ML032690718
| ML032690718 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 08/26/2003 |
| From: | Entergy Nuclear South, Entergy Operations |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| CNRO-2003-00033 M-EP-2003-002, Rev. 1 | |
| Download: ML032690718 (68) | |
Text
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:=
l 0
1 l
-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 13 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 16 2.7830 35.4650 27.1090 16.3050 17 2.9930 39.9490 31.3960 12.4040 18 3.0820 39.5470 37.1560 1.4480 AxlLen := AllData IDAII:= AllData MidWall:= Allata DAIL := Al~ata (3)
Entergy Operations Inc.
Central Enginenng 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 (0)
ALen :=Data (1)
IDiim= Data MW'im := Data 2)
(3)
ODlim= Data Regression for the full data set RIDAII := regress(AxlLen, IDAII, 3)
RMWAII:= regress(AxlLen,MidWall,3)
RODAII:= regress(AxlLen,ODAII,3)
Regression for selected data set RIDdata:= regress(ALenIDlim,3)
RMWdata:= regress(ALen, MWlim, 3)
RODdata:= regress(ALen,ODijm,3)
Bottom:= 0 Top:= 3.2 WB:= 1.74 Dist:= Top - Bottom Dist Incr 20 D := WB - Bottom Incri =-
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 LenO:= 0 - IncrI i:= I.. 20 L. := L
+ Incr i*
i-I Len. := Len.-
+ IncrI Determination of Stresses at three locations across wall thickness, using the full data set Maili RIDAII + RDAII L + RIDAII (Li) + RIDAII (Li)'
3 4 i 5
IJ6 MWaII := RMWAII + RMWAII L + MA115 (Li)2 + RMWAII (Li)3 ODall RODAII + RODAII L + RODAI (Li)2+ RODAII (Li)
Determination of Stresses at three locations across wall thickness, using the selected data set IDdata := RIDdata + RIDdata Len. + RIDdata (Len)
+ RIDdata D
(Len.\\ 3 da 3 d 4 d 5 d 6 MWdata = RMWdata + RMWdata Len. + RMWdata5 (Len))
(R data
(
i) i 3
4 ODdata = RODdata3 + RODdaa'Len t + RoDdata5i.(Len if + ROdata6 ( Le )3
Entergy Operations Inc.
Central Enginefing 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 In-vu 00 50 0
Nodal stress data plotted for the ID and the OD distribution. This plot is based on the full data set.
-50 _0 0.5 1
1.5 2
Axial Length (inch) 2.5 3
3.5 ID Distribution Mid-Wall distribution M
'A c
0.0 To 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.
-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
L_
Entergy Operations Inc.
Central Enginering Programs Appendix D; Attachment I Page 5 of 7 Enginering Report M-EP-2003-002-01 8
100 50 0
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.
-50 0 0.5 1
1.5 2
2.5 Axial Elevation from Bottom (inch}
OD Regression Using All data OD All Nodal Data MidWall - Regression vs Nodal Data 3
3.5 50 40 30 20 cj 0.00 l0
/
I 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 Enginenng 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 0
-10
-20
-30 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.
t) e
-l0
-20 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 Enginering Programs Appendix D; Attachment 1 Page 7 of 7 Enginering Report M-EP-2003-002-01 OD - Selected Data Set 80 60 OD Stress Distribution (Selected Data Set):-
Comparison of regression fit versus the selected data set. The third-order polynomial provides an accurate fit.
'n 8
40 20 0
-40 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. Bnhmadesam 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 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 necessary to evaluate the stress distribution on the flow both for the initial flow and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represents the reference point elevation measured upward from the nozrle end.
Refpoint = 1544 To place the flow with respect 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 := I The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist = 2.75 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Bnhmadesam Veriied by:
S. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 2 of 8 Engineering Report M-EP-2003-00201 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 0*
2 L
co:= 2 id Rid t:= Ro Rid t
Rm:id+2 Timopr:= Years-365-24 Rm Rt :=-
Developed by.
J. S. Bdhmadesam Verified 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 'On = 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:=
0 L
1 2
3 4-5
-0 0
8 10 12 14 16 1
0.35 8
10 12 14 16 2
0.63 8
10 12 14 16 0.85 8
10 12 14 16 54 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 7 1.59 8
10 12 14 16
' 8 1.74 8
10 12 14 16 10 1.89 8
10 12 14 16 11 2.04 8
10 12 14 16 AXLen:= AlIData(O)
ID~i := AlIDatael)
ODAII := A13atP()
Developed by.
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 4 of 8 Engineering Report M-EP-2003-00201 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 Stress Distribution 20 Usg co 15 10 I
I I
I III I
I I
I II 5 0 0.5 I
1.5 2
2.5 3
3.5 Axial Elevation above Bottom [inch]
ID Distribution
OD Distribution Data :=
0 8
0.35 8
0.63 8
0.854 8 1.034 8 1.178 8 1.293 8 1.442 8 1.591 8 1.74 8
1.889 8 2.038 8 2.187 8 2.336 8 2.485 8 2.634 8 2.783 8 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 14 10 12 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. Brlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 5 of 8 Engineering Report M-EP-2003-00201 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(°)
MD := Data(3)
ID:= Data~l)
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(Axi, 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 =
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 InlcStrs.avg ULStrs.Dist - UTip 20 Developed by:
J. S. Bnhmadesam Venfled by:
. C. Gray
i -
Entergy Operations Inc.
Central Engineering Programs Apendix D; Attachment 2 Page 6 of 8 Engineering Report M-EP-2003-00201 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:= I..N +3 Incr; :=
c0 if i < 4 InCStrs.avg otherwise Loci := Loci-, + Incr; SID; := RID3 + RID 4*Loci + RID.(Loci)2 + RID6 (Loc;)
SQTi RQT3 + RQT Loci + RQT.(Loc1)2 + RQT (Loc;) 3 SMD;:= RMD + RMD 4Loci + RMD (Loci)'+ RMD (Loc;)3 STQ; = RTQ + RTQ *Loc; + RTQ.(Loci)2 + RTQ6(Loci) 3 SODi ROD + ROD4-Loci + ROD.(Loci)2 + ROD (Loc;)3 Developed by.-
J. S. Bnhmadesam VerMed by B. C. Gray
Entergy Operations Inc.
Central Engineering 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 + SDj+ + SIDj+2 3
Sid (j + I) + SDj+2 i-I j +2 if j =
Sqtj =
SQTj + SQTj+ + SQTj+2 3
Sq1 _(j + ) + SQTj+2 j+2 if j = I otherwise otherwise J
SMDj + SMDj+ + SMDj+2 3
Smd (j + ) + SMDj+2 0
j+2 if j =
Stqj =
STQj + STQj+l + STQj+2 ij
=
3 Stq.
'(j + ) + STQj+2 otherwise j+2 therwise Sod. =
J SODj + SODj+l + SODj+2 i
=
3 Sod
- (j + ) + SDj+2 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-2003-00201 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 5idj =
8 8
8 8
8 8
8 8
8 8
8 8
8 8
8 Quarter Thickness S
qtj 10 10 10 10 10 10 10 10 10 10 10 10 10 10 101 Mid-Wall Thickness Smd. =
J 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 Three -Quarter Wall Thickness Stq =
14 14 14 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 OD 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. Blihmadesam Verified by:
B. C. Gray
E7tergy Operations lic.
Central Engineering 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. Brihmadesom Verified by: B. C. Gray
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 Anput is to locate the Reference Line (eg. top of the Blind Zone).
The through-wall flow "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
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 nozzk bottom) below ULStrs Dist := 1-796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
I Edge Crack-Entergy-Comparison-OOO.mcd
Eateryy Operations I7c.
Central Engineering 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 Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)
Poissons ratio at 600 deg. F od R0 :
2 id 2
t:= Ro-Ri Rm:= Ri + -
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:= ULStrs.Dist bi := 2.886 b2 := 20 Bottom of J-weld Top of J-Weld Top of Nozzle b
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 I
Edge Crack-Entergy-Comparison-000.mcd
67tefyy Opetotibns Inc.
Central Engineernng Programs Appendix D; Attachment 3 Page 3 of 4 Engineering Report M-EP-2003-00201 Calculations:
a
=
N j := I..N - I a.:= a.
+ Inc J
i-I a.
J xJ.
b a.
J bj a.
X2
-ib2 Brown and Srawley Model For edge Crack in a Plate Fbsi- := 1.12 -
j.231-xi+
10.5-(xi)2_ 21.72-(x)3+ 30.39. (x )
Fbsl
= 1.12-0.231-x
+ 1055 (x ) 2-21.72 (xli)3+ 30.39
+
xi 4 Plate height as length below Fillet weld to tube bottom Plate height as length below Top of J-weld to tube bottom Fbs2
- 1. 12 - 0.23 1 2 + 10.55 (x2)
- 21.72(x2j)3 + 30.39(X2j)4 Plate height as Full length of Nozzle Through-wall Axial crack in a Thick Cylinder (Entergy Model)
K 1(
2)]0.25 2
Xj: [L'k2-
_Rv t
AeM:
1.009 + 0.3621-Xj + 0.0565-(A;)
- 0.0082 (Xj)3 + 0.0004. (Xj)4 - 8.326 10
- 6. (j) 5 AeB = 0.0029 + 0.0707 (j)'
- 0.0197 (j) 2 + 0.0034 (Xj)
- 0.00 0 3.(Xj) + 8.8052. 10 (Xj)
AbM: -0.0063 + 0.9194Aj - 0.168-(Xj) 2 - 0.0052.(Xj)3 + 0.0008-(j) 4 - 2.9701 10 (A;)
AbB = 0.9961 - 0.3806-Xj + 0.1239- (Xj)2 - 0.0211 (j) 3 + 0.0017.(j)4 - 4.9939. 10
-(Xj) 5 AM :=AeM J+ AbMj AB :=AeB. + AbB.
Edge Crack-Entergy-Comparison-OOO.mcd
Entergy Operotions Inc.
Central Engineering Programs Appendix D; Attachment 3 Page 4 of 4 Engineering Report M-EP-2003-002-01 c
0 urc E
a 0
C)5 a-o a
u)..
a a
a G
T a
a-o a-a a
I COl 03592 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
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 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: J. S. Brihmadesam Verified by: B. C. Gray
References:
- 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 Purpose :- This worksheet is used to compare the crack growth and SIF results between the conventional model (using a fixed Rit 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. Bnhmadesam Verified 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 (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 flow 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 nozzle end.
RefPo i nt =1544 To place the flow with respect to the reference point, the flow tips and center can be located as follows:
J) The Upper "c-tip" located at the reference point (Enter 1)
Z) 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 an := 0.0661 od := 4.05 id := 2.728 Plnt := 2.235 Initial Flaw Depth Tube OD Tube ID Design Operating Pressure (internal)
Years := 4 Number of Operating Years Ilim := 1500 T := 604 aOc := 2.67-10 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. Brlhmadesam Verified 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 od R := -
0*
2 id Rid :- 2 t:=
- Rid Rm := Rid+
Timopr := Years365-24 CFinhr := 1.417I105 Timopr Cblk urn h1im nim Prntblk :=50 L
2 Rm Rt :=
[
- Q (I
l
_lA e 1.103 10 3 T f+459.67l Tempratu)r e'
.01C Temperature Correction for Coefficient Alpha Co
=
CO:= C0 1 75 h 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 "n = Axial distance from minimum 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 W3n = Mid Thickness Stress data at each Elevation (ksi)
Column "4' = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5' = OD Stress data at each Elevation (ksi)
AllData :=
0 1
3 i
.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. Brihmadesam Verified by:
. C Gray
Entergy Operations Inc Central Engineering Progrns Appendix D; Attachment 4 Page 4 of 31 Engineering Report M-EP-2003-00201 AXLen:= AIIData(0)
IDAII := AData(i)
ODAII:= AllData(5)
Stress Distribution 100 IDAII k) v)
ODAII V2) 50 0
-50 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 DataAle that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the 'Data" statement below and delete it from the edit menu. Type "Data and the Mathcad 'equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0
-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 Data :=
1.428 33.623 27.792 24.8 24.321 26.989 1.627 32.364 28.469 27.591 34.284 45.104 1.786 27.394 28.918 31.388 43.882 63.718 1.919 21.498 25.556 33.55 48.089 66.365
\\2.051 16.944 23.793 34.064 49.472 67.672 )
Axl := Data(°)
MD:= Data(3)
()
ID: Data TQ := Data(4)
QT := Data(2)
OD:= Data(5)
Developed by:
J. S. Brhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs RID := regress(Axl,ID,3)
Appendix D; Attachment 4 Page 5 of 31 Engineering Report M-EP-2003-00201 RQT:= regress(Axl,QT,3)
ROD := regress(Axi,OD,3)
RMD := regress(AxI,MD,3)
RTQ := regress(Axl,TQ,3)
ULStrs.Dist := 1.786 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
FLCntr =
Refpoint -
if Val = I RefPoint if Val = 2 RefPoint + c0 otherwise Flaw center Location Location above Nozzle Bottom ULStrs.Dist - UTip U Tip:= FLCntr + CO lcStrs.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:=.. N+3 Incri :=
c0 if i < 4 InCStrs.avg otherwise Loci := Loci-1 + Incri Si RID + RID Loci + RID.(Loci) 2 + RID (Loci)3 Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Prograns Appendix D; Attachment 4 Page 6of3t Engineering Report M-EP-2003-002-01 SQT RQT + RQT4 Loci + RQT.(Loci) 2 + RQT (Loci)3 SMDi= RMD3 + RMD4 LoCi + RMD (Loci)2+ [RMD (Loci)3]
STQ; RTQ3 + RTQ4 LoCi + RTQ '(Loci) 2 + RTQ.(Loci) 3 SODi OD + ROD Loci + ROD (Loci)2 + ROD (Loci) 3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j:= I..N Sid. =
SIDj + SDj+ + SIDj+2 if j = I 3
Sid (j + ) + SIDj+2 J + 2 otherwise j+2 5qt.i SQTj + SQTj+1 + SQTj+2 3
Sqt
) (j + ) + SQTj+2 (i-I) j+2 if j = I otherwise Smd.
SMDj + SMDj+l + SMDj+2 f j =
3 Smd
- (j + I) + SMDj+2 otherwise j+2 5tqj =
STQj + STQj+ + STQj+2 if j =
3 StqI (j + I) + STQj+2 i-I otherwise j+2 Developed by:
J. S. Bnhmadesam Ven;-Ied by S. C Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 7 of 31 Engineering Report M-EP-2003-00201 Sod J
SODj + SODj+1 + SODj+2 if j =
3
- Sod,
- (j + I) + SODj+2 i-I otherwise j+2 Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution)
UO := 0.000 u := 0.25 U2 := 0.50 u3 := 0.75 U4 := 1.00 Y := stack(u0 u,u 2,u 3,u 4 )
SIG I := stack (Sod, 'Stq,, Smd' Sqt' Sid)
SIG3 := stack(Sod Stq3, Smd3 Sqt3, Sid 3 )
SIG5 := stack(Sod5 Stq5 Smd5 Sqt5 Sid5)
SIG7 := stack(Sod7, Stq7 'Smd7 Sqt7 Sid7)
SIG9 := stack (Sod9, Stq, Smd91 Sqt, Sid9)
SIG I I := stack(Sod, 'Stq Smd', Sqt 1 'Sid 11)
SIG2 = stack( Sod2 Stq2 Smd2 Sqt2 ' Sid2)
SIG4 := stack(Sod4 Stq 4 Smd4 Sqt4, Sid4)
SIG6 := stack (Sod6 Stq6 Smd6 Sqt6 ' Sid6 )
SIG8 := stack(Sod.,Stq8.SmdeSqt8 Sid8 )
SIG 0 := stack(Sod 0 Stq 10 'Smd10 ' Sqt10' Sid10 )
SIG 12 = stack(Sod12 Stq12' Smd12 ' qt 12' Sid12)
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 8 of 31 Engineering Report M-EP-200300201 SIG 13 = stack (Sod13' Stq13 S md13 Sqt 13 Sid13)
S1G 15 := stack(Sodi 5 Stq 5' Smd1 5 ' 'qt15' id15)
SIG 17 = stack(Sod17 ' Stq 17' Smd17' Sqt17' Sid17)
SIG I9 := stack (Sod 19 Stq 9 Smd 19> qt 19 ' Sid 19)
SIG1 4
= stack(Sod14' Stq14Smd14 sqt14 Sid14)
SIG1 6 = stack (Sod6'Stq6'Smd 6' qt16' id 16)
SIG 18 = stack(Sod 18 'S tq 18' Smd 8 ' qt18 ' id18)
SIG 2 0 := stack (Sod20 Stq20 ' Smd2 0 ' qt2 0 Sid2 0 )
Regression of Through-wall Stress distribution to obtain Stress Coefficients through-wall using a Third Order polynomial ODRGI regress(Y,SIG I,3)
ODRG2 := regress(Y,SIG 2,3)
ODRG3 regress(Y,SIG3,3)
ODRG5 regress(Y,SIG 5,3)
ODRG7 regress( Y.SIG7,3)
ODRG9 regress(Y,SIG 9,3)
ODRG I1 regress(Y, SIG 1, 3)
ODRG 13 regress( Y, SIG 1 3,3)
ODRG1 5 regress(Y,SIG 1 5,3)
ODRG1 7 regress(Y,SIG 17,3)
ODRG 9 : regress(Y,SIGj 9,3)
Developed by:
J. S. Bn7hmadesam ODRG4 := regress(Y,S1C4,3)
ODRG6 := regress(Y,SlG6,3)
ODRG 8 := regress(Y,SIGg,3)
ODRG 10 := regress(Y,SIG 10,3)
ODRG 12 := regress(Y,SIG 1 2,3)
ODRG1 4 := regress(Y,SIG1 4,3)
ODRG 16 := regress(Y,SIGj 6,3)
ODRG 18 := regress(Y,SIG 18,3)
ODRG2 0 := regress(YS1G2 0,3)
Verifed 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 ProPLength ULStrs.Dist - FLCntr - CO ProLength 0.044 Data Files for Flaw Shape Factors from NASA (NASA-TM-11 1707-SC04 Model)
{NO INPUT Required}
Mettu Raju Newman Sivakumar Forman Solution of ID Part through-wall Flaw in Cylinder Jsb :=
0 1
X 2
=0 1.000 0.200 0.000 1
1.000 0.200 0.200 2
1.000 0.200 0.500 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
.5 1.000 0.400 0.00 a
1.000 0.400 0.200 8
1.000 0.400 0.500 a
1.000 0.400 1.000 90 1.000 1.000 0.000
-11 1.000 1.000 0.200
_2 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 2000 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 23 2.000 0.400 0.800 Developed by:
J. S. Bnihmadesam Verified 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 24 2.000 0.400 1.000 25 2.000 1.000 0.000 26 2.000 1.000 0.200 27 2.000 1.000 0.500 28 2.000 1.000 0.800 29 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 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 51 10.000 0.400 0.200 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 83 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.0001 0.400 0.000 66 300.000 0.400 0.200 Developed by:
J. S. Bnhmadesam Venfed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 1 of 31 Engineering Report M-EP-2003-002-01 67 300.000 0.400 0.500 68 300.000 0.400 0.800 69 300.000 0.400 1.000 70 300.000 1.000 0.000 71 300.000 1.000 0.200 72 300.000 1.000 0.500 73 300.000 1.000 0.800 74 300.000 1.000 1.000 Sambi :=
_ 0
-1
_2 3-
- 4 5-7
-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
'-11 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 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 Developed by:
J. S. BrIhmadesam Verified by:
B. C Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 12 of 31 Engineering Report M-EP-2003-002-1 28 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 0.067 601 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 62 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. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 13 of 31 Engineering Report M-EP-2003-00241 W := Jsb(o)
X := Jsb( )
Y := Jsb(2) au := Sambi(o)
Sambi(l) aL =
aQ := Sambi(2)
- = Sambi(6) aC := Sambi(3) cc := Sambi(7)
CU := Sambi(4)
Sambi(5)
CL =
CQ 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(W,X,Y) faU(4,.4,.8) = 1.741 interP RaU Mau VaU, Ij Check Calculation Linear Term MaL := augment(W, X, Y)
VaL := aL RaL := regress( MaL VaL, n)
(W)-
faL(W, X, Y) := interp RaL, MaL, VaL X I Developed by:
J. S. Brihmadesam 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) = 0919 Check Calculation Quadratic Term MaQ := augment(W, X, Y)
VaQ:= aQ RaQ := regress( MaQVaQn)
(W)-
faQ(W, X, Y) := interp RaQ MaQ VaQ X Ij faQ(W~~~X jY) faQ(4,.4,.8) = 0.656 Cubic Term Check Calculation MaC := augment(W, X, Y)
VaC := aC RaC := regress(Mac, VaC, n)
~~~1W)-
faC(WXY) := interp RaC MaC VaC X I
- fyaW, faC(4,.4,.8) = 0.524 Check Calculation Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Centra I 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( Mcu, VCU, n) fcU(W,X,Y) := interp RCUMCUvCU'(X I fCU(4,.4,.8) = 1.371 Check Calculation Linear Term ML := augment(W, X, Y)
VcL := CL RcL := regress(McL, VcL, n) fcL(WX,Y) := interp RcLMcLVcL X I j
~)_
fcL(2,4,-8) = 0319 Developed by:
J. S. Brihmadesam Check Calculation Veified by:
- 8. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 16 of 31 Engineering Report M-EP-2003-00201 Quadratic Term McQ := augment(W,X,Y)
VCQ C
RcQ regreSs(MCQVCQ n) fcQ(WXY) := inter fCQ (4,.4.8) = 0.126 W)-
'McQ' VcQ X
C C )l Check Calculation Cubic Term MCC := augment(W, X, Y)
VCC := cc RcC := regress( McC, VcC, n) fcC(W, X, Y) := interp[RCCc McC VcC X Ij fcc(4,.4,.8) = 0.068 Check Calculation Developed by:
J. S. B7hmadesam Verified by
. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 17of31 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 CO E-CO NCBo0 - Cblk while j < 1im c0o-ODRG1 if j < Co ODRG2 if co < j < o + InCStrs.avg ODRG3 if c0 + InCStrs.avg < cj < Co + 2lnCStrs.avg ODRG4 if Co + 2 1CStrs.avg < Cj < co + 3flncStrs.avg ODRG5 if co + 3lncStrs.avg < Cj < CO + 4 IncStrs.avg ODRG63 if c0 + 4flncStrs.avg < Cj < co + 5flncStrs.avg ODRG7 if Co + 5 lnCStrs.avg < Cj < Co + 6f nCStrs.avg ODRG83 if co + 61fnCStrs.avg < Cj < Co + 7fInCStrs.avg ODRG9 if Co + 7 1lCStrs.avg < Cj < co + 8IfCStrs.avg ODRGI 1 0 if cO + 8flncstrs.avg < Cj < c0 + 9 InCStrs.avg ODRG I 13 iC 0 + 9 lncStrs.avg < Cj < co + 10flCStrs.avg ODRG1 2 if co+ I0 IncStrs.avg < cj < co + I IlnCStrs.avg ODRG1 33 if co+ II-ncStrsavg < cj < co+ 12flncStrs.avg Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs ODRG 14 ODRG 153 ODRG 16 ODRG 17 3 ODRG1 8 3 ODRG 19 ODRG2 0 3 ODRGI ODRG 2 4 ODRG3 4 ODRG 4 ODRG5 4 ODRG6 4 ODRG 7 4 ODRG 8 4 ODRG9 4 ODRGIO ODRGI1 4 ODRG12 4 ODRG13 4 0DRGI 4 4 ODRG 15 Appendix D; Attachment 4 Page 18 of 31 if o + 12 IncStrs.avg < j if co+ 13 IncStrs.avg < j if Co+ 14' IncStrs.avg < Cj if co + 15. 1ncStrs.avg <
if co + 16 Incstrs.avg <Kc if co+ 17 IncStrs.avg < C1 otherwise Engineering Report M-EP-2003-002-01
< co+ 13 Incstrs.avg
< o + 14 Incstrs.avg
< co + 15. 1ncstrs.avg
< co + 16 1 nCstrs.avg
< co + IT Incstrs.avg I < co + i8-IncStrs.avg if cj < Co if co < cj < co + IncStrs.avg if co + IncStrs avg < c < C+
2 lncStrs.avg if c + 2 ncStrsavg < cj < c + 3 ncStrs.avg if co + 3 Incstrs.avg <
< co + 4 IncStrs.avg if Co + 4 ncstrs.avg < cj < co +
IncStrs.avg if C0 + 5 Incstrs avg < cj < c0 + 6 IncStrs.avg if co + 6 1ncStrs*avg <
c < c0 + 7 ncStrs.avg if Co+ 7 IncStrs.avg < cj < C + 8 ncStrs.avg if c + 8 ncstrs avg < cj < c0 + 9 ncStrs.avg if co+ 9-Incstrsavg < cj co + 0. IncStrs.avg if c0 + 0- IncStrs avg < c < co +
IncStrs.avg if co +
Incstrs.avg < cj < co + 12 IlncStrs.avg if co + 12 IncStrs.avg < cj < co + 13. IncStrs.avg if co+ 13. lncStrs.avg < cj < co + 14. ncStrs.avg Developed by:
J. S. Brihmadesam Verified by:
. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 19 of 31 Engineering Report M-EP-2003-00201 Y2*-
ODRG 164 ODRG 17 4 ODRG18 4 ODRG1 9 ODRG 4
ODRG2 0 4 ODRG 1 ODRG 25 ODRG 35 ODRG 4 5 ODRG 5 5 ODRG6 5 ODRG7 5 ODRG8 5
ODRG 5 ODRG 14 5 ODRG1 2 5 ODRG13-5 ODRG 165 5
if Co+ 14lncStrs.avg < Cj < co + 151fnCStrs.avg if co+ I5-flCStrs.avg < Cj < co + 161fncStrs.avg if co+ 16]nestrs.avg < cj < co + 17lnCStrs.avg if co+ I7 ncStrs.avg < Cj < Co + 18f nCStrs.avg otherwise if Cj < Co if co < j < Co+ InCStrs.avg if co + Incstrs.avg < cj < C + 2 ncStrs.avg if co + 2nstrs.avg < c1 < Co + 3fncStrs.avg if CO + 3fnstrs.avg < c < o + 4 IncStrs.avg if co + 4ncstrs.avg < cj < co + 5 ncStrs.avg if co + 5Incstrs.avg < cj < Co + 6 IfnCStrs.avg if co + 6-1ncstrs.avg < cj < co + 71ncStrs.avg if co + 71ncstrs.avg < cj < co + 8-IncStrs.avg if co + 8.1nlstrs.avg < cj S co + 9-IncStrs.avg if co + 9. Incstrs.avg < cj < co + 10- IlnCStrs.avg if co+ I-IncStrs.avg < cj < co + IIIncStrs.avg if co+ II ncstrs.avg < cj < Co+ 12.lncStrs.avg if co + 12-IncStrs.avg < cj < co + 13-IncStrs.avg if Co + 13lncStrs.avg < i < co + 14Incstrs.avg if co+ 14-IncStrs.avg < Cj < co+ 15 IncStrs.avg Developed by:
J. S Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 20 of 31 UUKU 1 7 5 It Co+ 15 Incstrsavg < cj S co+ 16-fncStrs.avg 0DRG1 8 if c 0 + 16 InCStrs.avg < Cj S cO+ 17 1fncStrs.avg 5
ODRG 19 if cO+ 17 Incstrs avg <
j < co+ 18f nCstrs.avg 5
ODRG2 0 otherwise 5
ODRG1 if j < CO ODRG 2 if co < cj < co + ICStrs.avg 6
ODRG 3 if co + Ilncstrs.avg < cj < co + 2 lncstrs.avg ODRG4 if CO + 2 Incstrs.avg < cj < co + 3 flCStrs.avg 6
ODRG5 if co + 3 Incstrs.avg < cj < co + 4 InCStrs.avg 6
ODRG6 6 if co + 4 1CStrs.avg < Cj < co + 5 lncStrs.avg ODRG7 if co + 5 lncstrs.avg < cj < co + 6fncstrs.avg ODRG8 6 if cO + 6-IlCStrs. avg < cj < co + 7 1CStrs avg ODRG9 if c + 7 Ilncstrs.avg < cj < Co + 8 lnCStrs.avg ODRG 0 if co + 8 Incstrs.avg < cj < Co + 9 InlCStrs.avg ODRG1 16 if co + 9 Incstrs.avg < j < co + O lncstrs.avg ODRG 126 if cO+ 10 ICStrs.avg < cj < co+ I IlnCStrs.avg ODRG1 3 if co+
Il ncstrs.avg < cj < co+ 12 lnCStrs.avg ODRG146 if co+ 12-flCStrs.avg < cj C0+ 13 ncstrs.avg ODRG1 5 if co+ 13 lncstrs.avg < c1 < co+ 141fnCstrs.avg ODRG166 if cO+ 14*1fncstrs.avg < cj co+ 15 lCStrs.avg ODRG 176 if co+ 15 IncStrs.avg < cj < Co + 16IlnCStrs.avg ODRG18 6 if co+ 16-lnCStrs.avg < Cj < co + 17InCStrs.avg Engineering Report M-EP-2003-002-01 Developed by:r J. S Brihmadesam Verifled 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 ODRG 1 9 ODRG20 6
~O -
O if Co + I7 ncsttrs.avg < cj < C0 + 18 inCStrs.avg otherwise 2
0+
Cl-(
I iA+
)0.2 t
)
+ ~03-.25-aj' IF r
t
)
2' (
t
)
3 (
t )
43 <-- 0 Cy I (0.75 aj) 02( 0.75 aj 2 + 03- 0.75 a;j3 3~~~ aj~
~~~~2
+
.j)
~4 <- G + G I t
) + (2- (
t (3
(
t)
X0 -
0.0 xi -
0.25 x2<- 0.5 x3 <- 0.75 x4 <- X <- stack(xO,xl,x 2,x 3,x 4)
ST <- stack(tO, ; 1 2,t3, '4)
RG *- regress(X,ST,3) 000 <- RG 3 + Pnt 010& RG4 020 & RG 5 030 -
RG 6 aj ARj _-
cj aj Developed by.
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix D; Attachment 4 Engineerng Report Central Engineering Programs Page 22 of 31 M-EP-2003002-01 Gau
- u ( RtARj tj) j Gal aL(RtARj,ATj)
J G aq faL(Rt, ARj, ATj)
J G CU.
faC ( Rt,ARjATj)
GCU i<- fcU (RtsARjsATj)
Gcl
- fCL(RtARjATJ)
Gcqj fcQ (Rt, ARj, ATj)
GCC i<- fCC(RtARjATj)
Qj l I + 1.464 1.6 if cj > aj I + 1.464-i otherwise Ka 4-t i"
(00Gau
+ fiIOGa +
20Gaqj +
30'.Gac.)
)0.5 Kc 4 (
)
(,aooGcuj +-Oa 1
GC +
20GCqj + 30GCCj)
Kaj - Ka. 1.099 i
J K yj<-K C. -1.099 Ka 9.o if Ka < 9.0 Ka otherwise j
K 9.o if K
< 9.0 Ky, otherwise Da - Co (Kai -9.0)1.16 Developed by.
. S. Brihmadesam Verfned by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 23 of 31 Engineering Report M-EP-2003-002-01 Da Ij Da CFinhr-Cblk if Ka < 80.0 4
-CFinhr Cblk otherwise DCji O-C(Kyj _ 9.)
.1 DCgj <-l DC CFinhr-Cblk if K, < 80.0 4 10- '0 CFinhr-Cblk otherwise output(j, 0) <
j output(j, 1) aj output(j, 2) *- Cj - Co output(j, 3), Dag.
OUtPUt(j, 4 ) *- Dcg.
output(j, 5) - Ka.
J output(j, 6) - Kc.
J NCBJ OUtPUt(j, 7) 36524 OUtPUt(j, 8)
- Gau J
output(j, 9) - Gal j
output(j, 10) < Gaq output(j, 1) <- Gac OUtPUt(j, 12) - Gcu OUtPUt(j, 13) <- GCl J
OUtPUt(j, 14)
Gcqj output(j, 15) <- Gccj
<-j+I Developed by-e J. S. Bnihmadesam Ver tred by
. C Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 24 of 31 Engineering Report M-EP-2003-002-01 aj - aj-i +
ag cj & cj-l + Dcg aj -
t if aj > t aj otherwise NCBj - NCBj- + Cblk output Developed by:
J. S. Brihmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 25 of 31 Engineering Report M-EP-2003-00241 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}
CGRBam. Bam aO <- aO cO <- CO NCBo0 - CbIk while j <
rlim yo 0
- ODRG 01 (- ODRGI 02*- ODRG1 3 - ODRG 1 0
- I- 0 0+0<'I' 2 - 00+0<
0.25-aj) +
t
)
2s2 (
+
0.25 aj3 0Y2{
+ 04-t
)
0.5-aj)
)0.5-a;>
2 +
0 5-a; 3 t
+ 0 t
)
3"t (o.7s aj'A (075-aj2 (0.75.aj)3 3 <- F0+0 1 t
)+
2 t
) + 0 3 t
)
~4 <-- GO +
(
1.0.a)+
04 2
aj 0 3 i.o aj 3 44v'y0+61t )
t ) +ott
)
X0<-0.0 xi -
0.25 x2 0.5 x3 - 0.75 x4 <-- 1.0 Developed by:
J. S. Bihmadesam Venfied 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(x0,x1,x 2,x 3,x 4 )
ST <- stack(40, 4 3 44)
RG - regress(X, ST, 3) oo00- RG3 10- RG4 020*- RG5 30<-- RG6 ARj<- aj cj aj t
Gau -
faU(4,.3,ATj)
J Ga -
faL(4,3,ATj)
Gac - faC(4,.3,ATj)
I +.464{aj 165 I +1.464 165 if cj aj otherwise
)0.5 Kaj 9
(
Qj )
fOO Gauj +a I O Gal + 020 Gaqj + 030 Gacj)
K i-Ka..099 J
j K (X <--
i 9.0 if Ki<90 Ka otherwise Da *- co}Kc
_ 9.0) 1.16 I
Developed by:
J. S. Bhhmadesam Venfied by:
B. C Gray
Entergy Operations Inc Appendix D; Attachment 4 Engineering Report Central Engineering Progrants Page 27 of 31 M-EP-2003-002-01 Dag -
Da (i"' nhr-(blk it Ka < 80.0 4 10 CFinhr Cblk otherwise Dcg-Dag 3 output(j, 0) < j output(j, ) <- aj OUtpUt(j, 2) *- Cj - Co output(j, 3) <- Dag OUtpUt(j, 4)
Dcg.
output(j, 5) <v Kaj NCBj OUtpUt(j 7}
365 24 output(j, 8) <- Gau J
output(j, 9) <- Gal.
Output(jR 10) *F Gjq.
output~j, II) *F Gac jv i- + I aj <- aj-1 + Dag Cj <
Cj-I + Dcgj_
ajF It if aj > t aj otherwise NCBj <- NCBj- + CbIk output k
o.. Ium Developed by:
J. S Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 28 of 31 Engineering Report M-EP-2003-002-01 Flaw Growth in Depth Direction 0.6 U
C 0
am 0
0.4 0.2 The Current model, in the time period of interest provides a higher growth.
00 1
2 Operating Time {years}
Entergy-CEP Model I...Conventional Model 3
4 U
to)
-c c
I-5a:0 0.8 0.6 0.4 0.2 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.
00 1
2 3
Operating Time {years}
Entergy-CEP Model
.Conventional Model 4
Developed by.:
J. S. Blhmadesam Verlfed by S. C G'ry
Entergy Operations Inc Central Engineering Programs Appendix D; Attachment 4 Page 29 of 31 Engineering Report M-EP-2003-002-01 Stress Intensity Factors
-:0 v.)__
a, L
._0 Q
(C)
'A cn 80 -
60 40 20 X 0 -0 0.5 1
1.5 2
2.:
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Conventional Model Depth Point 5
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. Brihmadesam B. C Gray C-O-Z--
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 I (o0
-20
-40 1.0 1.5 2.0 Distance from N ozzle Bottom (inches)
Axum plot showing the comparison for Crack growth between Conventional and Current Model 0.5 En te r y M o de I Ind u stry M o d e I 0.4 0.2 0.1 0
1 2
3 4
0 perating Tim e (years}
Developed by:
J. S. B17hmadesam Verified by:
B. C. Gray 0921
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)
Conventional Model (Industry) 70 -
U) 0
° 50 -
C
.E4 30 10 Verified by.
B. C. Gray Cob
=
0 1
2 3
4 Operating Time {years}
Developed by.
J. S. Brihmadesam
Entergy Operations.Tc.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 1 of 17 M-EP-2003-00201 Comparison for Through-wall Cracks beveloped by Central Engineering Programs, Entergy Operations Inc beveloped by: J. S. 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 55-Rev. 1.
Through Wall The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Axial Flaw
Entergy Operations nc.
Central Engineering Programs Appendix D; Attachment 5 Page 2 of 17 Engineering Report M-EP-2003-00201 The first Input is to locate the Reference Line (eg. top of the Blind Zone).
The through-wall flow "'pper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.3 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the Upper Limit for the evaluation, which is the bottom of the filet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (meastred from nozzk bottom) below.
ULStrs.Dist:= 1.786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
I I
Entelyy Operations nc.
Central Engineering Programs Appendix D; Attachment 5 Page 3 of 17 Engineering Report M-EP-2003-00201 Input Data :-
L :=.794 OD:= 4.05 ID:= 2.728 Pl, := 2.235 Years:= 4 llim:= 1500 T:= 604 v := 0.307 aoc := 2.67 10 12
% := 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
[ -Qg (
I Ir
]
1 =
.103 10~ (T+459.67 Tref+459.67JJ Tiniopr:= Years 365-24 OD R,: =-
ID 2
t:= Ro - Rj Rm:= Ri + -
2 CFinhr:= I.417-105 Timopr Cblk :=-rip Ilim Ilim Prntblk:=
50 L
I 2
LI:= BZ I
I
Ehtty Operations Inc.
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 "" = 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)
DataAll.
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 0.87 17.66 16.42 14.61 12.41 9.38 E3 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 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 0 AIID := DataAlll AIIOD:= DataAIl5 100 75 50 25 0
-25
-50 0
0.5 1
1.5 2
2.5 Axial Distance above Bottom [inch]
ID Distribution
.~--OD distribution 3
Entergy Operations DI.
Central Engineering Programs Appendix D; Attachment 5 Page 5 of 17 Engineering Report M-EP-2003-00201 Observing the stress distribution select the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. 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 0.483 0.633
-1.486 0.87 17.665 16.422 1.18 29.798 26.049 1.428 33.623 27.792 1.627 32.364 28.469
-22.209 -20.407 -18.978)
-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 Data:=
t 1.786 27.394 28.918 31.388 43.882 63.718 )
(5)
OD:
Data (a)
Axli Data (1)
ID:
Data RID := regress(Axl, ID, 3)
FLCntr:= BZ - I ROD:= regress(Axl,OD,3)
Flaw Center above Nozzle Bottom ULStrs.Dist - BZ lcStrs.avg =
20 IJLStrs.Dist - BZ IncrEdg:=
20 RIDAI := regress(AIIAxI,AIIID,3)
RODAI := regress( AllAxi, AIIOD, 3)
No User Input required beyond this Point
- I
Entrly Operatrons Inc.
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 Number of locations for stress profiles N := 20 Loc 0:= FLCtr-L i:= I.. N + 3 Incr :=
I if i <4 InCStlrs.avg otherwise Loc. := Loc.
1 + Incr.
SID := RID + RID Loc. + RID (Loc)
+ RID.(Loc 3 I
3 4'
1 5
i)
A i)
Incredg if i <4 IncrEdg otherwise Locl; := 1° if i =
Loc I
+ Incredg otherwise SOD. := ROD + ROD4 Loci + ROD5 (LoCi) + RODA Loc.i)
SIDAUI =
IDAll + RIDAll Loci + RIDAII (Loci
+ RIDAII 1
(Locl J3 SOD II3 4:
I Al
- i.
6 SODAII.:
RODAII + RODAII Loci.,+ RODAI (Locli) 2 + RODAII (LoclY3 1
3 4
- 115, 6I I J
Enteryj Operations lic.
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 :=I.. N Sid. =
SID. + SIDj+I + SlDj+2 if j = I 3
So d-:=
SOD. + SOD.
+ SOD Sod
- (j + 1) + SODj+2 j
J otherwise Sid (j + 1) + SID.
j-j j+2 j +2 otherwise Sid.all. :=
J SIDAII + SDAII.
+ SIDAII if l
Ij+2 if
Sid.all.-l (j + I) + SDAIIj+2 otherwise j+2 Sod.all :=
SODAIL
+ SODAII
+ SODAII2 j
j+I j+2 if j=
Sod.aII (j + I) + SODAII j-I t J+2otherwise j + 2 Sod + Sid.
Om :=
j j +P i-2
~+ Pint Sod. - Sid.
Gsb.:=
j (lbj 2
Sod-all + id.all.
Gm.all. :=
2
+ Pnt i
~2 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
Enft37 Operations.Thc.
Central Engineenng Programs Appendix D; Attachment 5 Page 8 of 17 Engineering Report M-EP-2003-00201 Stress Distributions for use in Fracture Mechanics Analysis Membrane Stress Bending Stress OD Stress ID Stress Membrane stress (Edge Crack)
.. IO 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
-4.426
-4.184
-3.905
-3.594
-3.254
-2.885
-2.489
-2.066
-1.617
-1.142
-0.64 Sod 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 0
17.766 21.408 23.65 25.184 26.306 27.164 27.839 28.381 28.821 29.18 29.471 29.705 29.889 30.029 30.128 0Ym.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 PropLength :
ULStrs.Dist - (FLCntr + I)
Pr°PL,,_eth = 0486 i
i
Entwy' Operations nc.
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 TWCPWscc:=
i <- O 10<
NCB
<- Cblk while i rlim lam.appld 4-am if II< 0 a
if I0< I 10+ lCStrs.avg TM 3 if1 + lncStrs.avg < I <5 10 +
Ic lCStrs.avg M4 if 10 + 2Ilncstrsavg < I I 1 + 3 ncStrs.avg m 5 if10 + 3 ncSrs.avg < I < 0+ 4lncStrs.avg am6 if 1 +
IlncStrs.avg < I1 < I0 +5-lncStrs avg am7 if 10 + 5flncStrs.avg < I*
10 +
1 "cCStrs.avg am 6 if 10 + 4 IncStrs-avg < Ii < 10 + 7 fnCStrs.avg am 9 if 10 + 7fInCStrs.avg < I < 10+ 8 IfnCStrs.avg (m 8 if 10 + 8-ncStrs.avg < Ii < 10 + 9lnCStrs.avg Gm9I if 1 + 9 InCStrs.avg < Ii< I + 10InCStrs.avg Gm12 if I0+ 10lnCStrs.avg < I < I + I l inCStrs.avg am13 if I0 + I lncStrs.avg < Ii < I + 12 InCStrs.avg Tm 14 if 10+ I lnctrs.avg< I 1<l 0 + 13 lnCStrs.avg (m 15 if 10+/-3-IlncStrs.avg < 1* <I0+ 14 InCStrs.avg am 16 if I0+ 14-lncStrs.avg < Ii < 10 + 5-lnCStrs.avg am 17 if Io + 15 InCStrs.avg < Ii < 10 + 16 lncStrs.avg anm 18 if 10 + I6 IncStrs.avg < Ii *10 + 17 lncstrs.avg (m 19 if 10 + 17 Ifncstrs.avg < 1* 10 + 18 IncStrs.avg am'n otherwise
Entefy Operations Dic.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 10of17 M-EP-2003-002-01 b.appid b-yb if I 1__
Ob2 if 10 < I < l + InCStrs.avg ob3if 10 + ICStrs.avg < Ij < 10 + 2InCStrs.avg ob4 if 10 + 2 CStrs.avg < Ii S 10 + 3 lncStrs.avg Ob 5 if I0 + 3-lncstrs.avg<l <
I
+ 4ncStrs avg ab 6 if 10 + 4 -IncStrs.avg <
10 + 5-IncStrs.avg ab 7if 10 + 5-lncStrs avg < I < 0+ 6-IncStrs.avg b 8if Io + 6 IncStrs.avg < I S I0+ 7-ncStrs.avg Ob 9if 10 + 7-lncStr.avg < i < 10 + 8 Inc Sti.avg Oblo if I0 + 8 Incstrs.avg < I <
+ 9incStrs-avg Ob 1 if I0 + 9-ncStrs avg < I < 0+
10-InCStrs.avg oh,2 if 10 + 0°lnCstrs.avg < I < I0 + I IncStrs.avg Ob13 if 10+
I ncstrs.avg < 1I< 10 + 12-ncStrs.avg Ob14 if I0 + 12.lncStrs.avg < -
0 lO+f13IncStrs.avg Ob 15 if I + 13-lncstrs.avg < I < 10 + 14-Incstrs.avg Ob 16 if 10 + 14-Incstrs.avg < I < 10 + 15Incstrs.avg Ob 17 if 10 + 15 Incstrs.avg < I
- 0 + 16 Incstrs.avg Ob 1 if 10 + 16-lncstrs.avg < I < 10 +
l 4 fnCstrs.avg Ob 1 if 10 + 17IlncStrszavg < 1i < 10 + 18-incstrs.avg Obi otherwise 20 xi -
12.(1-v 2)] 025 1.
(Rm t) '.
Aem *- 1.0090 + 0.3621 X + 0.0565. (X) 2 - 0.0082-(Xi)3 + 0.0004-(x1)4 - 8.326 10 (i)
Abm c- -0.0063 + 0.0919-X - 0.0168 (x1 )2 - 0.0052. (X)3 + 0.0008. (x)
- 2.9701 10 (k)
Aeb e- 0.0029 + 0.0707-Xi - 0.0197 ()
2 + 0.0034. (X) - 0.0003.(x )4 + 8.8052-10 6(
)
Abb <- 0.9961 - 0.3806Xi + 0.1239 (X)2 - 0.021 1i(xL) 3 + 0.0017.(X) 4 - 4.9939 10- 5 (i)5
Enter§y Operations lr.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 11 of 17 M-EP-2003-002-01 Kpm G rmappld' (Rlt i)
Kpb Gb appld (XI i)
KmembrnODI F (Aem + Abm,) Kpm KmembrnlDI
- (Aerm - Abm,)-Kpm KbendOD I (Aeb + Abbj).Kpbj KbendIDI (Acb - Abbj)-Kpb, KAppOD K
KmembrnOD + KbendOD KAppID r
KmembrnID + KbendlD KWHI CF -m I
(li)
KAppoDi + KAppID.
Kpp1 2
0.5 KWH.lcnr.Strsj Grm.appld (E-i)
Ka-KApp-1.099 Ka 9.0 if Ka 9.0 Ka otherwise Dlen F Co-Ka -9.0)1.16 Dlengrth *-
Dien ICFinhr CbIk if Ka S 80.0 4-10 CFinhrCblk otherwise output (i
) - i NCB.
output(i )
365-24 output(i 2) i output(i,3)
I - I output(i, 4) i 0
output f-KI p
outPut(. 5)
- KApp.
output( i 6 ) - KAppOD.
output
- 7)
KAppiD _
Enteryy Operations Inc.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 12of17 M-EP-2003-002-01 output 9 v KmembmlD output(j 10) -
KbendOD output I
- KbendlD.
output (i, 12)
KWH output(i 13) & KWH.Icnr.Strs, i - i+ I IE<
i-I + Dlengrth 1-NCB. - NCB.i
+ CbIk output I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Entergy Operations Inc.
Central Engineering Programs Appendix D; Attachment 5 Page 13 of 17 Engineering Report M-EP-2003-002-01 Recursive Loop For Edge Crack Model TWCEDGPxVsCC =
i - o LI 0 <- LII NCB0
- Cblk
((while i < li, 11 I Gm.appld m.all (Gm.all, am.al13 Gm.all4
(;m.al]5 Gm.aII6
(;m.al[7 Om.all8 Gm.all, Gm.alll im.all (Fm.all2 Gm.all F m.all1 4 9m.all Gm.all Gm.all Gm.all Gm.all (m.all,)
b
- ULStrs.Dist I
I.
if L
< LI if LI <LI I < LI + IncrEdg if L
+ ncrEdg < L
< L I+2-lncrEdg if LI + 2ncrEdg < L
< L
+ 3ncrEdg if Ll
+ 3 1ncrEdg < LI S L
+ 41ncrEd if LI + 41ncrEdg < L
< L
+5-incrEdg if L
+ 5 ncrEdg < Ll < LI + 6-lncrEdg if LI + 61ncrEdg < L
< L
+7-lncrEdg if L
+ 7-lncrEdg < Ll < LlI + 8-lncrEdg if L
+ 81ncrEdg < L
< L0 + 9-IncrEdg if LI
+ 9-lncrEdg < L
< L
+ 1-incrEdg if LI + 10-lncrEdg < LI I < L
+ II
-IncrEdg if LI l+
I I-IncrEdg < L I < LI0+ 12-incrEdg if LI l+
12-ncrEdg<LI ILI
+ 13-lncrEdg if L
+ T ncrEdg < LI <LI + 14-lncrdg if Ll + 14incrEdg < Ll S LI0+ 15-incrEdg if LI + 15 IncrEdg < LII LI0+ 16-IncrEdg if L
+ 16 ncrEdg < LI <L
+ ITlIncrEdg if L1
+ IT IncrEcdg < Li < L
+ 18 ncrEdg otherwise
Eity3 Operations Inc.
Appendix D; Attachment 5 Engineering Report Central Engineering Programs Page 14 of 17 M-EP-2003-002-01 Z_ _
0.99 if 1.0 b
othe-wise Fab- < 1 0231 Z,)+ 10.55. (Z;)2 - 21.72.(z.)3 + 30.39-Z 4 Kedg.Crk <
l m.appd4 if (Om.appdj7) <0 lm.appld- (7t Lj )05 Fab-otherwise KA Kedg.Crk 1099 I
I Ka*
9.0 if KAI< 9-0 KA otherwise Dlen <- CO-(Ka - 9.0)1.16 Dlengrth.
l Dlen: CFinhr-Cblk if Ka < 80.0 101 4 10
-CFinhrCblk otherwise output 0)
- i NCB.
output(i 1) -
365-24 oUtput(i 2) -- L1i -L output(ij 3) -
Dlengrth output(j 4) E Kedg.Crk output(j 5) & Fa-b ii+
I Li L
l + Dlengrth 1_
NCB <- NCB il + Cbik output j:= I im
Entergy Operatons Inc.
Central Engineering Programs Appendix D; Attachment 5 Page 15 of 17 Engineering Report M-EP-2003-002-01 PropL ength = 0.486 Flaw Length vs. Time 1.5 a
TWCp-scc WCEDS.C 131 2
0.5 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* inAO.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 OJ In order to meet the "alb" 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 inchi 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).
0._
-0.5L0 1
2 3
4 5
TWCPWSCC j 1)
Operating Time years}
Entergy Model Edge Crack Model I
I
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 0
300 q
250 c
200 v)
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 0
1 2
3 4
Operating Time {Years}
OD SIF - Entergy Model ID SIF - Entergy Model SIF Conventional approach {Constant Stress Model}
SIF Conventional approach ( Increasing Stress Model)
Entergy Model - Average used for Flaw Growth Edge Crack T
=
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 Ho o p S tre s s P lot 60 40 D
2 0 g
0
-20
-40:
0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istance from N ozzle B ottorn
{inch)
Axum plot showing the comparison for the SIF between the Current and Conventional Models.
200 -
1 5 0 -
V0 C:
A 100 -
U cri 50 -
0 -
Current Model (Entergy)
I Conventional model (Industry) 0 2
Operating Time {years) 3 4
COG