azimuth 1.544 inch above Nozzle Bottom In this worksheet a comparison between the SICF for an Edge Crack and the axial through-wall crack of the current model are compared. For the edge crack the SICF is dependent on the ratio of crack length to plate height. For the application to the CEDM nozzle the plate height can be assumed at three locations, these are:
- 1) The nozzle length upto the bottom to the J-weld (the bottom point of fixity for the nozzle)
- 2) The nozzle length upto the top of the J-weld (the upper point of fixity for the nozzle)
- 3) The nozzle length assuming no fixity.
For the current model only the SICF for the membrane loading is used for comparison because the SICF for these two conditions are separate and are applied to the SIF for equivalent plate geometry. Hence three is no single SIF that represents a composite SICF. However a comparison using the membrane SICF should facilitate a rational assessment.
The first Dzput is to locate the Reference Une (eg. top of the Blind Zone).
The through-wall flaw HIper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle boffom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second npout is the Upper Limit for the evalution, which is the bottom of the fillet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULSts Dist:= 1.796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Edge Crack-Entergy-Comparison-OOO.mcd
57te/yy Operations Zc.
Central Engineenng Programs Appendix D; Attachment 3 Page 2 of 4 Engineering Report M-EP-2003-002-01 The input data below are only for those variables essential to this assessment.
Input Data :
L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 v := 0.307
_od Ro.=
Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)
Poissons ratio at 600 deg. F Ri:= i2 t:= Ro - R Rm := R + -
2 N:= 500 The plate height are set to three elevations as follows:
- 1) Bottom of the J-weld.
- 2) Top of the J-weld.
- 3) Full length of Nozzle.
b := UI-Str&Dist bj := 2.886 b2:= 20 Bottom of J-weld Top of J-Weld Top of Nozzle Inc :=
N It is important to note that the SICF for the Edge Crack model are limited to the a/b ratio (Crack length/height) of 0.6.
Therefore, for the crack length when the a/b ratio is violated are as shown below.
Case 1: Plate height equal to nozzle length to bottom of weld:-
b-0.6 = 1.078 Case 2: Plate height equal to top of J-weld:-
bl-0.6 = 1.732 Case 3: Plate height equal to Nozzle Length :-
b2 0.6 = 12 Edge Crack-Entergy-Comparison-000.mcd
Entery Operations Ic.
Central Engineering Programs Appendix D; Attachment 3 Page 3 of 4 Engineering Report M-EP-2003-002-01 Calculations:
aO = 0 j:= 1..N-I a.:=a.
+Inc j-1 a.
- x. :=-
J b
a.
XI :=-i J bI a.
aj X2 :=-
Brown and Srawley Model For edge Crack in a Plate Fbs i= 1.12-0.231 x. + 10.55lx.j) - 21.72-(xj) + 30.39-(xJ)
Plate height as length below Fillet weld to tube bottom FbSI = 1.12 -0.231.xl i+ 1O.55- (XI j - 21.72.(xlj)3+ 30.39. (XI j)
Plate height as length below Top of J-weld to tube bottom Fbs2j := 1.12 - 0.231-x2 + 10.55 (X2j) - 21.72.(x2j)3 + 30.39 (X2 )4 Plate height as F Through-wall Axial crack In a Thick Cylinder (Entergy Model)
Full length of Nozzle
((j
=
12.1l AeM. := 1.009 + 0. 36 21.j + 0.0565.(A) 2 - 0.0082. (j) 3 + 0.0004. (j) 4 - 8.326-10 6(Xj)
AeB. := 0.0029 + 0.0707-(Xj)' - 0.0197-(Xj) 2 + 0.0034 (Xj)3 - 0.0003.(Xj)4 + 8.8052. 10 (kj)
AbM. = -0.0063 + 0.919-Xj - 0.168 (Xj)2 - 0.0052.(Xj) 3 + 0.0008.(Xj) 4 - 2.9701. 10-(j)
AbB. := 0.9961 - 0.3806.Xj + 0.1239.(Lj) 2 - 0.0211.(Xj)3 + 0.0017.(Xj) 4 - 4.9939-10 (Xj)
AM := AeM.+ AbM.
J J
J AB := AeB.+ AbB.
Edge Crack-Entergy-Comparison-OOO.mcd
Entergy Operations Inc.
Central Engineering Programs Appendix D; Attachment 3 Page 4 of 4 Engineering Report M-EP-2003-002-01 Comparison of Magnification Factors 20
~l)
C) 0 C) 0.003592 0.12 0.24 0.36 0.48 0.6 0.72 0.84 0.96 1.08 1.2 1.32 1.43 1.55 1.67 1.79 Flaw length {inch}
Edge Crack Panel Height upto Bottom of fillet weld Edge Crack Panel Height upto Top of J-weld Edge Crack Panel Height equal Full Nozzle Length {20 inches}
Entergy Model Membrane Edge Crack-Entergy-Comparison-OOO.mcd I~~~~~~~~~~~~~~~~~~~~~~~~
(q9
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 1 of 31 Engineering Report M-EP-2003-002-01 Comparison of Surface Crack Models: Conventional Model with the Current Model Developed by Central Engineering Programs, Entergy Operations Inc Developed by: T. S. Brihmadesam Verified by: B. C. SMy
References:
- 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 Purpose :- This worksheet is used to compare the crack growth and SIF results between the conventional model (using a fixed Rht ratio and a fixed flaw aspect ratio-a/c) and the current model. The current model uses the R/t ratio appropriate to the CEDM nozzle tube geometry and the flaw aspect ratio is not fixed. The flaw aspect ratio is determined at each crack growth interval based on the seperate growth for both the depth direction (a-tip) and the length direction (c-tip). Therefore, the current model permits the evaluation of crack growth through the wall thickness and along the nozzle surface simultaneously.
The evaluation, using the same residual stresses distribution, compares the results form both models. The worksheet is essentially the same as that used in the analyses. The only difference is that a separate loop. The graphical presentations towards the end of the worksheet present the comparative results.
Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8.8" Degree Nozzle, "0" Degree Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face 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.
OD Surface Flaw Developed by:
J. S. Btihmndesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 2 of 31 Engineering Report M-EP-2003.002-01 The first Required input is a location for a point on the tube elevation to define the point of interest (eg.
The top of the Blind Zone, or bottom of fillet weld etc.). Thi reference point is necessary 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 represents the reference point elevation measured upward from the no2zle end.
Refpoint =.544 To place the flow with respect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "r-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 Input Data :-
L := 0.3966 Initial Flaw Length ao := 0.0661 od := 4.05 id := 2.728 P~nt := 2.235 Initial Flaw Depth Tube OD Tube ID Design Operating Pressure (internal)
Years := 4 Number of Operating Years Irim = 1500 T := 604 Xo, := 2.67-o- 12 Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Tref := 617 Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Developed by:
J. S. Bnhmadesam Veiffied by.-
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 3 of 31 Engineering Report M-EP-2003.002-01 R od 0 2 Rid := id Rid
-=
t := R - Rid Rm=Rjid+ 2 Timopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk m
- I1im, rimn Pmtblk :=
50 L
C0 2
Rm Rt
[
Qg (1 l' A
1.103-1-3 tT+459.67 Tref+459.67)
T CO I = e -*
aC Temperature Correction for Coefficient Alpha Co:= C 0 1 75 t percentile MRP-55 Revision 1 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "Om = Axial distance from minimum 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 74" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
~~~~~2 3
4 5
0 0
-27.4
-24.36
-22.21
-20.41
-18.98 1
0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4
1.43 33.62 27.79 24.8 24.32 26.99 5
1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67 9
2.18 14.83 22.26 34.78 49.05 63.38 Developed by:
J. S.
Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineenng Programs Appendix D; Attachment 4 Page 4 of 31 Engineering Report M-EP-2003-002-01 AXLen =Afll~ata(0)
IDAII:= A11DatP)
ODA11:= A11Data()
Stress Distribution 100 IDAll 0DAll 50 0
O 0
0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
Observing the stress distribution select the region In the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection In the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-27.404 -24.356 -22.209 -20.407 -18.978) 0.483 0.633 0.87 17.665 1.18 29.798
-1.486
-3.599
-4.44
-5.268 16.422 14.61 12.415 9.376 26.049 22.723 18.95 14.201 Data :=
1.428 33.623 27.792 24.8 24.321 26.989 1.627 32.364 28.469 27.591 34.284 45.104 1.786 27.394 28.918 31.388 43.882 63.718 1.919 21.498 25.556 33.55 48.089 66.365 y2.051 16.944 23.793 34.064 49.472 67.672 )
MI := Data)
NMD:
Data~~
ID:= Datal)
TQ :=Data~~
QT := Data(2)
(5)
OD:= Data Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineerng Programs RID := regress(Axl,ID,3)
Appendix D; Attachment 4 Page 5 of 31 Engineering Report M-EP-2003-002-01 RQT:= regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axl, MD, 3)
ULStrsDist = 1.786 UpperA) nozzle bc RTQ:= regress(Axl,TQ,3)
Jial Extent for Stress Distribution to be used in the Analysis (Axial distance above
)ltom)
FLcntr =
Refpftin - c0 if Val =
Refpoint if Val = 2 Refpoint + co otherwise Flaw center Location Location above Nozzle Bottom UTip := FLCntr + cO ULSrs.Dist - Ufip Inlc~stj.avg :20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locations for stress profiles Loco := FLCntr - L i:= 1..N+3 Incri :=
c0 if i < 4 InCstrs.avg otherwise Loci := Loci-, + Incri SIDi = RID3 + RID4 ' Loci + RID 5(Loci)'+ RID 6(Loci)
Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 6 of 31 Engineering Report M-EP-2003-002-01 SQT R QT3 + RQT4 LoCi + RQT.(Loci)2 + RQT6*(Loc;) 3 SMD;:= RMD + RMD 4Loci + RMD.(Loci)2+IRMD *(Loci)3]
STQ: RTQ3 + RTQ4 LoCi + RTQ -(Loci)2 + RTQ. (Loci) 3 SOD ROD3+ ROD 4-Loci + ROD.(Loci) 2 + ROD *(Loc;)3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j := I..N Sid =
SIDj + SIDj+l + SIDj+2 if j =
J
~~~~~3 sid
- (j + 1) + SIDj+2 i-I otherwise j +2 sqtj =
SQTJ + SQTj+j + SQTj+2 3
Sqt(j_) (j + 1) + SQTj+2 j+2 if j = 1 otherwise Smd J
SMDj + SMDj+l + SMDj+2 3
Smd
- (j + 1) + SMDj+2 i-I~~~~~
II J -
I Stq.
STQj + STQj+
1
+ STQj+2 if j = I tqj
~~~~3 Stqji *(j + I) + STQj+2 5tq. ;O~i)+STQJ÷2 otherwise j+2 otherwise v
j+2 Developed byV J. S. Bnhmadesam Vef tried b.Y.
B. C. Gra.y
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 7 of 31 Engineering Report M-EP-2003-002-01 Sodj =
J SODj + SODj+j + SODj+2 if j =
3 Sodj
- (j + 1) + SODj+2 otherwise j+2 Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution)
U0 := 0.000 ui = 0.25 U2 := 0.50 u3 := 0.75 u4 := 1.00 Y :=stack(u0,u1,u 2,u3,U4)
SIG 1 := stack(Sod1IStq, Smd, Sqt, Sid )
SIG3 := stack(Sod3 9 Stq3 ySmd3 ' 5qt3 ' Sid3)
SIG 5 := stack (Sod5 ' tq5 ' Smd 5'qt 5 Sid5)
SIG7 = stack(Sod7 ' Stq7 ' Smd 7 ' Sqty Sid7)
SIG9 := stack( Sod9 Stq9, Smd9 Sqt9, Sid 9)
SIG, 1 := stack( Sodt Stq l^Smdl l Sqt l9Sid 1)
SIG 2
= stack (Sod 2 ' S5tq2 ' Smd2 ' Sqy Sid2 )
SIG4 := stack (Sod 4, Stq4,Smd4,Sqt4,Sid4)
SIG6 := stack(Sod6 Stq6
% Smd6 Sqt6 Sid6)
SIG8 := stack( Sod 8' Stqg Smd 8~Sqt8 Sid8)
SIG 1 0 = stack(Sod109 Stq 10 Smd10 Sqt1 0' Sid10)
SIG 12 := stack(Sod1 2 Stq1 2 Smd 12 ' qt1 2 Sid12)
Developed by:e J. S. Brihmadesam Velirled by.,
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 8 of 31 Engineering Report M-EP-2003-002-01 SIG 1 3 = stack (Sod 3 'Stq 13 ' Smd13 ' Sqt13 ' Sid13 )
SIG 15 = stack(Sod 1 5 'Stq 15 ' Smd 15 ' Sqt,5, Sid15 )
SIG17 := stack(Sod 17 'Stq17 ' Smd17 ' qt]7 Sid17)
SIGI9 := stack (Sod 19 'Stqj' Smd 19'Sqt 19 S'Sid 19)
SIG 14 := staCk(Sod14'Stq14 Smd 14 Sqt1 4 Sid 14)
SIG 1 6 = stack (Sod16 S'tq16' Smd16' Sqt16' Sid16)
SIG 18 := stack(S od 8' St q 8 ' Smd1 8 ' Sqt 1 8 ' Sid18)
SIG2 0 := stack (Sod 2 0 'Stq 20'Smd20' qt0 Sid20)
Regression of Through-wall Stress distribution to obtain Stress Coefficients through-wall using a Third Order polynomial ODRGI := regress(YSIGI,3)
ODRG2 := regress(Y,SIG 2,3)
ODRG3 regress(Y,SIG3,3)
ODRG5 regress(Y,SIG5,3)
ODRG7 regress( Y, SIG 7,3)
ODRG9 regress(Y,SIG 9,3)
ODRG 1 1 regress(Y, SIG I 1, 3)
ODRG1 3 regress(Y,SIG1 3,3)
ODRG1 5 regress(Y,SIG15,3)
ODRG1 7 regress(Y,SIG17,3)
ODRG1
- regress(Y,SIGj 9,3)
Developed by:
J. S. Bnhmadesam ODRG4 :=regress(Y, SIG 4,3)
ODRG6 := regress(Y,SIG6,3)
ODRG8 := regress(Y,SIG8,3)
ODRGio := regress(Y,SIGI 0,3)
ODRG12 := regress(Y,SIG12,3)
ODRG1 4 := regress(Y,SIG1 4,3)
ODRG 16 := regress( Y, SIG 1
6,3)
ODRG1 8 := regress(Y,SIG1 8,3)
ODRG2 0 := regress( Y, SIG 2 0,3)
Venfled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 9 of 31 Engineering Report M-EP-2003-002-01 Stress Distribution in the tube. Stress influence coefficients obtained from third order polynomial curve fit to the throughway stress distribution PrOpkengh UL~ts.Dist - FLCntr - co Prokengh = 0.044 Data Files for Flaw Shape Factors from NASA (NASA-TM-I 1707-SC04 Model)
(NO INPUT Required}
Mettu Raju Newman Sivakumar Forman Solution of ID Part through-wall Flaw in Cylinder Jsb :=
0 1
2 1.000 0.200 0.000 1
1.000 0.200 0.200 2
1.000 0.200 0.500 3
1.000 0.200 0.800 4
1.000 0.200 1.000 5
1.000 0.400 0.000 6
1.000 0.400 0.200 7
1.000 0.400 0.500 7
1.000 0.400 0.800 9
1.000 0.400 1.000 fh 1.000 1.000 0.000 11 1.000 1.000 0.200 12 1.000 1.000 0.500 13 1.000 1.000 0.800 14 1.000 1.000 1.000 15 2.000 0.200 0.000 16 2.000 0.200 0.200 17 2.000 0.200 0.500 18 2.000 0.200 0.800 19 2.000 0.200 1.000 20 2.000 0.400 0.000 21 2.000 0.400 0.200 22 2.000 0.400 0.500 IZ~J Developedby:
J. S. Biihmadesam 2.000 0.400 _
0.800 Venf led by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 10 of 31 Engineering Report M-EP-2003-002-01 4
2.000 0.400 1.000 25 2.000 1.000 0.000 2-2.000 1.000 0.200 27 2.000 1.000 0.500 28 2.000 1.000 0.800 2.000 1.000 1.000 30 4.000 0.200 0.000 31 4.000 0.200 0.200 32 4.000 0.200 0.500 33 4.000 0.200 0.800 34 4.000 0.200 1.000 35 4.000 0.400 0.000 36 4.000 0.400 0.200 37 4.000 0.400 0.500 38 4.000 0.400 0.800 39 4.000 0.400 1.000 40 4.000 1.000 0.000 41 4.000 1.000 0.200 42 4.000 1.000 0.500 43 4.000 1.000 0.800 42 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 45 10.000 0.200 0.500 48 10.000 0.200 0.800 9
10.000 0.200 1.000 48 10.000 0.400 0.000 4
10.000 0.400 0.200 2_
10.000 0.400 05 50 10.000 0.400 0.800 10.000 0.400 1.000 51 10.000 1.000 0.000 6_
10.000 1.000 0200 72 10.000 1.000 0.500 8
10.000 1.000 0.800 54 10.000 1.000 1.000 1300.000 0.200 0.000 1
300.000 0.200 0.200 1300.000 0.200 0.500 3
300.000 0.200 0.800 300.000 0.200 1.000 5
300.000 0.400 0.000 61 300.000 0.400 0.200 Developedby:
J. S. Bnihmadesam Verfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 11 of 31 Engineering Report M-EP-2003-002-01 z67 300.000 0.400 0.500 8
300.000 0.400 0.800 300.000 0.400 1.000 0
300.000 1.000 0.000 1
300.000 1.000 0.200 t2 300.000 1.000 0.500 3
300.000 1.000 0.800 4
300.000 1.000 1.000 Sambi :=
0 1
2 3
4 5
6 7
0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1
1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2
1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3
2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4
4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5
1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6
1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7
1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8
2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9
2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 1-1 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21-1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 271 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 Developed byB
- 1. S. Snhmadesam Venried by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 12 of 31 Engineering Report M-EP-2003-002-01 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 0.596 1.16 0.242 0.097 0.051 34-3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 35 1
0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 6z 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Developed by:
J. S. Blhmadesam Verfiedby.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 13 of 31 Engineoring Report M-EP-2003-002-01 W := Jsb(°)
X := Jsb)
Y := Jsb(2) au := Sambi(O) aL = Sambi(l) aQ
- =Sambi (2) aC := Sambi(3)
CU := Sambi(4)
Sambi(5)
Sambi(6)
CL =
CQ :=
cc := Sambi<7) n:=
3 if Rt<4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W, X, Y)
VaU := aU Rau :=regress(MaU,VaU,n) faU(WX, Y) := interP[RaU, MaU, VaU, [X I faU(4,4,.8) = 1.741 Check Calculation Linear Term MaL := augment(W,X,Y)
VaL := aL RaL :=regress(MaL,VaL,n) faL (W, X, Y) :=interp RaL, MaL, VaL{X II Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 14 of 31 Engineering Report M-EP-2003-002-01 faL(4,.4,.8) = 0.919 Check Calculation Quadratic Term MaQ := augment(W,X,Y)
VaQ := Q RaQ := regress(MaQ, VaQ, n) faQ(W, X, Y) := interp[RaQ, MaQ VaQ X I]
f'WXY' MaQ ~
a faQ(4,.4,.8) = 0.656 Check Calculation Cubic Term MaC := augment(W, X, Y)
VaC :=aC RaC := regress(MaC,VaC, sn)
[W{
faC (W,X, Y) := interp aC, MaC, VaC X I faC(4,.4,.8) = 0.524 Check Calculation Developed by:V J. S. Bnhmadesam Velffied by B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 15 of 31 Engineering Report M-EP-2003-002-01 "C" Tip Coefficients Uniform Term MCu := augment(W, X, Y)
VCu := cu Rcu := regress(McuVcun) fcu(W,X,Y) := interp{RcU, McU, VcU{ X I fcu(4,A4,.8) = 1.371 Check Calculation Linear Term MCL := augment(W,X,Y)
VcL := CL RCL: regress( McL, VcLn) fCL(WX,Y) := interp[RCLIMcLtVcL, Xj fcL(2,.4,.8) = 0.319 Check Calculation Developed by:
J. S. Brihmadesam Venffied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 16of31 Engineering Report M-EP-2003-002-01 Quadratic Term MCQ := augment(W,X,Y)
VcQ := CQ RCQ :=regress(MCQ, VCQ, n) fcQWXY):=interp{RcQ MCQ ~VCQ{IX I1 fCQ(W~~~~
XY))
fcQ(4,.4,.8) = 0.126 Check Calculation Cubic Term MCC := augment(W, X, Y)
VCC := Cc R~CC= regress(M~cCV~C,n) tW{V fcC (W, X, Y) := interpRC' MCC, VcCC X I fcc(4,.4,-8) = 0.068 Check Calculation Developed by:
J. S. Bihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 17 of 31 Engineering Report M-EP-2003-002-01 Calculations: Recursive calculations to estimate flaw growth.
Recursive Loop for Calculation of PWSCC Crack Growth Entergy Model CGRsambi :-
ao*-ao aO C O NCBo -
Cbok while j < 11im 0o <- ODRG3 if cj < CO ODRG2 if c0 < cj < co + InCStrs.avg ODRG3 if c0 + InCStrs.avg < cj < C0 + 2 InCStrs.avg ODRG4 if CO + 2 Incstrs.avg < Cj < Co + 3 IlncStrs.avg ODRG5 if co + 3 InCStrs.avg < Cj < Co + 4fIncStrs.avg ODRG6 if CO + 4 IlncStrs.avg < Cj < Co + 5 IncStrs.avg ODRG7 if C0 + 5-IncStrs.avg < cj < cO+ 6-Incstrs.avg ODRG83 if co + 6. lCStrs.avg < Cj < co+ 7flncStrs avg ODRG9 if CO + 7 InCstrs.avg < cj < co + 8IlnCStrs.avg ODRGIO if cO + s-IlnCStrs.avg < cj < co + 9fInCStrs.avg ODRGi 3 if co+ 9-IlnCStrs.avg < cj < co + 10 InCStrs.avg ODRG1 2 if co + lOI-lncStrs.avg < cj < co + l1-Incstrs.avg ODRG 1 3 if co + I-Incstrs.avg < cj < Co + l2dlncStrs avg Developed by:
J. S. Bnhmadesam Ventfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs ODRG1 4 ODRG1 5 ODRG16 ODRG1 7 ODRG1 8 ODRG19 ODRG2 0 3 ODRG1 8 ODRG2 9 ODRG3 3 ODRG234 ODRG 44 ODRG24 ODRG34 ODRG4 4
ODRG5 ODRG9 4
ODRG1 4 ODRG1 4 ODRG84 ODRG94 ODRG14 4 ODRG12 Appendix D; Attachment 4 Page 18 of 31 if co + 12-InCStrs.avg < cj if co+ 13* IncStrs.avg < cj if co + 14 IncStrs.avg < cj if co+ 15IncStrs.avg < cj if co + 16-InCStrs.avg < Cj if co+ 17 IncStrs.avg < cj otherwise Engineering Report M-EP-2003-002-01 Co+ 13-IfCStrS.aVg Co+
14-flCStr.aVg co + I5* Iflc~st.avg Co+ 16* Inc*ts~v C0o+ 17 IflcStrs.avg c0 + 18-IflcSrs.avg if cj < CO if co < cj < co + InCStrs.avg if co + Incstrs.avg < cj < Co + 2 lnCStrs.avg if co + 2-Incstrs.avg < cj < co + 3-IncStrs.avg if ce + 3-lncstrs.avg < cj < co + 4 IncStrs.avg if C0 + 4-lncStrs.avg < cj < co + 5IflCStrs.avg if c0 + 5 Incstrs.avg < cj < co + 6-InCStrs.avg if co + 6 Ilncstrs.avg < cj < co + 7-IncStrs.avg if co + 7-Incstrs.avg < c < co + S-IncStrs.avg if co + 8.Incstrs avg < Cj < co + 9. IlncStrs.avg if co+ 9-Incstrs avg < cj < co + oI lnCStrs.avg if co + oflncstrs.avg < cj < c0 + II lnCStrs.avg if co + I -l ncstrs.avg < cj < co + 12-IncStrs.avg if co+ 12-lncStrs.avg < cj < co + 13.IncStrs.avg if co + 13-lncstrs.avg < cj < co + l4. lncStrs.avg Developed by:
J. S. Bnlhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 19 of 31 M-EP-2003-002-41 ODRG 1 6 4 if co + 14-IncStrs.avg < cj <
0o+ 15-IncStrs.avg ODRG1 74 if co + 15-IncStrs.avg < cj < CO + 16-Instrs.avg ODRG1 8 4 if Co + 16-InCStrs avg < cj < Co + 17 InCStrS avg ODRG 19 if co + 17-flncStrsavg < cj < co + 18IncStrs.avg ODRG2 0 otherwise 2 e-ODRG1 if cj < cO ODRG2 if co < Cj < co + InCStrs.avg ODRG 3 if co+ Incstrs.avg < Cj < Co+ 2-Incstrs.avg ODRG4 if co+ 2-lncstrs.avg < Cj < co + 3-InCstrs.avg ODRG 5 if CO + 3 Ilncstrs.avg < Cj < co + 4 IlncStrs.avg ODRG 6 if Co + 4fIncstrs.avg < Cj < co + 5fInCStrs.avg ODRG 7 if Co + 5 Incstrs.avg < Cj < co+ 6-flCStrs.avg ODRG8 if Co + 6 Ifncstrs.avg < cj < Co+ 7IncStrs.avg ODRG9 if Co + 7-Incstrs.avg < cj < co + 8IncStrs.avg ODRGIO if CO + 8-IncStrs.avg < Cj < Co + 9 InCStrs.avg ODRGI 15 if co + 9InCStrs.avg < cj < co + IlOInCStrs.avg ODRG1 2 if co+ IOIncstrs.avg < cj < co + 1-lnCStrs.avg ODRG13 if Co+ 1 -InCstrs.avg < Cj < C0+ 12fInCStrS.avg ODRG145 if co + 12dlncstrs.avg < cj < co+ 13 InCStrs.avg ODRG1 5 if co + 13-lncstrs.avg < cj < Co+ l4flncStrs.avg ODRG1 6 if co + l4-Incstrs.avg < Cj < cO + 15flncStrs.avg 5_r
- Developed by:
J. S. BShmadesam Ven fled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs U)KkI 1 75 ODRG1 85 ODRG 19 ODRG2 0 ODRGI6 ODRG2 6 ODRG 3 6 ODRG4 6 ODRG5 ODRG 6 6 ODRG 7 ODRG8 6 ODRG9 6 ODRG1 o ODRG11 ODRG1 2 ODRG13 6 ODRG1 48 ODRG1 5 ODRG 16 6 ODRG 17 ODRG 18 Appendix D; Attachment 4 Page 20 of 31 t Co + 1s lnCstrS.avg < Cj S C0 + 16 lnCStrs.avg if co + 16-IncStrs.avg < Cj < cO + 17flncstrs.avg if co + 17-Incstrs.avg < cj < cO + 18lncstrs.avg otherwise if cj < CO if co < cj < co + InCStrs.avg if co + Incstrs.avg < cj < co + 2-InCStrs.avg if co + 2-Incstrs.avg < cj < co + 3. Incstrs.avg if c0 + 3. Incstrs.avg < cj < co + 4-Incstrs.avg if co + 4. Incstrs.avg < cj < cO + 5. Incstrs.avg if co + 5-Incstrs.avg < cj < C0 + 6 InCStrs.avg if co + 6-Incstrs.avg < Cj < co + 7 IncStrs.avg if co + 7-Ilncstrs.avg < Cj < co + 8IlnCStrs.avg if co + 8flCnStrs.avg < cj < co + 9 lncStrs.avg if co + 9-Ilncsts.avg < Cj < co + 10IfnCStrs.avg if co + I0. IncStrs.avg < Cj < co + I IncStrs.avg if co + 1-Incstrs.avg < Cj < co + 12flncStrs.avg if co + 12-lncstrs.avg < Cj c Co + 13-IncStrs.avg if co + 13.flnstrs.avg < Cj < co + 14fInCStrs.avg if c 0+ 14 Incstrs.avg < Cj c Co+ 15IlncStrs.avg if co + 15-lncstrs.avg < cj c cO + 16Incstrs.avg if cO + 16-lncsttrs.avg < cj c Co+ 17 IncStrs.avg Engineering Report M-EP-2003-002-01 Developed by:
J. S. Bnhmadesam Veriffed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 21 of 31 Engineering Report M-EP-2003-002-01 ODRG19 6 if co + 17 lnCStrs.avg < Cj < CO + 18 IncStrs.avg ODRG2 0 otherwise 0~~~
G (J0.25-aJ8 0o.25.aj82 0o.25-aj'8 3
-S00+ 01-
+ 02-(
t g
I) 40
<- 0
( -+(Y-+tY t )
0.75.aj'~
2 0.75 aj") 3
+-GO+
t
)2C t
)
YYt t )+
0 2y
)~
~ t.a)'
I - 0.0
<-- 0.25
+- 0.5
,- 0.75
<-- 1.0 Ix2,x 3, x4)
ST - stack(40tI142,43 44)
RG3 + PInt RG4 RG5 RG6 A~ -aj Cj
+a Developed by:
J. S. Blhmadesam Venried by:
B. C. Gray
Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 22 of 31 M-EP-2003-002-01 L
G au-- faU (Rt1,ARj,ATj)
Gal +- faL(RtARj,ATj)
Gaq 4-faQ (Rt, ARj, ATj)
Gac. <-- faC(Rt, ARj,ATJ)
GCUj -fCU (Rt, ARj,ATJ)
GC
-- fCL(Rt'ARjATj)
Gcqj fcQ(Rt'ARj'ATJ)
Gccj -fCc(Rt,ARj,ATj) 1.464{A1.6 Qj+- 1 + 1.464i-f cj 2 aj (C~1.65 1 + 1.464-( -
otherwise aj)
Kaj <.
(O
- Gau+
+ (IIGai+ ay2oGaqj + O30Gacj)
Kc
(. C (oo-Gcuj + olO.Gcl + O2OGcqj + t33 OGcc)
Ka
- Kaj 1.099 K
<Yj-K cj 1099 Ka -
9.0 if Ka < 9.0 K a otherwise Ky +i9.o if K Y < 9.0 K 7 otherwise Da i CO (Ka;i
- 90) 11 Developed by:
- 1. S. Bnlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 23 of 31 M-EP-2003-002-01 Dag +-Da
-CFinhr-Cblk if Ka < 80.0 4-1(-' '0 CFinhriCbIk otherwise Dc4-Co.(Kyj -9.0) 6 Dcgj <-l D CFinhr-Cblk if K Y < 80.0 4 10-CFinhr-Cbk otherwise output(j, 0) 4-j output(j, 1)
- aj output(j,2 ) 4 Cj -
CO OUtPUt(j, 3) - Dagj OUtPUt(j, 4) 4-Dcgj OUtPUt(j, 5) 4K-OUtPUI(j,6)
K 4
C NCBj OUtPUt(j,7) 4-365-24 OUtPUt(j, 8) 4 Gau.
oUtpUt(j,9)4-Gali output(j 10) 4 Gaqj output(j, 11)
Gac OUtPUt(j, 12)
GCu-output(j, 13) 4-Gcl outPut(j, 14)4-Gcqj OUtPUt(j, 15) - GCC j4-j+I Dova/aped by:
Vernfied by:
J. S. Bdhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 24 of 31 Engineering Report M-EP-2003-002-01 aj v-aj-, + L)agj_,
Cj (
Cj9-
+ Dcgi 1 aj - It if aj>t aj otherwise NCBj +- NCBj-j + CbIk output Developed by:
J. S. Blihmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 25 of 31 Engineering Report M-EP-2003-002-01 Recursive Loop for Industry Model
{R/t = 4.0 and a/c=0.33 The R/t lower Limit for Original Raju-Newman model and aspect ratio was fixed at 1:6)
CGRgam Barnm I j-0 ao - aO cO - CO NCBo
- CbIk while j < Ilrm 0o ODRGi 01 - ODRGI 3
4 2 <- ODRG, 3 +- ODRG, 5
-t, 40 *- (lo 1 -Go G
0 1 (I i
+
02.(0.25-aj) 2 t
)
~2+- 00+(71.
+"
___05 a) r 0.25* aj) t )
(Y3.5-aj)3 t )
o07 **
(1.0 3 (I.o aj)3
~3 +-GO+(I
+ 02.(0.75-aj)1 4 v f
+ o l.O-a) + o(I.Oaj)2
- 0 - 0.0 X-0.25 x2 +- 05 x3 - 0.75 x4 +- I 10 Developed by J. S. Bdhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 26 of 31 Engineering Report M-EP-2003-002-01 X--
stack(xOxIx 2 x3,x 4 )
ST*- stack(40 1 42S 3s 4)
(oo < RG3 a 1 0 E RG4 C2 0
- RG5 0 3 0 E RG6 ARj +- a Cj aj t
Gau faU(4,.3,ATJ)
Gal i faL(4,*3,ATj)
Gaqj faQ(4,*3, ATj)
Gacj +- faC (4,.3, ATJ)
I +1.464{2j 16 cj)
.cj) 65 1 + 1.464-a) if cj 2 aj otherwise Kaj +
J Ka E Kaj 1.099 Ka<- 19.0 if I (aOO Gauj +u lO GaIj + 020Gaqj + 030OGacj)
IKa x 1 K
<9.0 tj gtherwise Da
- CO (Ka - 9.0)1.16
_ j cc__
Developed by:
J. S. Bnhmadesam Verified by B. C. Gray
Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Programs Page 27 of 31 M-EP-200300201 Dag <
Da -CFinhr Cbik i Ko < 80-0 4 10- 10-CFinh.Cblk otherwise DCgj Dag*3 output(j, 0) j output(j, 1) <
aj output(j, 2)
- Cj - co OUtpUt(j, 3) <- Dag output(j, 4) v Dcg.
OUtpUt(j, 5) & Kaj NCB-OUtpUt(j, 7) 4 36524 OUtpUt(j, 8)
- Gau output(j, 9) & Gal.
output(j, 10) < Gaqj output(j, II) & Gacj j*-j+I aj-aj
+ Dagj_
Cj E
+ Dcg. 1 ajF It if aj > t aj otherwise NCBj <- NCBj-I + Cblk output k
o.. Ilim Developed by:
Venifled by:
- 1. S. Blhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 28 of 31 Engineering Report M-EP-2003-002-01 0.6 U
0~
c I
0.
A:
EJ 0.4 0.2 The Current model, in the time period of interest provides a higher growth.
0 1
2 3
4 Operating Time {years}
Entergy-CEP Model
- .... Conventional Model Flaw Growth in Length Direction U
0
..J 2
0 0.8 0.6 The flaw growth in the length direction for the conventional model is controlled by the flaw aspect ratio. Hence the observed higher growth rate for the conventional model doe not signify a truly higher growth rate.
0.4 0.2 0
1 2
3 Operating Time {years}
Entergy-CEP Model Conventional Model 4
Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 29 of 31 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 2'Q 0
.tU V-
'A coz;
_u4 80 60 40 20 0
0.5 1
1.5 2
2.5 Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Conventional Model Depth Point 3
3.5 4
The SIF comparison shows that the current model has higher SIF for the period of interest (one operating cycle). The conventional model SIF rises above the current model SIF for the depth point (a-tip) but remains below that for the surface point (c-tip).
Developed by.
Verified by:
J. S. Bnhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 30 of 31 Engineering Report M-EP-2003-002-01 Axum plot showing the ID and the OD stress distribution for the CEDM 60 -
40 -
z' 20
- Z I
o 0
-2 0
-4 0 lID D is trib ution t
Il
=
OD Di s Itrib u tio n, T
,~.
se onef I1Z I
Bottom of W oId I
I I
g I
I I
I 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istance from N ozzle B ottom
{incItes)
Axum plot showing the comparison for Crack growth between Conventional and Current Model 0.5 Z
c 0 4 a
0 2 o2 0.1 0 o 0
1 2
3 4
0 perating Time (years}
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 31 of 31 Engineering Report M-EP-2003-002-01 Axum plot showing the SIF comparison between the Conventional and Current Models Current model (Entergy)
I-Conventional Model (Industry) 70 -
.' 5 ILJ u?
30 -
10 -
I I
I I
I 0
1 2
3 4
Operating Time {years)
Developed by.
J. S. Brihmadesam Verified by.
B. C. Gray
Enteloy operations Dic.
Appendix D; Attachment 5 Engineering Report Cental Engineering PRgrams Page 1 of 17 M-EP-2003-002-01 Comparison for Through-wall Cracks Developed by Central Engineering Programs, Entergy Operations Inc Developed by: T. 5. Brihmadesam Verified by: B. C. Gray
References:
- 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 Purpose :- This worksheet is used to compare the results from the conventional model, edge crack model and the current model. The SIF comparison is made between the conventional model and the current model. The crack growth and SIF comparisons are made between the edge crack and current model. The SIF equations for the conventional model are included in the current model's recursive loop structure. The edge crack is modeled separately in a recursive loop immediately following the loop for the current model. Graphical results show the comparisons at the end.
The salient differences between the three models considered are:
- 1) Current model is based on X, which is limited to 20. The closed form solutions are based on a thick wall cylinder.
The applied stresses are based on a moving average. Therefore an increase in the stress field as the crack advances is considered in the analyses
- 2) The conventional model is based on a Center Cracked Panel with a SICF of 1.0. The applied stresses are at the initial flaw location and remain constant over the entire crack growth regime.
- 3) The edge crack model uses the plate height (b) equal to the nozzle length from the bottom of the nozzle to below the weld. The initial flaw length (a) is equal to the blind zone (1.544 inches). When this is done the ratioa/b (crack-length/plate-height) is larger than the validity limit of 0.6. Therefore, the estimated SIF is considered non-representative.
Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8.8"degree Nozzle, "0" Degree Azimuth 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 55Rev. 1.
Through Wall The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Axial Flaw
Ehfteyy Operoions r.h Central Engineering Programs Appendix D; Attachment 5 Page 2 of 17 Engineering Report M-EP-2003-002-01 The first Daput is to locate the Reference Line (eg. top of the Blind Zone). The through-wall flaw 'Vtpper Tip-is located at the Reference I Me.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.3 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:= 1.786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Ebfteyy Opertions Inc.
Central Engineenng Programs Appendix D; Attachment 5 Page 3 of 17 Engineering Report M-EP-2003-002-01 Input Data :
L :=.794 OD:= 4.05 ID:= 2.728 Pint:= 2.235 Years:= 4 1jim:= 1500 T:= 604 v := 0.307 aoc:= 2.67-10 12 Qg:= 31.0 Tref := 617 Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F co:e.10~~3(
13T+459.67 Tref-+459.67)]
Tinilopr= Years-365-24 OD Ro:= O2 ID Rid:= ID 2
t:= Ro - Ri Rm:= Ri + 2 CFinh,:= 1.417-1 0 TTimopr Cblk =
jim Pmtblk := -50"m I
L 2
LI:= BZ I
I
Enteryy Operations.Tc.
Central Engineering Programs Appendix D; Attachment 5 Page 4 of 17 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:
Column "on = 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 :=
-W1
- l 0
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:= DataAll AIIID:= DataAll AIIOD:= DataAjll Axial Distance above Bottom [inch]
ID Distribution
-- OD distribution I
I
Enteryy Operations Ie.
Central Engineering Programs Appendix D; Attachment 5 Page 5 of 17 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of Interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the 'Data' statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(
0
-27.404 -24.356 -22.209 -20.407 -18.978) 0.483 0.633 0.87 17.665 Data:= 1 1.18 29.798
-1.486 16.422 26.049 27.792 28.469 28.918
-3.599
-4.44
-5.268 14.61 12.415 9.376 22.723 18.95 14.201 24.8 24.321 26.989 27.591 34.284 45.104 31.388 43.882 63.718 )
1.428 33.623 1.627 32.364 1.786 27.394 Axl:= Data(
ID:= Data OD:= Data RID: regress(Axl, ID, 3)
ROD:= regress(Axl, OD, 3)
FLCntr:
BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ IncStrs.avg :=
20 ULStrs.Dist - BZ IncrEdg :=
20 RIDAJI:
regress(AlIAxl,AIlID,3)
RODAII := regress(AIIAxI, AIIOD, 3)
No User Input required beyond this Point I
I
En tergy Opemaions hc.
Central Engineering Programs Appendix D; Attachment 5 Page 6 of 17 Engineering Report M-EP-2003-002-01 Calculation to develop Stress Profiles for Analysis Hoop Stress Profile in the axial direction of the tube for ID and OD locations N:= 20 Number of locations for stress profiles Loco:= FLCntr - L i:= 1..N + 3 Incr.:=
I if i <4 1 Incstrs.avg otherwise Loc.:= Loc i- + Incr.
SID := RID + RID *Loc. + RID.(LoC 2 + RID.(Loc 3 1
3 4'
1 5
i) 6\\(i)
Incredg
-=
l if i <4 I
2 IncrEdg otherwise Locl i:= 10 if i = I Locl i-l + Incredg. otherwise SOD. = ROD3 + ROD 4-Loc + ROD -(LoC.)
+ ROD6 (LOci)
SIDAIIj := RIDAJI3 + RIDAII 4-Locl + RIDAJI.-( LoCi.
+ RIDAII*(Locl i)3 SODAlII = RODAII3 + RODAII 4-Locl + RODAII -(Locli)2 + RODAnI6.(LocCI )3
Enfte operations Dc.
Central Engineering Programs Appendix D; Attachment 5 Page 7 of 17 Engineering Report M-EP-2003-002-01 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j:= l.. N SID. + SID.
+ SID.
Si+l J+3 if j = I Sid H, (j + 1) + SIDj+2 j-1 otherwise j+2 l SIDAII + SIDAII
+ SIDAII ij2
_j~ II:
I fj SOD. + SODJ+l + SODJ+2 Sod j:l j+2 if jl=
Sod j -0 + 1) + SODj+2
-otherwise j+2 Sod.all. :=
.3 i
- 3 Sid.all.
'(j + 1) + SIDAII2
-1 J+2 otherwise j+2 SODAJI i+ SODAII + + SODAII 2 lj+
if j = I 3
Sod.allj-l (j + 1) + SODAIIj+2 otherwise j+2 Sod. + Sid.
GM i :=
2 J + Pint Sod. - Sid.
-b
- =
J 2 Sod.all. + Sid.all.
Gm.allj :=
2
+ PInt I
I
Entergy Opertiwons rhc.
Central Engineenng Programs Appendix D; Attachment 5 Page 8 of 17 Engineering Report M-EP-2003-002-01 Stress Distributions for use in Fracture Mechanics Analysis Membrane Stress Bending Stress OD Stress ID Stress Membrane stress (Edge Crack)
- m =
0 15.27 18.819 21.119 22.794 24.115 25.215 26.169 27.022 27.802 28.53 29.217 29.874 30.507 31.122 31.723 0
-4.731
-4.823
-4.766 4.625
-4.184
-3.905
-3.594
-3.254
-2.885
-2.489
-2.066
-1.617
-1.142
-0.64 Sod =
0 0
8.303 11.761 14.117 15.934 17.454 18.796 20.029 21.193 22.314 23.41 24.493 25.572 26.655 27.745 28.848 Sid =
0 17.766 21.408 23.65 25.84 27.164 27.839 28.381 28.821 29.18 29.471 29.705 29.889 30.029 30.128 Gm.all =
0 0
5.53 12.037 16.08 18.889 20.99 22.646 24.005 25.153 26.146 27.022 27.807 28.518 29.169 29.77 30.329 PrOPLenghi := ULStrs.Dist - (FLCnt + I)
PropLength = 0.486 I
I
Eaftiyy Operations hc.
Central Engineering Programs Appendix D; Attachment 5 Page 9 of 17 Engineering Report M-EP-2003-002-01 Calculations : Recursive calculations to estimate flaw growth Recursive loop for Entergy Model and Industry Model TNCWsCc:~ F 10PI NCB 0
0 Cb1k while i S Ilim lI m.appld F am if l; I0 am2 if I0<
1; I0 + InCStrs.avg aM3 if I0+ InCStrs.avg < Ii S I0 + 2-InCStrs.avg am4 if 10 + 2-InCStrs.avg < Ii S 10 + 3-IncStrs.avg
- m5 if 10+ 3 IlncStrs.avg < I; S 10 + 4IncStrs.avg aM6 if 10+ 4 fIncStrs.avg < Ij S I0+ 5-IncStrs.avg iM7 if I0+ 5-IncStrs.avg < I; S I0 + 6-InCStrs.avg Gm8 if I0+ 6-IncStrs.avg < I1 S I0 + 7-IncStrs.avg am 9 if 10+ 7-IncStrs.avg < I; S 10 + 8-IncStrs.avg am if Io + 8-InCStrs.avg < I; S I + 9 fInCStrs.avg am if 1o + 9 lncStrs.avg < Ii I 0o + 10-IncStrs.avg am12 if Io + 10-lIncStrs.avg < Ii *10 + IllncStrs.avg am13 if 10 + I lflncStrs.avg < Ii S 10 + 12fInCStrs.avg (m14 if 10 + 12-lncStrs.avg < I; S 10 + 13-lncStrs.avg am 5 if 10 + 13lfnCStrs.avg < I; S lo + 14-lncStrs.avg sm 16 if I0 + 14-IncStrs.avg < I; S I0 + 15InCStrs.avg am if if
+ I 5InCStrs.avg < I; S 10 + 16-InCStrs.avg am if 10 + 16fInCStrs.avg < I S 10 + 17-fnCStrs.avg (Fm 9 if 10 + 17flncStrs.avg < I; *10 + 18-InCStrs.avg am20 otherwise I
I
Enteryy Operations.Thc.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 10 of 17 M-EP-2003-002-01 Ob.appid Ob if li S10 ab2 if 10 < Ii S 10 + IncStrs.avg Gb3 if 10 + Incstrs.avg < I S < I + 2.IncStrs.avg Ob 4 if 10 + 2 IncSts~avg < I; S 10 + 3 1ncStrs.avg Ob5 if I0 + 3-IncStrs~ag < I; S I+ 40 ncStrs.avg Gb6 if I0 + 42 IncStrs.avg < I < I0+ 5 IncStrs.avg Ob7 if lo +5-IncStrs.avg < I; S I0 + 6-IncStrs.avg ob8 if 10 + 6-IncStrs.avg < Ii S 10 + 7-IncStrs.avg b 9 if lo + 7-IncStrs.avg < I; S< I0+ 8-0nCStrs.avg blo if I1 + 8lInCStrs.avg < I < 10 + 9-IncStrs.avg GbI I if I0 + 9LncStrs ag < li< 5lo- + 10 IncStrs.avg GbI2 if 1 + 10 Incstrs.avg < I < 10 + 116IncStrs.avg bI3 if I0 + 11-IncStrsavg < I-S10 + 12-IncStrs.avg Gb84 if 10 + 12 Incstrs avg < I < 10 +13-IncStrs.avg GbI5 if 1I + 13IncStrs.avg < I < 10 + 14IncStrs8avg CGbI6 if 10 + 14. ncstrs.avg < II S 10 + 15Incstrs.avg Gb17 if 10 + 15 Incstrs.avg < I S 10 + 16InCstrs.avg Gb18 if 10 + 16 IncStrs.avg < Ij S 10 + 17InCStrs.avg
<Tb, 9 if I0 + 17-lIncstrs.avg < Ii S 10 + 18-Incstrs.avg ob2o otherwise
+- [12(1 - v 02)]
05 i
(Rm t).
Aem 1.0090 + 0.3621 A + 0.0565-(A;) 2 - 0.0082.(;i) 3 + 0.0004. (i) 4 - 8.326. 10 6(A;)
Abm +- -0.0063 + 0.0919 Xi- 0.0168. ()
2 _ 0.0052. (X)3 + 0.0008 (AX)4 - 2.9701. 10 (i)
Aeb i-0.0029 + 0.0707 XA - 0.0197. (X)2 + 0.0034 (X)3 - 0.0003. (X) 4 + 8.8052. 10 6 (A)
Abb
- 0.9961 - 0.3806 XA + 0.1239 (Xi)2 - 0.0211. (i) 3 + 0.0017. (i) 4 - 4.9939-10 5 (Xi)
F--
-1
Entwiyy Operations Icr.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 11 of 17 M-EP-2003-002-01 Kpm. 4 am appld-I()X.]_
Kpb.
G 0b.appld (X-. i;)05 KmembmOD +- (Aemi + Abmi).Kpm, KmembmID 4- (Aemi - Abm,)-Kpm KbendoD; + (Aeb4 + Abbj)-Kpb, KbendlD <- (Aeb, - Abbj)-Kpbj KAppoD. +- KmembmOD. + KbendOD.
KAppID, + Kmembm4D- + KbendID, KWHj am I.(IC-i) 0.5 KAppODi + KApplD, KAppi 2
KWH.Icnr.Strs.
- Um.appld (It i)
Ka KApp: 1.099 Ka. -
9.0 if Ka. 5 9.0 Ka. otherwise DIen 4-CO(Ka - 9.0)1.16 Djengrth, 4 Dieni-CFinhrCblk if Ka S 80.0 4-10
- CFinhrCbIk otherwise outputo 4-P(i,O)
NCB.
output(i, 1) 365.24 output(i,2) 4-,i output (i, 3) ' Ij-output(i 4) +- i output( 5)4-KApp; output(i 6) 4 KAppOD, output(i 7) - KAppfDl outflut.
K- -t-_
nterfg' Opectins Xne Central Engineering Programs Appendix D; Attachment 5 Page 12 of 17 Engineering Report M-EP-2003-002-01 output(; 10) v KbendOD, outputo I I) - KbendIDi output(i
- 2) - KWH.
Output(i 3) 4 KWH.Icnr.Stsi i--i+ I I;
Ii-i + Dlengrtfi,_
NCB.i - NCB.i- + CbIk output
Ertery Operawons Za.
Central Engineering Programs Appendix D; Attachment 5 Page 13 of 17 Engineering Report M-EP-2003-002-01 Recursive Loop For Edge Crack Model TWCEDGpwscc:=
i -O L10-ILII NCB00 Cb-k
((while i S 1Jim II I am.appld 4-m.allI Cym.all2 Om all3 0m.al4 Om.all, C~m.all6 am.all7 am.all8 Gm.all9 Gm.all Om.al11 Gm.all 2 Gm.all1 O~m.ail 1 19m.all 1 Om.all 1 Om.all Am.all Cm.all Cm.all b
ULStrs.Dist I
1.
if LI S LIj if LI <LI S<LI + IncrEdg if L1
+ IncrEdg < LIi S LIi+ 2 fInCrEdg if LI + 2InCrEdg< LI LI + 3 InCrEdg if LI + 3-IncrEdg< LI S LI0+ 4 fInCrEdg if LI + 4.IncrEdg< LIjS LI0+ 5 -IlnCrEdg if LI + S-IncrEdg< LI LI + 6-IncrE if LI 0+ 6.IncrEdg < LI iLIo+ 7-InCrEdg if LI 0+ 75 InCrEdg< Ll I0 L1
+
+IncrE if LI + 8-IInCrEdg < LI
9-Incr.Edg <
LI S:
LI0+ 10-Incr~
if LI + I 7
IncrEdg < LIjS LI0+ I11nc ifo
+ 11-IncrEdg< LI <LI+ 12InCEdg if LI 0 + 12 IncrEdg < LIj LI0+
InCEdg if LI + 13-InCrEdg < LI
- LI0+14Inc if LI 0+ 14.
IncrEdg < L S LI0+IO15IncEdg if L 0 + 15-IncrEdg< L1. *I
+
L f16ICrEdg if L l + 16IncrEdg< LIi L
+
LI17InCrEdg if Ll 0 + ITnCrEdg< L lS LI+18nCrEdg otherwise l
l l l l
Entelyy Operaions.he Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 14 of 17 M-EP-2003-002-41
_Z. -- 0.99 if 21 I.0 Llb
- otherwise Fab I 1.12 - 0.231(Z.) + 10.55. (Zi) 2 - 21.72. (Z.) 3 + 30.39.(Z.) 4 Kedg.Crk. 4-Urm.appldjFi if (cm.appld4i)
- 0 lym.appld-t c-Li)
Fab; otherwise KA. 4-Kedg.Crk; 1.099 Ka
- 19.0 if KA
- 9.0 l KA. otherwise Dien *- CO-(Ka - 9.0)1.16 Dlengrth. 4-DieniCFinhrCblk if Kac
- 80.0 4.10 CFjhrp CbIk otherwise outputo, 0)-
i NCB.
oUtput(i 1)
~
365-24 Output(i 2 ) - L1 -LI Output(i 3 ) 4 Diengrthi output(i 4) 4 Kedg.Crk.
output(i,5)
Fab.
i4i+1 L1I LI i-I + Dlengrth; l NCB NCBi-I + CbIk output j := 1. jim I
I
Enteryy Operatimns Inc.
Central Engineering Programs Appendix D; Attachment 5 Page 15 of 17 Engineering Report M-EP-2003-002-01 Propiength~ = 0.486 Flaw Length vs. Time TWCS zc (j,3)
R/
g TWCED'P--(j,2) 0.5
/
o~~~~~~
A/
0.5 1
2 3
TWCPWSC(j j)
Operating Time {years}
Entergy Model Edge Crack Model Comparison for crack growth between Edge Crack and Current Model. The edge crack mc provides a constant crack growth rate equal tc the asymptotic growth rate of about 05.
inch/year. The edge crack model produces a SIF much greater than the asymptotic value ol ksi* inA0.5 or 80 Mpa*mAO.5. This is because the "a/b" ratio (crack-length/plate-height) is significantly greater than the validity limit of 0.E In order to meet the "a/b" ratio validity limit of (
the crack length, for the assumed plate height cannot be greater than 1.073 inches, which is lower than the blind zone length of 1.544 inch.
As shown in attachment 3 of this appendix, assuming a longer plate height produces SICF that can be lower than the membrane compon SICF. Therefore, the SICF for the modeled ed crack configuration is considered incorrect because the validity regime is violated (since.
ratio is in excess of 0.6).
4 5
Entergy Operations Inc.
Central Engineering Programs Appendix D; Attachment 5 Page 16 of 17 Engineering Report M-EP-2003-002-01 500 450 400 350 r-0V 0,
07
'C 04 UC 01 300 250 200 The SIF for the current model is always higher than the conventional model. Hence the estimated crack growth produced by the current model will be higher than that produced by the conventional model. Hence the current model is shown to be more conservative than the conventional model.
The SIF for the edge crack is very high owing to the large SICF produce by a large a/b ratio, which is beyond the validity limit for the determination of the SICF (discussed in the previous figure).
150 100 50 n
v 0 1
2 3
4 Operating Time {Years}
OD SIF - Entergy Model I.....ID SIF - Entergy Model SIF Conventional approach {Constant Stress Model}
.. I..SIF Conventional approach ( Increasing Stress Model)
Entergy Model - Average used for Flaw Growth Edge Crack
Entergy Operations Inc.
Central Engineering Programs Appendix D; Attachment 5 Page 17of 17 Engineering Report M-EP-2003-002-01 Axum Plot for the ID and OD Stress distribution along nozzle length used in the comparison H oop S tress P lot 60 -
40 -
e 20 -
Ir 0 -
-2 0 -
-40 Top or Blind Zone
- //
-~~~__
.ot 0 eld 0.0 0.5 1.0 1.5 2.0 D istance from Nozzle Bottom
{inch )
2.5 3.0 Axum plot showing the comparison for the SIF between the Current and Conventional Models.
200 C u rre nt M ode (En te rg y)
____Conventional model (Industry) 50 Z 1 00 5 0 0
0 1
2 3
4 Operating Time {years)
C2*
I ENCLOSURE 5 CNRO-2003-00033 LICENSEE-IDENTIFIED COMMITMENTS
LICENSEE-IDENTIFIED COMMITMENTS TYPE (Check one)
SCHEDULED ONE-TIME CONTINUING COMPLETION COMMITMENT ACTION COMPLIANCE DATE
- 1. The final results of the inspections will be X
60 days after included in the 60-day report submitted to startup from the the NRC in accordance with Section IV.E next refueling of the Order.
outage
- 2. If the NRC staff finds that the crack-growth X
Within 30 days after formula in MRP-55 is unacceptable, the NRC informs Entergy shall revise its analysis that Entergy of an NRC-justifies relaxation of the Order within 30 approved crack-days after the NRC informs Entergy of an growth formula.
NRC-approved crack-growth formula.
- 3. If Entergy's revised analysis (#2, above)
X Within 72 hours8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br /> shows that the crack growth acceptance from completing the criteria are exceeded prior to the end of revised analysis in Operating Cycle 17 (following the
- 2, above.
upcoming refueling outage), Entergy will, within 72 hours8.333333e-4 days <br />0.02 hours <br />1.190476e-4 weeks <br />2.7396e-5 months <br />, submit to the NRC written justification for continued operation.
- 4. If the revised analysis (#2, above) shows X
Within 30 days from that the crack growth acceptance criteria completing the are exceeded during the subsequent revised analysis in operating cycle, Entergy shall, within 30
- 2, above.
days, submit the revised analysis for NRC review.
- 5. If the revised analysis (#2, above) shows X
Within 30 days from that the crack growth acceptance criteria completing the are not exceeded during either Operating revised analysis in Cycle 17 or the subsequent operating
- 2, above.
cycle, Entergy shall, within 30 days, submit a letter to the NRC confirming that its analysis has been revised.
- 6. Any future crack-growth analyses X
N/A performed for Operating Cycle 17 and future cycles for RPV head penetrations will be based on an acceptable crack growth rate formula.
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