ML032690652
| ML032690652 | |
| 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: ML032690652 (109) | |
Text
Engineering Report M-EP-2003-002-01 Appendix B Appendix B Explanation of Mathcad worksheet used in the deterministic Fracture Mechanics Analyses.
This Appendix has three (3) Attachments.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page of 23 ID Surface Flaws Entergy Operations In.
Centul Enginerinng Progran Apendix C; Attachment yV Page of 30 Engineering Report M-EP-2003-00201 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams Entergy Operations Inc.
Developed by: J. S Brihmadesam Verified by: B. C. Gray Refrences:
- 1) 'Stress Intensity factors for Part-through Surface cracks": NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8.8" Degree Nozzle, "0" Degree Azimuth, 1.54.V above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "R,,t" - between 1.0 and 300.0 Note : Used the Metric form of the equaton from EPRI MRP 55-Rev. I The correction is applied in the determination of the crack extension to obtain the value in nchr ID Surface Flaw General information containing the Component Identification for analysis. Note the information for Nozzle group, Location, and Elevation at which the analysis is being performed. This information is not critical to the analyses; it is general information but it is important for cataloging the analyses files.
Engineerng Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 2 of 23 The first RAwuvred input is a lction fr a point n the tube elevation to define the point of nterst (e.g.
The t of the Blind Zone, or bottom of filet weld etc.). This reference paint Is ncessar to evaluate the stress distribution e the flaw both for the itial flaw and for a grovtng flaw.
This is defined as the refawnce point Enter a numnber anh) that represnets the reference paint elevation measured upward from the nozzle end.
Refpoint = 1.544 To place the fw with repsect to the reference pint the flaw tips and center can be loated as follows:
- 1) The Upper T-tip" lcated at the rfrnce point (nter I)
- 2) The Center of the flaw at the referce point (Enter 2)
- 3) The lower 'C-tip" located at the fernce point (Enter 3).
Val:= I Te Input Below is the lpper Limit for the evaiatin, which s the bottom of the filkt wld leg.
This is shown on te Excel spread sheet as weld bottom. Enter this dimension (measured from nozre bottom) below.
ULSts.SDist := 2.05 Upper axial Extent for Stress Distribution to be used In the Analysis (Axial distance above nozzle bottom).
Three critical information are required in the three entries on page one.
- 1) the first entry required {RefpointJ is the "Reference Location"; this entry defines the reference line (e.g. the blind zone elevation) with respect to the nozzle bottom.
- 2) The second entry {Val} defines the location of the Crack. In the current analysis a value of two (2) is selected. This value locates the center of the flaw at the reference line described above.
- 3) The third required input is the upper limit, elevation above nozzle bottom, to be used for the stress distribution that will be used in the analyses. This location for the current analyses is chosen to be slightly above the bottom of the weld such that the appropriate stress profiles are incorporated into the analyses.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 3 of 23 Input Data L :=.35 Initial Flaw Length a=
0.035 Initial Flaw Depth od 4.05 Tube OD id 2728 Tube ID Pint := 2.235 Design Operating Pressure (internal)
Years := 4 Number of Operating Years im 1500 Iteration limit or Crack Growth loop T := 604 Estimate of Operating Temperature aOc := 2.67 -I 12 Constant in MRP PWSCC Model for 1-600 Wrought Q 617 deg. F Qg 31.0 Thermal activation Energy for Crack Growth (MRP)
Tref := 617 Reference Temperature for normalizing Data deg. F
- 1) General Input data for tube and flaw geometry. In addition other parameters required for the analyses are defined. These inputs remain unchanged for this set of analyses.
- 2) The input for internal pressure Plnt is used to add the internal pressure to the flaw face.
- 3) The operating time Years is set to four (4) such that proper analysis for one cycle of operation is obtained.
- 4) The iteration limit Lim is prescribed as a large number (1500) such that small time increments for crack growth are used in the crack growth analysis.
- 5) The remainder of the inputs are for crack growth model, which is based on MRP-55 at the seventy-fifth percentile.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 4 of 23 od id Rid:
2 t:= Ro-Rid Rm:= Rid+
Timopr := Years 365*24 CFinhr := 1417 105 Timopr Cblk =
urn Pnitblk I im L
Co:- -
Rm
[
Qg
(
I lR Co I':'a1103 o-Tcf+459.67J c
a0 Temperature Correction for Coefficient Alpha CO Co0 75 th percentile MRP-55 Revision 1 General calculations to develop the constants needed for the analyses.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment I Page 5 of 23 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
XII)at :=
0
-28.32
-18.3
-12.16
-6.2
-002 0e35
-18.79
-12 49
-661
-1.37 365 063
-17.84
-10 52
-4.41
-0.48 2 08 0 85
-20.52
-12,97
-59
-0.87
-1 54 103
-19.66
-11 83
-529 0.23 146 118
-17.2
-1059
-052 16.33 21.02 1 29
-8.02
-2.2 10.46 32.66 37 29 1 44 4.78 9.56 24.9 38.18 54.09 1 59 13.25 18.57 35.28 52.81 6652 1 74 16 22.02 39.19 62.95 75 1 89 15.86 23.14 40.23 64.33 74.87 2,04 12.63 23 76 41.26 58.67 66,78 AXLcn:= Ali)ata0) ll)ArIl:= ADatai)
Stress D~islribUdiol (l)All := Alil~ata (4)
Axial Ic atitri ah so c iottu iu liac ili ItID l)istlibution
- [) Distribution
- 1) the nodal stress data is imported from an Excel spread sheet provided by Dominion Engineering. The appropriate data set in the spread sheet is provided in the import command in Mathcad. It is important not to import the node number column.
- 2) The data imported is plotted for the ID and OD distribution along the length of the nozzle.
- 3) The plot presents all the nodal stress data imported. This plot is used to define the region of interest for analysis and to select the sub-set of stress distribution data pertinent to the analysis.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 6 of 23 Observing the stress distribution select the region In the table above labeled Datal that represents the region of Interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and dreg the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select Copy Selection "; this will copy the selected area on to the clipboard. Then click on the 'Matrix' below (to the right of the dtat statement) to highlight the entire matrix and delete It from the edit menu.
When the Mathcad input symbol appears, use the paste function In the tool bar to paste the selection.
0
-28.324
-18.299 -12.16 -6.201 021 (035
-18794
-12.495 -6.607 -1.366 3.655 Data:=
0.63 0.854 1.034 1.178 1.293 1.442 1.591 1.74 1.889 2.038
-17838
-20.517
-19.663
-17.203
-8.023 4.778 13.252 16.001 15.857 12.629
-10,518
-12.968
-11.831
-10.587
-2.205 9.557 18.569 22.017 23.14 23.76
-4.407
-5.902
-5.288
-0.515 10.461 24.903 35.278 39.194 40.235 41.263
-0.477
-0.874 0.227 16.326 32.658 38.177 52.808 62.945 64.335 58.673 2.08
-1.536 1.46 21.019 37.289 54.089 66-517 75.001 74.874 66.777 )
Axi := Data(0)
MD :=Data(3>
ID : Data(')
TQ := Data(4)
QT = Data(2)
OD := Data(5)
RID := regress(Axl.ID,3)
RQT:= regress(Ax1,QT,3)
ROD:= regress(Axi,OD,3)
RMD:= regress(AxIMD,3)
RTO := regress(AxITQ,3)
- 1) Shows the incorporation of the selected data into a Data matrix that will be used in the analysis.
- 2) The definiton of the axial distribution at the five locations through the wall thickness are defined.
- 3) A third-order polynomial regression is performed at each of the five through-wall locations to define the curve used to develop the through-wall distributions.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 7 of 23 FLCntr co if Val =
Flaw center Location above Nozzle Bottom Refoint if Val = 2 Refpon + cO otherw ise 1Tip FLCntr+ co lncStrs.avg =
tJLStrs.Dist - UTip 20
- 1) defines the upper tip of the flaw based on reference line and flaw location (Val) inputs provided in the first sheet.
- 2) Determination of segment length above the initial crack upper tip location.
Twenty (20) segments are used.
N :=20 Number of locations for stress profiles Loco := FLCntr-L i:=.. N+3 Incri :=
Co if i < 4 I1nCStrs.avg otherwise Loci := Loci-1 + Incri
- 1) Setting of the iterative loop to develop the through-wall stress distribution.
- 2) Initialization of the loop to define axial elevation and segment length required to obtain the through-wall stress profiles at defined locations.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment I Page 8 of 23 SID
= RID + RID Loci + RID (Loci)2+RID (Loci)3 SQTi RQT + RQT -LoCi + RQT (Loci )
+ RQT.(Loci)3 SMDi RMD + RMD Loci + RMD (Loci) + RMD (Loci) 3 3
4 6
STQi:
RTQ3 + RTQ 4-LoCi + RTQ (Loci)2 + RTQ.(Loci)3 SODi:= RoD + RD 4Loci + RoD. (Loci)I+ RoD6. (Loci)3 Determination of stresses at the five locations through the thickness and at defined elevations. This structure develops the matrix for the through-wall stress distributions for the defined locations that will be used in the moving average method for developing the stress profiles.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 9 of 23 j :=.. N llSIDj + SIDj+I + SIDL+ 2 Sidj =l Smd =
if j = I 3
Sid (j + I) + SDj+2 j+2 Sqt =
SQTj + SQTj+ + SQTj+
3 F2 othersise S t j+
) + SQTj+2 STQj + STQj+, + STQj+2 1
~~3 i j = I other ise it j = I otherwise SMDj + SMDj+j + SMDj+2 if j =
3
-ij Stq =
Smd (j + ) + SMDj+2 j+2 otherwise Stq (j + ) + STQj+2 j+2 C
sod- '=
Si SODj + SODj+1 + SODj+2 if j=I Sod (j + I) + SDj+2 j+2 otherm ise Loop structure to perform the calculations for stress profiles at the defined locations along the nozzle height.
- 1) All five locations through the thickness are similar.
- 2) The first conditional statement defines the average stress at the initial flaw location, which is the average of the stress at the lower tip, the flaw center, and the upper tip. These stresses are used to calculate the applied stress for the initial flaw.
- 3) The second conditional statement performs the moving average at each segment location. Thus the moving average accounts for the changing stress field as the crack progresses towards the bottom of the weld. In the current analyses the stress field increases in magnitude as the crack progresses towards the weld bottom.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page Oof23 U4 := 1 00 U0 (1 o.0 U I := 0.25 U2 := 0.50 U3 := 0.75 Y := stack(uo u I u2
, u3, u4)
SIGI :=stack(Sidl Sq1. Smd' Stq, Sod3)
SIG 3 = stack(Sid. Sqt35 Smd3 Stq3.Sod3)
SIGs :=stack(Sid-Sqt7'smd7' 5tq7 Sod7)
SIG7 =stack Sid4 Sqy7SSmd, Stq7 Sod)
SIG 9 stack(Sid, Sqy Smd Stq.Sod 9)
SIG I =stack Sidi.Sqt1 I'* Smd, l Stqj Is Sod 11)
SIG 13 = stack (Sid 1 3 Sqt13
- Smd, 'Stq, Sod 3)
SI(i,5 stack(Sid 5 Sq 1 5 Smd 1 5 Stq]'
Sod 1 5 )
SIG 17 := stack( Sid 7 ' Sqt17 Smd 17 'Stq 7 Sod17)
S(i 19 := stack(Sid 19 Sqt19.Smd, tq1 9 Sod 19)
SIG2 stack(Sid,, Sqt, I Smd, Stq, Sod2)
SIG4 stack( Sid4 Sqt4 Smd4' Stq4 Sod4)
SIG6 stack(Sid6 qt6 ' 5md6' Stq6' od6)
SIG8 stack(Sid8. Sqt8 Smd8 Stq Sod8)
SIG1 o stack( Sidio Sqt]O Smdo Stq10 'Sod10)
S1G1 2 stack(Sid12 'Sq 12 Smd 12 'Stq12,Sod 12)
SIG14 stack(Sid1 4 Sqt 14.Smd1 4 'Stq 14 Sod14)
S1G16 stack( Sid16 Sqt16 Smd16 Stq 6 Sod16)
SIG 18 stack(Sid18,Sql 8 Smd 8, Stq, Sod18)
SIG 2 0 stack(Sid2o' Sqt20 Smd2o0 Stq2 0 'Sod20)
Setting of a column matrix for the stresses at each segment for the five through-wall location.
l Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page I 1 of 23 IDRG2 := regress(Y*SIG.,.3)
IDRG I := regress( Y.SIGI,3)
IDR(i3 :=
IDRG5 :=
IDRG7 :=
IDRi 9 :=
IDRGI I IDRG1 3 IDRG 15
- regress(Y.SIG3, 3) regress(Y. SIG 5, 3)
IDR6 4 := regress(Y,S1G4.3)
= regress(Y.SIG 7.3)
= regress( Y, SIG 9, 3)
- = regress( Y, SIG I 1, 3)
= regress(Y, SIG 13, 3)
- = regress(YSIGj 5,3)
IDRG 6 := regress(YSIG 6.3)
IDRG 8 := regress(Y, SIG 8,3)
IDRG1 O := regress(Y.SIji0 3)
IDRG1 2 := regress(Y.SIG1 2,3)
IDRG14 := regress(YS[G14,3)
IDRG 16 := regress(Y,SG 16,3)
IDRG 18 := regress(YS1G1 8,3)
IDRG2 0 := regress(Y -SS(i 2 0 3)
IDRG17 := regress(YSIG17,3)
IDR(I 9 := regress(YSIG19,3)
Third-order polynomial regression to determine the coefficients that describe the stress distribution through the wall at the defined locations.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 12 of 23 SICF Coefficient Determination Jsb :=
0 1
2.
1.000 0.200 0.000 O
1.000 0.200 0200 2
1.000 0.200 0.500 13 1.000 0.200 0.800 4
1.000 0.200 1.000 3
1.000 0.400 0.000 1.000 0:400 0.200 8
~1.000 0.400 0.800 9
1.000 0.400 1.000 10 51.000 1.000 0.000 61 1.000 1.000 0.200 12 1.000 1.000 0.500 813 1.000 1.000 0.800 14 1.000 1.000 1.000 1
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 0.4001 0.500 Partial data table for the SICF determination.
- 1) Column 0 is the Rm/t ratio.
- 2) Column 1 is the a/c ratio (crack aspect ratio)
- 3) Column 2 is the a/t ratio (normalized crack depth)
This table in conjunction with the table in the following page together is used to determine the particular SICF
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 13 of 23 imbi:=
0 1
1 2
3 4
5 6
7 0
1.076 0.693 0.531 0.434 0.608 0.083 0023 0.009 1
1-056 0.647 0.495 0.408 0.815 0.085 0.027 0.013 2
1.395 0.787 0.557 0.446 0.871 0.171 0.069 0.038 3
2.53 1.174 0.772 0.58 1.554 0.363 0.155 0.085 4
3.846 1.615 0.995 0.716 2.277 0.544 0.233 0.127 5
1.051 0.689 0.536 0.444 0.74 0.112 0.035 0.015 6
1.011 0.848 0.504 0.421 0.745 0.119 0.041 0.02 7
1.149 0.894 0.529 0.435 0.916 0.181 0.073 0.04 8
1.6 0.889 0.842 0.51 1.334 0.307 0.132 0.073 9
2.087 1.093 0781 0.589 1.752 0.421 0.183 0.101 10 0.992 0.704 0.534 0.506 1.044 0.169 0.064 0.032 1I 0.987 0.701 0.554 0.491 1.08 0.182 0.067 0.034 12 1.01 0.709 0.577 0.493 1.118 0.2 0.078 0.041 1
1.07 0.73 0.623 0.523 1.132 0.218 0.095 0.051 14 1.128 0.75 0.675 0.558 1.131 0.229 0.11 0.06 1!
1.049 0.873 0.519 0.427 0.8 0.078 0.021 0.008 1
1.091 0.661 0.502 0.413 0.614 0.083 0.025 0.012 PartialI table of the influence coefficients (SICF) as describe
- 1) Column 0 is the uniform coefficient for the a-tip.
- 2) Column 1 is the linear coefficient for the a-tip.
- 3) Column 2 is the quadratic coefficient for the a-tip.
- 4) Column 3 is the cubic coefficient for the a-tip.
- 5) Column 4 is the uniform coefficient for the c-tip.
- 6) Column 5 is the linear coefficient for the c-tip.
- 7) Column 6 is the quadratic coefficient for the c-tip.
- 8) Column 7 is the cubic coefficient for the c-tip.
cd below:
Both tables, (labeled Jsb and sambi), have the same number of rows.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 14 of 23 W
Jsh<(")
X Jsb(I)
Y := Jsbh')
at :=Sambi(O) aL Sambi'l) aQ Sambi(2) aC Sambi(3) cj:
Sambi 4)
CL Sambi(5)
CQ Sambi(6) cc Sambi(7) n :=13 if Rt 4 O 2 othenvise
'a-Tip' Uniform Term r 1aIJ := augment(W7.X.Y)
Vatl au RaU regress(Mau jVau n)
Iau(W X. Y) := interp Ra)MaU VaU[ XI1 Y) tl (4. 4. 8) = 1.424 Check Calculaion Programming steps shown for determining the SICF.
1 ) First is the definition of the column matrix defined with respect to the tables above.
- 2) Second is the conditional statement that defines the polynomial order based on cylinder property (Rm/t ratio). For thick cylinder the polynomial order is cubic (3) whereas for thin cylinder it is quadratic (2).
- 3) Third the Mau statement assembles the matrix required for regression and interpolation for the uniform a-tip SICF.
- 4) Fourth the Rau statement performs the nonlinear regression on the assembled matrix to determine the regression coefficients needed for the interpolation routine. This is for the uniform a-tip term.
- 5) Fifth the fau statement defines the interpolation function. This is for the uniform a-tip term.
- 6) Sixth the fau(4,.4,.8) statement is the check calculation for Rm/t = 4, a/c =
0.4 and a/t = 0.8. The calculated value of 1.424 compares favorably with the text value of 1.443.
- 7) Similar structure is followed for all the other SICF entries.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 15 of 23 Recursive Loop for Calculation of PWSCC Crack Growth CGRsambi = j 0
ao - ao CO - CO NCBO - Cbik while j < Jim Start of the recursive loop showing the loop initialization.
- 1) Index "j" is set to zero (0).
- 2) Initial crack depth and half length are defined.
- 3) The Time for corrosion interval is initialized.
- 4) The internal loop for each corrosion time span is initiated.
IDRG1 IDRG9 3
-3 Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 16of23 i f Cj Co if co < cj < co+ InCStrs.avg IDRG 3 if co + 1ncStrs.avg < C9 < Co + 2-lncStrs.avg IDRG4 if co + 2' Inctrs.avg < cj IDRG5 if c + 3 IncStrsavg < j_
53
,tsag<c IDRG6 IDRG7 3 IDRG8 3
IDRG1 0 IDRGIO3 3
if CO + 4 lncstrs.avg < cj if co + 5 IfCstrs.avg < c <
if CO + 6lnCstrs.avg < cj if CO + 7-InCstrs.avg cjS CO + 3 IncStrs.avg CO + 4 InCStrsavg co + 5 ICiStrs.avg CO + 6 IncStrs.avg CO + 7-ICstrs.avg CO + 8-ICStrs-avg if cO+8[fncStrs.avg cj < co + 9'Ilncstrs.avg Partial statement showing assignment of the uniform stress coefficient. The assignment considers all twenty (20) segments. Similar assignment statements cover the other three stress coefficients (viz. linear -
,, quadratic- 02 and cubic 3). The assignment is based on the current flaw upper c-tip location. The conditional statement is based on current location "cj" as compared to the upper and lower limit for each segment.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 17 of 23 40- (To 41 70+
.1 t) 0.25 aj)
(0.25-aj)
+~~~~~
424- 0+
(5aaI'-
0)2.
4-Oo
( 0
+
7
+0
(-8
+ 3 (-
(s iaj' 2
+
(
3 t) 44 <- (YO+ a I
2 I.
)-aj+)3 44 v C° + ff l-tt
) + 2 t-)
+ Cy
-)
Using the stress coefficients for the through-wall stress distribution, this step determines the stress distribution across the crack face in the depth direction.
The crack depth is divided into five equal segments. The stress distribution across the crack face is calculated for each current crack location.
X0 0.0 X
- 0.25 x2-05 X3-0.75 X4 o
1.0 X - stack(xO,xl x 2,x 3 x4)
ST*- stack (4 l
t2 3
Developing the appropriate matrix and performing a third-order polynomial regression to determine the stress coefficients for the stress distribution across the crack face. These stress coefficients are used in the SIF dteremination.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 18 of 23 aoo RG 3 + Pint a 0 RG4 (20 RGs
( 130 K06 Assignment of the stress coefficients. The stress coefficient for the uniform term o0o contains the coefficient for the uniform stress (operating+residual) and the addition of the internal pressure (Pint). This is the step where the internal pressure is added to the calculation. This step ensures that the crack faces are pressurized.
aj ARj ATJ -
aj t
Gauj v faU(RtARj ATJ)
Gal faL(RtARjATi)
Gaq v faQ(RtARj ATJ)
Gac
- fac(RtAJ~iATj)
GCLI fCU(RtARjvATj)
GCj1 fcL(RtARjATj)
Gcq v fCQ(Rt ARj, ATj)
GCC
- fc(Rt ARJATj)
Step showing calculation of current crack aspect ratio (a/c), the current crack normalized depth (a/t) and the function call {Gxx; e.g.(
. ) for the eight SICF associated with the current crack dimensions.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment I Page 19of23 Qjv l + 1.464 (-
6 if c aj
+ 1.464{(J otherwise Determination of the crack shape factor depending on the current crack aspect ratio.
Kaj-v-J L.(LOO (auj + a IfOfGal.i + a2OGaqj + a30'Cac)
K
(
7 o
c
+
- (F00-iCUj 0.i
+a20Gcqj + 030cc.)
Kajv Ka'.099 K'j -K C-1.0"9 Determination of the SIF at the two crack tips (a-tip and c-tip) in English units and conversion to metric units.
Ka v 9.0 if Ka < 9.0 Ka otherwise Conditional statement to test for the threshold value for the SIF. This is needed for PWSCC crack growth analysis. Done for both the a-tip and c-tip. Only the a-tip is shown.
I iD Co.(Ka 9.0)1' 6 Calculation of the crack growth rate {da/dt) in metric units (m/sec). Shown for the a-tip but sthe same calculation is performed for the c-tip.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 20 of 23 D a <
Da CFinhr Cblk i Ka < 00 4 l-
'0 CFinhr CbIk otherwise Calculation for crack growth in one time block. This block for the current analysis is about twenty-four hours (24 hrs.). The crack growth is in English units (inch) because the conversion factor {CFinhr} is used. The first statement is set when the SIF is below the upper asymptote and the second statement is used when the SIF is greater than the upper asymptote. When the SIF is greater than the upper asymptote, the SIF independent crack growth is about 0.5 inch per year.
output(j,O) 4-j output(j 1 aj OutPUt(j,2) v--
Cj - Co OUtPUt(j 4<- Dag outpt~i3)
Dagj OUtPUt(j4)4-DCgj output( j 5) v-Kaj OUtPUt(j 5 ) <-- K C OUtPUt(j, ) -
KC NCB OUIPUt(j7) 4-365-24 Typical output statements within the recursive loop showing the storing of variables that are required for loop operation and those of interest in displaying the time dependent trend.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 21 of 23 iv+1 aj v aj-1 + Dagj_
Cj - Cji + Dcg aj -
t if aj t
a otherwise NCBj - NCBj-j + Cbk output The recursive loop is incremented and the required variables (crack depth, crack length, and the time variable are updated for the start of the next recursive loop operation. The last statement is a dummy statement to terminate the recursive loop.
PrOPL.ength = 0 506 Flaw Growth in Depth Direction I
I I
I I
I I
0.6 0.4 2
02 0
0.5 I
IS 2
2S 3
3.5 4
Operating Time J.carsj Typical Mathcad graphical display used to evaluate the important parameters.
The PropLength in the upper left corner is used to ascertain the growth to the weld.
This number is calculated internally before the recursive loop is started. This is the difference between the weld bottom location (ULtrs.Dst) and the Crack Upper Tip location (UTip).
CGRsambi (k. 8) 1 1
1 1
1 I
I 1
1 1
1 1
1 1
1 1
m Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 22 of 23 CGRsanbi
=
CGiRsambi (k,6)
(
0.163 0.111 0.163 0.111 0-163 0.111 0163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 Typical numerical output in tabular form used to ensure proper functioning of the model.
e s 10.
I
.0.6 0
1 2
Operoting Tima yeare)
Typical Axum graphics for use in the report.
3 4
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 23 of 23 End of the Mathcad worksheet Description
Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Programs Page 1 of 30 M-EP-2003-00201 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw beveloped by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmodesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM '8.8" Degree Nozzle, "0" Degree Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmt"- between 1.0 and 300.0 Note: Used the Metric fonn of the equation from EPRI MRP 55-Rev. 1.
OD Surface Flaw The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Note - The two differences between this model and the ID surface flaw model are:
- 1) Use of SICF tables from Referencel for External flaws (pages 9 - 12).
- 2) The stress distribution is from the OD to the ID (pages 6 - 8).
These diffetences are noted (in bold red print) at the appropriate locations.
The first ReqVired input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPoint = 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Ulpper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "-
tip" located at the reference point (Enter 3).
Val := I Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix B; Attachment 2 Page 2 of 30 Engineering Report M-EP-2003-00201 L := 0.3966 ao := 0.0661 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pint := 2.235 Years := 4 him := 1500 T := 604 aoC := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R. od 0*
2 id Rid 7=
t:= Ro - Rid Rm := Rid+
Timopr := Years-365-24 CFinhr := 1.417 105 Timopr Cblk -m Ihim Prntblk =
50 L
2 Rm Rt :=
-103 10 3 T+459.67 Tref+4 59.67 Co:= Co]
Stress InDut Data 010C Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bnhmadesam Verified by:
- 3. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 3 of 30 Engineering Report M-EP-2003-00201 Input all available Nodal stress data in the table below. The column designations are as follows:
Column "Om = Axial distance from minumum to maximum recorded on data sheet(inches)
Column 'I' = ID Stress data at each Elevation (ksi)
Column 2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column 4' = Three Quarter Thickness Stress data at each Elevation (ksi)
Column 5' = OD Stress data at each Elevation (ksi)
AllData :=
H -- 0~0 l
0 1
2-2 3
4 5
o 0
-27.4
-24.36
-22.21
-20.41
-18.98 1
0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4
1.43 33.62 27.79 24.8 24.32 26.99 5
=
- 1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 57 1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67 9
2.18 14.83 22.26 34.78 49.05 63.38 AXLen := AllData(° ID
= Al]Data(l)
All ODAII:= Alll)ata(5
Stress Distribution 100 IDAI ODAll 50 0
-50 _0 0.5 1
1.5 2
2.5 3
AXLen Axial Elevation above Bottom [inch]
Observina the stress distribution select the reaion in the table above labeled DatamA that reDresents the Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 4 of 30 Engineering Report M-EP-2003-00201 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 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 Data :=
1.919 21.498 25.556 33.55 48.089 66.365 k2.051 16.944 23.793 34.064 49.472 67.672 )
AxI := Data(0)
MD:= Data(3)
ID:= Dataei)
TQ := Data(4)
QT := Data(2)
OD := Datp)~
RID := regress(Axl,ID,3)
RQT:= regress(Axl,QT,3)
ROD := regress(Axl,OD,3)
RMD:= regress(Axl,MD, 3)
ULStrs.Dist = 1.786 Upper A) nozzle bc RTQ:= regress(Axl,TQ,3) dal Extent for Stress Distribution to be used in the Analysis (Axial distance above ottom)
FLCntr =
Refp0 int - c0 if Val =
Refpoint if Val = 2 RefPoint + c0 otherwise Flaw center Location Location above Nozzle Bottom UTip := FLCntr + CO IlcStrs.avg ULStrs.Dist - UTip 20 Developed by:
J. S. Bnihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 5 of 30 No User Input is required beyond this Point Engineering Report M-EP-2003-00201 Calculation to Develop Hoop Stress Profiles in the Axial Direction for Fracture Mechanics Analysis N :=20 Loco := FLCntr - L i:=I.. N + 3 Number of locations for stress profiles Incri :=
co if i < 4 lICstrs.avg otherwise Loci := Loci-j + Incri SIDi := RID3 + RID4. Loci + RID5 (Loci)
+ RID6 -(Loci)
SQT RQT + RQT4-LoCi + RQT.(Loc,)2 + RQT6.(Loc) 3 SMDi:= RMD + RMD 4Loci + RMD.(Loc;)2 +IRMD (Loc;)3]
STQi:
RTQ + RTQ -LoCi + RTQ.(Loci)2 + RTQ (LocI) 3 SOD; ROD + ROD 4 Loci + ROD.(Loc1)2 + ROD (Loci) 3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j:=..N I SIDi + SlDi+1 + SIDi+2 ISQTi+SQTi+I+SQTi+2 Developed by:
J. S Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 6 of 30 Engineering Report M-EP-2003-002-01 Sid. =
J 3
Sid
- (j +)
+ SIDj+2 j+2 it j = I sqt. -
j it
= I 3
Sqt (j + I) + SQTj+2 otherwise otherwise j+2 5md. = l
.1 SMDj + SMDj+j + SMDj+2 i
=
3 Smd (j + ) + SMDj+2 nth.riijce Stqj =
STQj + STQj+ + STQj+2 if j=
3 Stq
- (j + ) + STQj+2 otherwise j+2 Ut1x9t VtJW j+2 5od..1 SOD + SODj+ + SDj+2 3
Sod.
( + I) + SDj+2 i-I~~~~~-I if j = I otherwise I
j+2 Note the Change here to develop stress distribution form OD to ID Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution)
U0 := 0.000 u := 0.25 U2 := 0.50 U3 := 0.75 U4 = 1.00 Y := stack(u 0,uIu 2,u 3,u 4 )
SIGI := stack (Sod, Stq, smd 19 Sqt, s Sid 1)
SIG2
= stack(Sod 2 Stq2 Smd2 ' Sqt2 Sid2)
Developed by:
J. S. Bnihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 7 of 30 Engineering Report M-EP-2003-002-01 SIG3 = stack(S od3 SStq3 Smd3 Sqt3 Sid3 )
SIG5 = tack(Sod 5 Stq5, Smd 5Sqt 5Sid5)
SIG7 := stack( Sod; Stq7 Smd7 Sqt7, Sid7 )
SIG9 := stack( Sod9 Stq9' Smd 9 Sqt9' Sid9 )
SIG I := stack(Sodl, Stql, Smd s' Sqtii Sid 1)
SIG1 3
= stack(Sod 3 'Stq 3 ' Smd 13 ' sqt13Sid13 )
SIG15 := stack(Sod 15'Stq' 5 Smd1 5'5 qt15' Sid 5)
SIG 17 := stack(Sod17 'Stq17 ' Smd17 ' Sqt 17 ' Sid17)
SIG 19 := stack(Sod 19Stq 9 md19 qt19 ' Sid 9)
SIG4 := stack( Sod4 Stq4 Smd4 ' Sqt4' id4)
SIG 6 := stack( Sod69 Stq69 Smd 6 9 qt 6 ' Sid6 )
SIG 8 := stack( Sod8 Stq8 Smd8 Sqt8 ' Sid8 )
SIG 10 = stack(SodI0 Stql Smd0 Sqt0 'Sid o)
SIG 12 = stack (Sod 12' stq 12 ' Smd12 Sqt 12 ' Sid12)
SIG 14 = stack(Sod 14 ' stq14 'Smd 14 ' Sqtl ' Sid14)
SIG1 6
= stack(Sod 6'Stq 6'Smd16 Sqt16 Sid16)
SIG1 8
= stack(Sod1 8 ' Stq 18' Smd18 'Sqt18 ' Sid18)
SIG 2 0 := stack(Sod2 0 'Stq2 0 ' S
' Sqt20' Sid2 0)
Regression of Throughwall Stress distribution to obtain Stress Coefficients throughwall using a Third Order polynomial ODRG1 := regress( YSIG,3)
ODRG2 := regress(Y,SIG 2,3)
Developed by:
J. S. Bihmadesam Vefied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs UUK(j 3 regress( Y, S1 3, 3)
ODRG5 regress( Y, SIG5, 3)
ODRG7 regress(Y,SIG7,3)
ODRG9 regress(Y,SIG9,3)
ODRG II regress( Y, SIG 1, 3)
ODRG 13 regress( Y, SIG 13,3)
ODRG1 5 regress(Y,SIG 1 5,3)
ODRG1 7 regress(Y, SIG 17 3)
ODRG 1 9 regress( Y, SIG 9, 3)
Appendix B; Attachment 2 Engineering Report Page 8 of 30 M-EP-200300201 UIJKUj4 regress Y, SlU4,3)
ODRG6 regress(Y,SIG 6,3)
ODRG8 regress(Y,SIG 8,3)
ODRGo: regress(YSIG 1 0,3)
ODRG 12 regress( YSIG12,3)
ODRG1 4 regress(YSIG14,3)
ODRG 16 regress( Y.SIG 16,3)
ODRG 18 regress( YSIG18,3)
ODRG2 0 regress(YSIG2 0,3)
Stress Distribution in the tube. Stress influence coefficients obtained from thrid order polynomial curve fit to the throughwall stress distribution ProPLength = ULStrs.Dist - FLCntr Co ProPLength 0.242 Data Files for Flaw Shape Factors from NASA (NASA-TM-1I 1707-SCO4 Model)
(NO INPUT Required)
Developed by.
J. S. Bnhmadesam Verifled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 9 of 30 Engineering Report M-EP-2003-002-01 Data Tables for External falws from Reference I Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=
0 1
2 0
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 8
1.000 0.400 0.800 9
1.000 0.400 1.000 10 1.000 1.000 0.000
,11 1.000 1.000 0.200 12 1.000 1.000 0500 3
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 0
2.000 0.400 0.000 1
2.000 0.400 0.200 2
2.000 0.400 0.500 23 2.000 0.400 0.800 24 2.000 0.400 1.000 25_
2.000 1.000 0.000 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 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
l Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page to of 30 Engineering Report M-EP-2003-002-01 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 41 4.000 1.000 0.500 431 4.000 1.000 0.800 41 4.000 1.000 1.000 4
10.000 0.200 0.000 41 10.000 0.200 0.200 46 10.000 0.200 0.500 4
10.000 0.200 0.800 49 10.000 0.200 1.000 5
10.000 0.400 0.000 51 10.000 0.400 0.200 5
10.000 0.400 0.500 53 10.000 0.400 0.800 5
10.000 0.400 1.000 5
10.000 1.000 0.000 5
10.000 1.000 0.200 10.000 1.000 0.500 58 10.000 1.000 0.800 56 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 63 300.000 0.200 0.800 64 300.000 0.200 1.000 6
300.000 0.400 0.000 6
300.000 0.400 0.200 64 300.000 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 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix B; Attachment 2 Page *1 of 30 Engineering Report M-EP-2003-002-01 Sambi :=
0 1
2
-3 4
r 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 0
1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 1i 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 9
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 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 4
2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 5
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 7
1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 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 1
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 4_
096 0711 0.589 0 513 1.127 0.189 0
0-068 0-034 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 12 of 30 Engineering Report M-EP-2003-002-01 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 5f, 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 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 W := Jsb(°)
X := Jsb( )
Y :
Jsb(2) aU := Sambi(O)
CU := Sambi(4) aL := Sambi'l)
CL := Sambi aQ := Sambi(2)
CQ = Sambi(6) ac := Sambi(3)
CC := Sambi(7)
Developed by.
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 13 of 30 Engineering Report M-EP-2003-002-01 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) := interp{RaU MaU, VaU{XII 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 RaLMaL VaL X I Yj _
faL(4,.4,.8) = 0.919 Check Calculation Quadratic Term Developed by:
J. S. Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 14 of 30 Engineering Report M-EP-2003-00201 MaQ := augment(W, X, Y)
VaQ := aQ RaQ := regress(MaQVaQgn) faQ(W, X, Y) := inte faQ(4,.4,.8) = 0.656 W)-
,MaQVaQ X
Check Calculation Cubic Term MaC := augment(W, X, Y)
VaC := aC RaC := regress( MaC, VaC, n)
(W)-
faC (WXY) := interp RaC Mac Vac X I
_a(
W
,)
faC(4,.4,.8) = 0.524 Developed by:
J. S. Bhimadesam Check Calculation Verifled by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 15 of 30 Engineering Report M-EP-2003-002-01 "L
Tip coetticients Uniform Term Mcu := augment(W, X, Y)
VCU := U RCu := regress( MCu, VCU n) fcu(W,X,Y) := interP[RcUMcU, VcU X I fcu(4,.4,.8) = 1.371 Check Calculation Linear Term MCL := augment(W, X, Y)
VcL := CL RCL := regress(McL, VcL, n) fcL(W, X, Y) := interP RcL, McL, VcL, X I fcL(2,.4,.8) = 0.319 Developed by:
J. S. Bnhmadesam Check Calculation Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 16 of 30 Engineering Report M-EP-2003-002-01 Quadratic Term McQ := augment(W, X, Y)
VcQ Q
RcQ := regress( McQ, VcQ, n) fCQ(WXY) := inter fcQ(4 4.8) = 0.126 W)-
McQ, VcQ X I
)c Check Calculation Cubic Term Mcc := augment(W,X,Y)
VCC := c Rcc := regress( MCC, VcC, n) fCC (W, X, Y) := interprRcc, McC, VcC, X I fcc(4,.4,.8) = 0.068 Check Calculation CI-.-.
Developed by:
J. S. Bflhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Engineering Report Page 17of 30 M-EP-2003-002-01
- c-GUauons ecurmve ralcuauons Lo estimate riaw growin.
Recursive Loop for Calculation of PWSCC Crack Growth Entergy Model CGRsambi =
j*-o ao Fao NCBo( Cblk while j <
rlim yo --
ODRG3 if cj < CO ODRG2 if co < j < co + InCStrs.avg ODRG3 if co + ICStrs.avg < cj < C + 2-InCStrs.avg ODRG4 if co + 2 Incstrs.avg < cj < co + 3 IncStrs.avg ODRG5 3 if co + 3 Incstrs.avg < cj < Co + 4-IncStrs.avg ODRG6 3 if CO + 4 InCStrs.avg < cj < C0 + 5 InCStrs avg ODRG7 if co + 5 lnCStrs.avg < Cj < co + 6-lfCStrs.avg ODRG8 3 if C0 + 6 lnCStrs.avg < cj S C0 + 7 lncStrs.avg ODRG9 if CO + 7 lncStrs.avg < Cj < C0 + 8 lnCStrs.avg ODRGI 0 if co + 8 Incstrs.avg < j co + 9 InCStrs.avg ODRGI 13 if co + 9Ifncstrs.avg < cj < co + Il lncStrs.avg ODRG1 2 if co + IflncStrs.avg < Cj < co + IlneStrs.avg ODRG13 if co+ I IncStrsavg < j < Co + 12 lnCStrs.avg ODRG1 43 if Co + 12-nCStrS.avg < j < o + 13 Inestrs.avg Developed by:
J. S. Blnhmadesam Verified by:
- 8. C Gray
l-J Entergy Operations Inc Central Engineering Prograns JUNLJJ 1 5 ODRG1 6 ODRG1 7 3 ODRG18 ODRG 19 ODRG2 0 ODRG14 ODRG2 4 ODRG 3 4 ODRG44 ODRG 5 4 ODRG6 4 ODRG 7 4 ODRG8 4 ODRG9 4 ODRG1 2 ODRG 1 ODRG12 4 ODRG13 4
ODRG14 4
ODRG 15 4
Appendix B; Attachment 2 Page 8 of 30 1 c t J
'cStrs.avg ' 'i - c t 1' "'Strs.avg if c 0 + 14-IncStrs.avg < cj < co+ I5 lnCStrs.avg if c + 15]fncStrs.avg < cj < co + 16IlnCStrs.avg if c + 16flncStrs.avg < Cj < C0 + 17Incstrs.avg if co+ 17-lncStrs.avg < cj < co+ 18flnCStrs.avg otherwise if cj < Co if co < cj < co + InCStrs.avg if co + ncStrs avg < cj < co + 2-IncStrs.avg if co + 2-1ncStrsavg < cj < co + 3 1ncStrs.avg if c + 3-ncStrs* avg < c S co+ 4-IncStrs.avg if co + 4Ilncstrs.avg < cj < co + 5 ncStrs.avg if c0 + 5 Incstrs.avg < cj S c0 + 6-InCStrs.avg if co + 6 1ncstrs.avg < cj < c0 + 7 IlncStrs.avg if c0 + 7 Incstrs.avg < cj < co + 8-IfnCStrs.avg if co + 8-1ncstrsavg < Cj < co + 9 lncStrs.avg if c0 + 9 ncstrsavg < ci < c0 + I0 lnCStrs.avg if co + lo Incstrsavg < cj < Co + II f nCStrs.avg if co + Il-ncstrs avg < cj < co + 12.lncStrs.avg if co + 12 lncStrs.avg < cj < co + 13 ncstrs.avg if co + 13-lncStrs.avg < cj < co + 14 lncStrs.avg if c0 + 14-IncStrs.avg < cj < co + if lnCStrs.avg Engineering Report M-EP-2003-00201 Developed by:
J S. Brihmadesam Verifled by:
B. C. Gray
Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Programs Page 19 of 30 M-EP-2003-002-01 ODRG 1 7 if CO+
5-lncStrs.avg < cj < Co + 6IncStrs.avg ODRG1 8 4 if CO+ 16 IlncStrs.avg < j < Co + 7llnCStrs.avg 0DRG1 9 4 if Co + 17-Incstrs.avg < j < Co + 18-Incstrs avg ODRG2 0 otherwise 4
02 -
ODRG1 if Cj < cO ODRG2 if Co < Cj < CO + InCStrs.avg ODRG 3 if co+ InCStrs.avg < Cj < C0 + 2 InCStrs.avg ODRG4 if Co + 2lncstrs.avg < j < Co + 3-InCstrs.avg ODRG5 if Co + 3-Incstrs.avg < Cj < Co + 4-nCstrs.avg ODRG6 5 if co+ 4InCStrsavg < j < co + lncStrs.avg ODRG7 if CO + 5IncStrs.avg < Cj < Co + 6Incstrs.avg ODRG 85 if CO + 6-lncstrs.avg < j < Co + 7-lncstrs.avg ODRG9 if CO + 7InCstrs.avg < Cj < CO + 81lnfstrs.avg ODRGIO5 if cO + SIncstrs.avg < Cj < o + 9.lnCstrs.avg ODRG 115 if co+ 9lncstrs.avg < cj < C0 + 10lncstrs.avg ODRG1 25 if co+ 10IncStrs.avg < cj < co + I[ IncStrs.avg ODRG1 3 5 if CO + 1 -lncStrs.avg < Cj < cO+ 12 IfncStrs avg ODRG1 4 if co+ 12lncStrs.avg < Cj < co+ 13flCStrs.avg ODRG1 5 5 if co+ 13.lncStrs.avg < Cj < co + 4.lncStrs.avg
°DRG1 6 5 if co+ 14lncStrs.avg < cj < co+ 1l5fnCStrs.avg ODRG1 7 if co + 15-Incstrs.avg < cj <
+ 16lnCStrs.avg ODRG, o if Cn + 16 Incc.--
< C; < Cn + 7 lCc--
Developed by:
Verifed by:
J. S. Bnhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs ODRGI 6
ODRG 2 6
ODRG46 ODRG5 6
ODRG6 6
ODRG 6 ODRG7o 6
ODRG8 ODRG 16 ODRG19 6 ODRG106 ODRG1 2 6 ODRG1 3 6 ODRG14 ODRG 1 6 ODRG16 ODRG17 6
ODRG19 6 Appendix B; Attachment 2 Page 20 of 30 JIIS.UVg J
LIs.Vg if co + 17 lncStrs.avg < j S co + 18flnCStrs.avg otherwise if Cj CO if co < cj S co + ICStrs.avg if co + IncStrs avg < c co + 2 IncStrs.avg if co + 2 ncStrsavg < cj S co+ I IncStrs.avg if co + 3 nc Strs avg < c Sc + 4 IncStrs.avg if co + 4 Incstrs avg < cj S co+ 5 IncStrs.avg if co + 5 Incstrs.avg < cj S co + 6 IflCStrs.avg if co + 6 Incstrs.avg < cj < co + 7 InCStrs.avg if co + 7IncStrs.avg < cj s c0 +
InCStrs.avg if co + 8-1ncStrsavg < cj < co + 9-1nCStrs.avg if co + 9 IncStrsavg < cj S co + lo flCStrs.avg if co + 0C IncStrsavg < cj S co + Il nCStrs.avg if co + 11-ncstrsavg < cj S co + 12 I-CStrs.avg if co + 12 lncStrs.avg < cj S co+ 13 InCStrs.avg if co+ 13 IncStrs.avg < Cj S co+ 14 InCStrs.avg if co + 14 lncStrs.avg < Cj < co + 15 ICStrs.avg if co + 15IncStrs.avg < cj < CO + i65lnCStrs.avg if co + 16 lncStrs avg < cj co + 17 Incstrs avg if co + 17IncStrs.avg < cj S co + 1-IfncStrs.avg Engineering Report M-EP-2003-00241 Developedby:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 21 of 30 Engineering Report M-EP-20034002-01 lODRG20 otherwise 40 (- GO (o.2s 0j)
(o.25 aj82 0.25-aj) 3 41 <--Go+ 13 I
)+
2-t t
)
3 t)
(0.25.
aj'~
___2
_____j) 42 o+
(yI -t
) +
(-t J
3 (+
t
)
(_____aj)
_____-a)2 0.75.aj)3
~ O~+Of (0.7s~a)~
(0I..
aj' 2
(..aj 3 44 Go + ( It
) + F2-t
)
+ '. 3 yt X <- 0.0 x E- 0.25 x2-0.5 x3 -
0.75 X - stack(xO, x Ix 2, x3, x4 )
ST <- stack(4O0 41 42,4344)
RG3 + Pnt y10 RG4 0204 RG5 630 - RG6 aj t
Gau
- faU(RtARjATj)
Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Programs Page 22 of 30 M-EP-2003-002-01 GalI4v faL(RtARj,ATj)
J Gaq faQ(Rt ARj, ATj)
Gac - faC(RtARjATj)
GCU.-
fCU(RtARATj)
GO d
fcL(RtARiATi)
Gcqj <- fcQ (Rt, ARj, ATJ)
GCC fC(Rt, ARj, ATj) j~~~~a Q~*- ll+ 1.464-I-8 if Cj 2Ža 0j) lI + 1.464-i -9 otherwise Ka (o~O, Gauj + a I OGaij + 020'Gaqj + 030Gacj)
Kc C.
(00
-(oo GCuj + 0I 0 Gc
+ 020 Gcqj + 030 Gccj)
Ka*
Kaj-1.099 i
i Kyj -
K
-Ls099 Ka 9.o if Ka < 9.0 Ka otherwise K
9.o if K
< 9.0 K
otherwise DaE F CO (Kaj 90)1 a
K Daj,-IDCFrCb if Kaj < 80.0 Developed by:
J. S. Bihmadesam Verified by.
S. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 23 of 30
- 4. 10- l0-CF inhr-Cblk otherwise D c; C0 (Kyj _.)
1 Dcgj
- DC. CFinhr-Cblk if K, < 80.0 4 10- l'-CFinhr-Cblk otherwise output(j,O) i output(j, )
- aj Output(j, 2 ) *- Cj -
Co OutPut(j, 3) E Dagj OUtpUt(j, 4) < Dcgj output(j, 5)
Ka.
J output(j, 6) - Kc NCBj OUtPUt(j. 7)
- 365 24 output(j, )
au output(j, 9 ) & Gal output(j, 10) E-Gaqj output(j, I 1) - Gac OUtpUt(j, 12) - GCj OutpUt(j, 13) v ~
output(j 14) + Gcq OUtPUt(j
- 15) -
GCC aj
- a
+ DagI c;< c: +
n-Engineering Report M-EP-2003-002-01 Developed by:
J. S. Bfihmadesam Verifed by:
. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 24 of 30 Engineering Report M-EP-2003-00201
-J.
is_.
g Iaj v-t if aj t
aj otherwise NCBj - NCBj-j + Cblk output k :=.. him Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 25 of 30 Engineering Report M-EP-2003-002-01 ProPLength = 0242 Flaw Growth in Depth Direction 0.6 uC U
D.
aS 0.4 I
I I
I I
I I
I I
I I
I I
I 0.2 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model 4
U C
3
('S 0.8I 0.61 I
~~~I I
I I
I I
2.03 36 42 I
I I
I I
i I L
<~~~~~~~
l 0.4 1 0.2 0 0 0.5 I
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model Developed by J. S. Bffhmadesam Venirled by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 26 of 30 Engineering Report M-EP-2003-002-01 ac 0
U.
Cu
'A 0a 80 60 Stress Intensity Factors I
I I
IIII
...., I 40 20 A
- 0 0.5 1
1.5 2
2.
Operating Time {years}
Depth Point Entergy-CEP Model
-..Surface Point Entergy-CEP model 5
3 3.5 4
Developed by:
J. S Bnihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Affachment 2 Page 27 of 30 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.2 I
v)
OD C'
0.8 0
E 0.6 a)E 0
0 i
0.4 C
0.2 0 0 0.5 1
1.5 2
2.5 3
3.5 4
Operating time {years}
"a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. 5. Brihmadesam VefedC by B. C. Gay COA~
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 28 of 30 Engineering Report M-EP-2003-002-01 CGRsambi (k, 8) 1.158 1.158 1.158 1.158 1.158 1.158 1.158 1.157 1.157 1.157 1.157 1.157 1.157 1.156 1.156 1.156 CGRsambi(k 6 16.383 17.9 17.905 17.91 17.915 17.919 17.924 17.929 17.934 17.939 17.943 17.948 17.953 17.958 17.962 17.967 CGRsambi (k, 5) 14 15.225 15.229 15.233 15.237 15.241 15.245 15.249 15.253 15.257 15.261 15.265 15.269 15.273 15.277 15.281 Developed by:
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs l
ID il 60 l
ODD 40 F 20 0,
I 0
-20
-40 Appendix B; Attachment 2 Page 29 of 30 Engineering Report M-EP-2003-002-01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance from Nozzle Bottom (inches) 0.3 o0.2 0 I 0.0 0
1 2
3 Operating Time (years)
Developed by.
Verified by J. S. Brihmadesam B. C. Gray C~ 2a-
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 30 of 30 Engin M-EI 40 -
ci 30 -
I 20 a
l Surface Point 'c':-tip) l-Depth Point {"a".- ip} I ttl 0
1 2
3 4
Operating Time {years}
eering Report P-2003-002-01 Verified by.
. C. Gray C 92 Developed by; J. S. Brhmadesam
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page I of 1 Through-Wall Axial Crack Model Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc Developedby: J. S. Brihmcdesam Verified by: B. C. Gray Note: Only for use when R a,/t is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350. Page 143; 1997 (Fracture Mechanics Model}
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -`8.8'degree Nozzle, "0" Degree Azimuth 1.294 Inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI URP 55-Rev..
The correction is applied in the determination of the crack extension to obtain the value in inchAr.
Through Wall Axial Flaw The same first part as the previous attachments. (see Attachment 1 of this Appendix)
The first Input Is to locate e Reference Line (eg. top of the Blind Zoe).
The throughwall flaw 1.pper Tip' is located at the Reference Line.
Enter the elevatlon of the Reference Line (e. Blind Zone) above the nozzle bottom in inches.
BZ:= 1544 Location of Blind Zone above nozzle bottom (inch)
The SeeOd Input is the LPper Limit far the evoetien, sich is the bottoe of the A/let xAld kg This is shown n the &cel spwead sheet as weld bottom. Enter this dimension (measurf from nozzk bottom) below.
UILS~rsDiS:
1.786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Only two inputs one defining the location of the reference line {BZ} and the other the bottom of the weld {ULstrs.Disd are needed. The flaw description is not needed for this crack type, because the flaw upper tip is placed at the reference line (i.e.
at the top of the blind zone)
Input Data :-
L :=.794 od := 4.05 id:= 2.728 PI,,,:= 2-235 Years:= 4 11,,,1= 1500 r =604 v := 0.307 Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 2 of I1 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 a(,-:= 2.67 10 12 Qg:= 31 1 1
617 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 The input data is similar to that in Attachment 1, except that the crack (flaw) length is based on stress distribution consideration. The flaw length determination is made by locating the lower tip of the flaw at a location where the average stress ([ID + OD]/2) is about 10 ksi. In this mannerthe lowertip is at a location where no PWSCC growth towards the bottom of the nozzle is possible.
-Q lI 1
110
-3 1+459.67 Trf+45967)I Co:= '
- r9o, od id Rt, :=-
K, :=-2 ri.pr = Years 365 24 t:=
,, - R.
Rr:= Rl + -
C Firier:= 1.417 10J "lrlipr Ibs Prliblk:=
-soi I =
Determination of constants. Note the conversion for crack growth rate da/dt}
from metric (m/sec) to English units (inch/hr) is obtained by the factor defined as CFinhr.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 3 of II Stress Distribution in the tube. The outside surface is the reference surface fr all analysis in accordance with the refere Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as foilo Cloumn 'O" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column 1' = ID Stress data at each Elevation ksi)
Column 5 = OD Stress data at each Elevation (ksi)
DataAtt
.- a-~:..
21
° 1 X t
H i 0 T 3
4 X,]
0
-27.4
-24.36
-22.21
-2041
-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 z3T 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 87.67 9
2.18 14.83 22.26 34.78 49.05 63.38 MIIxI:= tDaa,.XII A111D1:= DataAl (5)
A1101):= Data.AJI The nodal stress information is fully imported from the appropriate Excel spread sheet provided by Dominion Engineering. However, only the ID and OD distributions are required for this analysis. The stress input for this calculation uses the applied stress as defined by Membrane and bending components.
These components are dependent on the stresses at the ID and OD surface.
The model used uses the OD surface as the reference surface and the same method is followed in the calculation for this model.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 4 of II 1,
I 15
\\ial Dislanle aoe Bottoml linlchl iI) D)istrlblUt110
(
distribution The ID and OD distribution are plotted. The blind zone is located. The upper flaw tip is at the blind zone location and the lower flaw tip is located close to the region where the average stress (membrane) is about 10 ksi.
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).
Dala:=
(
-27 404 -24. 35 11 483 0I633
--1 486
(.87 17.66 16422 1 18 29,798 26 (149 1.428 33.623 27 792 1 627 32.364 28 469 1.786 27.394 289(18
-2.'_l)
-3 599 14.61 2.7)
-2o 4(7
-4.44 12 415 18"5 8.978
-5 268 9.376 14 21 26 089 4i 104 24.8 24 32 1 2759l 34 284 31,388 43882 63718 )
,XI :=I )ala tW II) =
I Rll) := rcgressfAxl, 11). 3 Rj)7
= rgressf A\\.(
0.3)
The Data matrix is obtained in a similar manner as described in Attachment 1 of this appendix. The regression is only performed on the ID and OD distributions as these are the only distributions required for the computation.
C C~ L
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 5ofl F'Iltr :=B - I Flaw Center above Nozzle Bottom IncStrs.avg :=
ULStrs.Dist - BZ 20 Location of the crack center and the segment height are defined. Once again twenty (20) segments are utilized.
Hoop Stress Profile In the axial direction of the tube for ID and OD locations N = 20 Number of locations for stress profiles Loco:= FLCnir - L i := I.N + 3 Incri:=
if i<4 nInCS rsavg otherwise Loci = Loc. 1 + incr; SID.:= RID3 + RlD4 Loci + RID- (Loci) + RID, (Locj)
SODi := ROD3 + ROD -Loc + ROD,-(Locy + ROD6.(LCi) 3 In a similar manner to Attachment I of this appendix, the ID and OD stress profiles along the nozzle length are determined.
j:= I..N Sid =
SilD + SIlDl SIlD j
j+I j+2 3
Sjdj l'/ + 1 + SD j+2 j +
S if j = I Sod-:=
SODj + SOD j+ + SODj+2 3--
+
if j = l 5odj iJ+hI>+ SOll Sodj--4-j + 1) + SO+2 otherwise j
2 othenvise SW + Sid.
(711j =
i 2
+ Pint Sod. - Sid b.:=
2 i
The moving average stress, the membrane (m) containing the internal pressure (Pint) and the bending component (b) are computed.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 6 of 11 Membrane Stress Bending Stress OD Stress ID Stress (amH =
0 0
23.795 27.339 29.561 31.121 32.304 33.253 34.044 34.727 35.33 35.875 36.374 36.839 37,276 37.69 38.088 tGb=
0 0
-3,536
-1.932
-0.851
-0.028 0.649 1.238 1.771 2.266 2.735 3.186 3.626 4.058 4,485 4 91 5.333 Sod =
0 i 0
18.023 23.172 26.475 28.858 30,719 32.256 33.58 34.757 35.83 36.828 37.766 38.662 39.526 40.365 41.185 Sid =
a 0
25.096 27.036 28176 28.914 29.42 29.779 30.039 30.226 30.361 30.453 30.513 30 54 30.555 30 545 30 518 Tabular display of the various stress components are printed to ensure that the regression and the moving average methods are functioning properly.
I'rmRsmith := (JiLJLrs.Dist - (FL-Caltr + I)
Irrpeugthl 0 242 Allowable Propagation Length {PropLength}is defined as the difference between the bottom of weld elevation and the blind zone (upper flaw tip location) elevation. Since the Flaw Center {FLcntr} is located at half flaw length below the blind zone the second term within the parenthesis is the location of the blind zone.
I['WCpVN.scc :=,
lo4l NCB 0 CM-Er while I <- 1il A Start and initialization of the recursive loop. The crack dimension used in the analysis is the half crack length defined as {.
Therefore the initial crack size is set to the initial crack half length {0}.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 7ofIl Gn.appld +-
a if I1< I Gil if I0 < I < 10+ ICStrs.avg GID 3if I0+ IncStrs.avg < i< I0 2 InCStrs.avg a ni if I + 2IncStrs avg Ii I + 3 nCStrs.avg nis if I0 3nCStrs.avg < I- < 0 + 4lncStrs.avg
- m if 10 + 4Ilncstrs.avg < I < I0 + 5-IncStrs.avg In 7i f I0 + 5-IncStrs avg < It 10 I+6InCStrs.avg a1In8 if I0 + 6InCStrs.avg < I <
10
+7-ncStrs.avg aGn if 10 + 7Incstrs.avg I < 10 +
lncStrs.avg nm10 if I + 8 nCStrs.avg I < I0 + 9-IlncStrs.avg GM 1m if 10 + 9InCstrs.avg < I < 0 + I0-ncstrs.avg Assignment of the applied stress component. This example shows the membrane component {am} for eleven segments. In the model all twenty (20) segments are considered and similar assignment is made for the bending component {fCb). The assignments are based on the current flaw location and the boundaries for the segment. This assignment is similar to the assignments described in Attachment 1 of this appendix.
As [2 (1 - v2)]
1 0.5 (R1mt)'
Definition of the Crack parameter with respect to cylinder geometry (mean radius and thickness). This parameter accommodates the effect of cylinder geometry on the SIF.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 8 of II Ac, 4
- 1. 90 + 0.3621 X +
0565
- 0.0082(?,()
+ 0.0004}(Xi) - 8 326 1 6_(Bit Abin --- 0.0063 + 0,0919 Xi 0168(X 1) - 0.0052 (XA) +.008.(A*) -
.9701 10 Aebn 0.(0029 +.0707
- 0.0197 (Xi) + 0.0034-(Xi) - 0.0003(Xi)4 + 8.8052 10
(
Abb.
0.9961 - 03806.XA + 0.1239A(Xi)
-0021 (i)
+ 0.0017-(Xi)'
-4.993910 -
(,
Determination of the SICF for the two component stress loadings based on current crack half length and cylinder geometry (using the non dimensional flaw length X.
lKpm. 4-antppId.(Jtli~)0.5 Kpb.
f'l.appid( I-)
Calculation of SIF for an equivalent flat plate geometry for the two applied stress conditions (membrane and bending).
KineniibnOD Aem + Abm) Kpi KminebnflD v (Aeni-Abnii) Kp"l KbendOD;
- (Aeb, + Abbj)-Kpb, KbendlD
- (Aebj - Abbj) Kpb, Calculation of the SIF at the ID and OD for the two component stresses. Note the SICF factors are used as multipliers to the equivalent plate solutions determined above in calculating the SIF for the cylinder geometry.
KAppOD4 KmiembniOD + KbetidOD KAppD -
KniiemiibrifIDi + KbendID.
The applied SIF at the ID and OD are determined by the sum of the sub-component SIF for the two conditions (membrane and bending).
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 9 of KAppOD. + KApplD K jpp v 2
Ka
- KApp 1.099 Ka.
19.° if Ka<9.0 lKa. otherwise The applied SIF used for determining the crack growth is taken as the arithmetic average of the ID and OD SIF. The second statement converts the SIF from English units to metric units. The third statement ensures that the threshold criterion is appropriately satisfied. This conditional statement is used to prevent obtaining an imaginary value for the crack growth rate {da/dt) by a negative value for the (SIF-SIFThreshold) term. Therefore this conditional statement ensures that the difference is zero (0) when the applied SIF is below the threshold value.
L)Ienl I-Co-(Ka-90)1.16 Dlengrlh
[)Ien_ CFinhr-Cblk if Ka < 80.0 10 4 10 CFinhrCblk othen rise Calculation of crack growth rate {da/dt} and the crack growth within a time block.
The crack growth rate is calculated in metric units (m/sec) and the crack growth in English units by use of the conversion factor {CFinhr}
- output,
) +- i NCB.
outPUt( 1i) 365-24 Output statements to store variables required for loop operation and those for evaluation of time dependent crack growth. This part is similar to the same step described in Attachment 1 of this appendix.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page Oofil N\\C.
i-N13.
+ C bik Loop increment and redefinition of parameters for the next recursive loop calculation.
Propi cngdil (',242 Fla" I Lngth s im U.5 11{II>
25 4
.~
I Ip
( puscI ii I )
-I fltLT~a\\ IIdcl Typical Mathcad graphics used to compute the impact of crack growth. Note the allowable propagation length information in the top left corner. In this example the crack growth in one cycle exceeds the allowable propagation length, therefore the postulated flaw would reach the bottom of the weld within one operating cycle (1.5 years).
COs
I \\\\ 'C'P% LL(
C f
31 965 38.727 38.756 38.784 38.813 38.842 38.871 38 9 38.929 38.958 38.987 39.016 39.045 39.074 39.103 39.132 IN~
WU)[,CL <(j7)
=
35 69 39.253 39 279 39 305 39.331 39.357 39.382 39.408 39434 39 46 39486 39.512 39.538 39 564 39 59 39.617 Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page II of 11 35.246 40.52 40.549 40.579 40.608 40.638 40.667 40.697 40.726 40.756 40.785 40.815 40.844 40.874
- 40. 904 40.933 Typical tabular output to ensure proper functioning of the model.
300 I
ID 0
S IF I
200 I 100 0
1 2
3 4
O Ce*
- i. i T i e
(y.. -
Typical Axum plot for use in the report. This is similar to Attachment 1 of this appendix.
CDCG
Engineering Report M-EP-2003-002-01 Appendix C Appendix C Mathcad worksheet for CEDM Deterministic Fracture Mechanics Analyses This Appendix has 48 Attachments. Attachment 32 is Intentionally Blank
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"0" Degree Nozzle, All Azimuths, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPo in t := 1544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "-
tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg.
This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist := 1.796 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Blihmadesam Verified by:
B. C Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment I Page 2 of 11 Engineering Report M-EP-2003-00201 Input Data :-
L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 PInt := 2.235 Years := 4 im := 1500 T := 604 aoC := 2.67 I 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth (MRP)
Reference Temperature for normalizing Data deg. F od R 2 id Rid :=2 t:= Ro-Rid t
Rm :Rid+ -2 Timopr := Years-365-24 CFinhr:= 1.417-105 Timopr Cblk.
rhim Pmtblk =
50 L
co := 2 Rm Rt :=
[ Qg
(
l
__I__
1.103-10--
T+459.67 T ref+459.671 C0 I := e'-
a0 C Temperature Correction for Coefficient Alpha Co := Col 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Bnhmadesam Verffled by:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment I Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "
= Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
-25.09
-27.55
-27.79
-25.62
-23.76 1
0.49
-0.56
-0.54
-2.11
-4.85
-6.16 2
0.87 21.52 18.64 17.12 14.84 10.09 3
1.19 32.75 28.49 24.14 19.64 14.45 4
1.44 35.67 29.6 26.17 25.59 28.42 5
1.64 34.24 29.57 28.29 35.41 45.38 6
1.8 29.45 29.81 31.39 43.34 61.71 7
1.93 23.67 26.5 33.26 47.61 64.65 a8 2.07 18.93 24.56 33.97 49.07 65.88 9
2.2 16.54 22.85 34.79 49.52 62.8 AXLen:= AllData(O)
IDAII:= AI1DatP)
ODAII := AllData()
Stress Distribution 100
._sV we 50.
1344 1.496
'~~~~~~~~~~~~~~~~~~~~~~~~~~-
0
-50 0 0.5 ID Distribution OD Distribution I
I.5 2
2.5 3
Axial Elevation above Bottom [inch]
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment I Page 4 of 11 Engineering Report M-EP-2003-00201 Observing the stress distribution select the region in the table above labeled DataAl that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select 'Copy Selection"'; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 0.485 0.874 1.186 1.436 1.635 1.796 1.932 2.068
-25.088
-0.563 21.515 32.751 35.667 34.244 29.45 23.674 18.928
-27.546
-0.539 18.635 28.494 29.598 29.574 29.814 26.502 24.564
-27.787
-2.111 17.122 24.136 26.166 28.286 31.385 33.261 33.968
-25.624
-4.851 14.843 19.645 25.589 35.408 43.337 47.609 49.071
-23.763 )
-6.157 10.089 14.45 28.417 45.379 61.713 64.65 65.876 )
Axi := Data(°)
MD:= Data(3 ID:= Dataei)
TQ :=Data (4)
QT:= Data(2)
OD: DatP)
RID := regress(Axl,ID,3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl,OD,3)
RMD := regress(Axl, MD,3)
RTO:= regress(Axl,TQ,3)
Developed by:
J. S. Bnhmadesam Venfled by:
. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment I Page 5 of 11 Engineering Report M-EP-2003-0021 FLCntr =
Refpoint-co if Val = I Refpoint if Val = 2 RefPoint + cO otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr + Co InCstrs.avg :=
ULStrs.Dist - UTip 20 No User Input is required beyond this Point n Sat Aug 09 10:59:39 AM T/][J3-Developed by J. S. Bnlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 0.092 0.6 U
-=
I-Z::
0.4 Flaw Growth in Depth Direction I
I I
I I
I I
I I
I I
III 0.2 O 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
2 U
I-0 31 ox I
I I
I I
I I
I 0.092 I
I I
I I
II
-I CI 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developed by.
J. S. Bdhmadesam Verffied by:
B. C. Gray
Entergy Operations Inca Central Engineering Programs Appendix "C"; Attachment I Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 100 Q
-.1 0
u I-CA co 80 60 40 20 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
4 Depth Point
-.Surface Point Developed by:
J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix '"C"; Attachment I Page 8 of I Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.I 0.9 0
0 C-v E
.U Q
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Verified by B. C Gray I
I 0.5 I
1.5 2
2.5 3
3.5 4
Operating time {years}
v" - Tip -- Uniform
".....I..
Ia" - Tip -- Linear
Va"- Tip -- Quadratic "I...Va"
- Tip -- Cubic 11c
- Tip -- Uniform
....... "c' - Tip -- Linear
Vc" - Tip -- Quadratic 9c" - Tip -- Cubic De velopedf by:
J. S. Brihfmadesam
l Entergy Operations Inc.
Central Engineering Programs CGRsambi(k 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment I Page 9 of 11 Engineering Report M-EP-2003-00201 CGRsambi(k 6) 16.561 16.414 16.42 16.426 16.433 16.439 16.445 16.451 16.457 16.463 16.469 16.475 16.482 16.488 16.494 16.5 CGRsambi 13.786 13.676 13.682 13.688 13.695 13.701 13.708 13.714 13.721 13.727 13.733 13.74 13.746 13.753 13.759 13.765 Developed by:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 10 of 11 Engineering Report M-EP-2003-002-01 60 4 0 I
I 20 0
-2 0
-40 0 0 0.5 1.0 1.5 2.0 2.5 3.0 Axial D istance From N ozzle Bottom
{inch}
0.16 -
014 -
u 0.12-E 0.10 -
a o 0.06 -
0.06 0.04 -
A A
A A
H A
Verified by.
S. C. Gray i
C A
0 1
2 3
4 Operating Time {years)
Developed by.
J. S. Brihmadesam
....1 1 ----- -.....
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 11 of 11 Engineering Report M-EP-2003-002-01
,0.15 S
o 0.10 0.00 0
1 2
3 4
0 perating Time years) 22 -
2 0 -
it 18 -
iI 14 -
12 -
S IF D1 p h P in I S= I F S rfa c e P o in Verified by B. C. Gray coG4~
0 perating Time years)
Developed by.
J. S. Brlhmadesam
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 1 of 11 Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"0" Degree Nozzle, All Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
OD Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPoint = 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "-
tip " located at the reference point (Enter 3).
Val := 2 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 = 1.796 Upper Axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom)
Developed by:
J. S. Bnhmadesam Vefiled by:
S. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix "C"; Attachment 2 Page 2 of I1 Engineering Report M-EP-2003-00201 L := 0.32 ao := 0.661-0.12 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID od := 4.05 id := 2.728 PInt := 2.235 Years := 4 Ihim := 1500 T := 604 OC := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 id Rid := 2 t := Ro-Rid t
Rm :=Rid+ -
Timopr:= Years-365-24 CFinhr := 1.417*105 Timopr CbIk :=
r h1im Pmtblk :=
50 L
Co := 2 Rm Rt =7 1.103lo-3tT+49.67Tref+459.67) co, :=
e
.6 10C Temperature Correction for Coefficient Alpha Co:= C01 Stress Input Data 75 th percentile MRP-55 Revision 1 Developed byV b
J. S. Brhmadesam Venired by B. C. Gray
Entergy Operations Inc Central Engineerng Programs Appendix "C"; Attachment 2 Page 3 of 1 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data in the table below. The column designations are as follows:
Column 'O" = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
-2 3
-A5
.0 0
-25.09
-27.55
-27.79
-25.62
-23.76 1
0.49
-0.56
-0.54
-2.11
-4.85
-6.16 2
0.87 21.52 18.64 17.12 14.84 10.09 3
1.19 32.75 28.49 24.14 19.64 14.45 4
1.44 35.67 29.6 26.17 25.59 28.42 5
1.64 34.24 29.57 28.29 35.41 45.38 6
1.8 29.45 29.81 31.39 43.34 61.71 7
1.93 23.67 26.5 33.26 47.61 64.65 8
2.07 18.93 24.56 33.97 49.07 65.88 E-9 2.2 16.54 22.85 34.79 49.52 62.8 AXLen := AllData(°)
IDAO1:= AliDatP~)
ODAI1:= AllData(5)
Stress Distribution t00 3-Id Us IDAI ODAll 50 I
IL$44 I,796 II I
I I
I 0
-50 0
0.5 1
1.5 2
AXLen Axial Elevation above Bottom [inch]
2.5 3
Observina the stress distribution select the reaion in the table above labeled Data AI that represents the Developed by.
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Prograns Appendix "C"; Attachment 2 Page 4 of 1I Engineering Report M-EP-200300201 region of interest This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type 'Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
(0
-25.088 -27.546 -27.787 -25.624 -23.763 Data:=
0.485
-0.563
-0.539
-2.111
-4.851
-6.157 0.874 21.515 18.635 17.122 14.843 10.089 1.186 32.751 28.494 24.136 19.645 14.45 1.436 35.667 29.598 26.166 25.589 28.417 1.635 34.244 29.574 28.286 35.408 45.379 1.796 29.45 29.814 31.385 43.337 61.713 1.932 23.674 26.502 33.261 47.609 64.65
\\2.068 18.928 24.564 33.968 49.071 65.876 )
AxI := Data(0)
MD:= Data(3)
ID := Data(I)
TQ := Data(4)
QT := Data(2)
OD = Data(5)
RID := regress(Axl,ID,3)
RQT := regress(Axl,QT,3)
ROD:= regress(Axl, OD, 3)
RMD:= regress(Axl,MD,3)
RTQ := regress(Axl,TQ,3)
FLCntr Refpoint -c if Val =
Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 RefPoint + c0 otherwise UTjp := FLCntr + C0 lnstrs.avg ULStrs.Dist - UTip 20 Developed by:
J. S. Bnihmadesam Verifed by.
. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 5 of 11 Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point ffi Sat Aug 09 10:21:18 AM 7nn-A Developed by:
J. S. Bdhmadesam Verfed by:
B. C. Gray
Entergy Operations Inc Central Engineering Progrants Appendix "C"; Attachment 2 Page 6 ofI 1 Engineering Report M-EP-2003-00201 ProPLength = 0.092 Flaw Growth in Depth Direction 0.6 C.)
a-2 cSD 0.4 I
I I
I I
I I
I I I 0.2 0 CI 0.5 I
1.5 2
2.5 Operating Time {years}
3 3.5 4
Entergy-CEP Model U
0 08 5
2:
c:
3 0.8I 0.6 I
I I
I I
II 0.4 1 0.2 0 0 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Entergy-CEP Model Developed by J. S. Blihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors I-0 c) c U.
t 80 60 1 40 I
I I
I I
I I
.~
~
~~~~~~~~~~~~~~~~~~~~~~~~~.
I I
I I
I I
I 20 o LI 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. Bhmadesam Veified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix C"; Attachment 2 Page 8 of 11 I
Influence Coefficients - Flaw 0.9 0.8 0
r-)
0 C
U 0.7 0.6 0.5 0.4 0.3
.~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.2 0.1 0
Engineering Report M-EP-2003-002-01 4
Verified by:-
B. C Gray Ck7)
I.........4-
------------------------------------- -p
-.-I..........................
... 1-1-.-.-.---.-----,
0 0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 "a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform
'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brihmadesam
Entergy Operations Inc Central Engineering Programs Appendix "C"; Attachment 2 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k, 8) 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 0.827 CGRsambi(k, 6) 18.307 19.315 19.322 19.33 19.337 19.344 19.352 19.359 19.366 19.374 19.381 19.388 19.396 19.403 19.41 19.417 CGRsambi (k,5) 13.252 13.936 13.941 13.946 13.951 13.956 13.962 13.967 13.972 13.977 13.982 13.988 13.993 13.998 14.003 14.008 Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs 60-C 40 I
2 a0
-2 0
-4 0 --
Appendix "C"; Attachment 2 Page 10 of 11 Engineering Report M-EP-2003-002-01 0.0 0.5 1.0 I15 2.0 2.5 3.0 Distance from N ozzle Bottom (inches) 0.4 -
2 I*° 0 3 8 0.2 -
a 0
° 0 O.0 -
0 1
2 3
4 O p e ra tin T im e (y e a rs A
A Verifed by:
B. C. Gray C
A Developed by:
J. S. Brnhmadesam
Entergy Operations Inc Central Engineering Programs 0.4-o 0.3 V
2 0.2 a
0 0.0 -
Appendix "C"; Attachment 2 Page 11 of 11 Engineering Report M-EP-2003-002-01 2
3 4
0 perating Time (years) 5 0 -
0
°; 4 0-30 -
II 20 I10 S u ra c Pio in t ( 'c " -t ip) I D e p t P o n t "a " - t
)
0 4
0 p era tin g Time
( Iyears)
Developed by.
J. S. Brihmadesam Verified by; B. C Gray Cr.
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 1 of 10 Engineering Report M-EP-2003-00201 Stress Corrosion Crack Growth Analysis Throughwall flaw beveloped by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmodesam Verified by: B. C. Gray Note: Only for use when R,,tS,d/t is between 2.0 and 5.0 (Thickwoll Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 {Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"O"degree Nozzle, All Azimuth, 1.544 inch above Nozzle Bottom Calculation
Reference:
MRP 75 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inchhr.
Through Wall Axial Flaw The first Input is to locate the Reference Line (eg. top of the Blind Zone).
e throghwal flaw pper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the 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 := 1796 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
[Develo~~~~~~~~~~~~~~~~~~~~~~~~~~~ed by:
Verified by:~~~~
IDeveloped by:
Vefified b I
Entergy Operatons Inc.
Central Engineenng Programs Appendix "C"; Attachment 3 Page 2 of 10 Engineering Report M-EP-2003-00201 Input Data :
L :=.794 od:= 4.05 id:= 2.728 Pint:= 2.235 Years:= 4 1im:= 1500 T:= 604 v := 0.307 aOc:= 2.67 10 12 Qg:= 31.0 Tref:= 617 Initial Flaw Length TWaxial (Based on 10 Ksi average stress)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F F
Qg r
l 1.103 10 T+45967 Tref+459.67)J Timopr:= Years-365*24 od 2
Ri:= id 2
t:= R0 - Ri Rm:= Ri + -
2 CFinhr:= 1.417 105 Tifl1~pr Cblk :=
r Itim Pmtblk:= l-l 150 I
L 2
Developed by:
Verified by:
lIDeveloped by:-
Verifedby. I
Entergy Operadons Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 3 of 10 Engineering Report M-EP-2003-00201 Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the reference.
Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as follows:
Cloumn "0" = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
DataAII =
0 1
2 3
4 0
0
-25.09
-27.55
-27.79
-25.62
-23.76 1
0.49
-0.56
-0.54
-2.11
-4.85
-6.16 2
0.87 21.52 18.64 17.12 14.84 10.09 3
1.19 32.75 28.49 24.14 19.64 14.45 4
1.44 35.67 29.6 26.17 25.59 28.42 5
1.64 34.24 29.57 28.29 35.41 45.38 6
1.8 29.45 29.81 31.39 43.34 61.71 7
1.93 23.67 26.5 33.26 47.61 64.65 8
2.07 18.93 24.56 33.97 49.07 65.88 9
2.2 16.54 22.85 34.79 49.52 62.8 10 2.34 17.56 22.68 33.81 47.49 63.56 AllAxl:= DataAII(0)
AIIID DataAIll AIIOD DataAII 5 D
b V
IDeveloped by:
Verified by: I
Entergy Operations nc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 4 of 10 Engineering Report M-EP-2003-002-01 v/)
-25
-50 0
0.5 1
1.5 2
2.5 3
Axial Distance above Bottom [inch]
ID Distribution OD distribution Observing the stress distribution select the region in the table above labeled 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).
t i
t-t fed by i
ClX -
A
( 0
-25.088 -27.546 -27.787 -25.624 -23.763)
Data:=
0.485
-0.563 0.874 21.515 1.186 32.751 1.436 35.667 1.635 34.244 1.796 29.45 1.932 23.674 2.068 18.928
-0.539 18.635 28.494 29.598 29.574 29.814 26.502 24.564 22.854
-2.111
-4.851
-6.157 17.122 14.843 10.089 24.136 19.645 14.45 26.166 25.589 28.417 28.286 35.408 45.379 31.385 43.337 61.713 33.261 47.609 64.65 33.968 49.071 65.876 y2.204 16.541 34.789 49.525 62.795 )
Axl:= Data ID:= Data (5)
OD:=Data RID:= regress(Axl, ID, 3)
ROD:= regress(AxI, OD, 3)
IDeveloped by:
Verih
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 5 of 10 Engineering Report M-EP-2003-002-01 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ lCStrs.avg :=
20 No User Input required beyond this Point M Sat Aug 09 11:44:49 AM 2003 Developed by:
Verified by:
lIDeveloped by Venfied by. I
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 6 of 10 Engineering Report M-EP-2003-002-01 ProPLength = 0252 Flaw Length vs. Time 1.5 C
<x TWCWSCC 0
0.5 0
-0.5 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
TWCPWSCC(
I)
Operating Time (years)
Entergy Model Increase in Half Length 2
.)
C C
.C
-2 1.5 0.5 O 0 0.5 l
1.5 2
2.5 3
3.5 Operating Time (Years) 4 I
y lDeveloped by:
Verified by:l
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 7 of 10 Engineering Report M-EP-2003-002-01 C)
C r
C v:
0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years}
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 4
a f
i t
A f
Verified by: l I t C \\efn A
IDeveloped by:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 8 of 10 Engineering Report M-EP-2003-002-01 TWC
.8) -
TWCpWscc(j,6) =
35.366 42.321 42.355 42.39 42.424 42.459 42.494 42.528 42.563 42.598 42.633 42.668 42.702 42.737 42.772 42.807 TWCPWSCC
.7) 37.917 41.494 41.524 41.555 41.586 41.616 41.647 41.678 41.708 41.739 41.77 41.801 41.832 41.863 41.894 41.925 TWCPWSCC(J 8) 38.137 43.512 43.547 43.582 43.617 43.652 43.687 43.723 43.758 43.793 43.828 43.864 43.899 43.934 43.97 44.005 Developed by:
Verified by:
lIDeveloped by Verified byI
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 9of10 Engineering Report M-EP-2003-002-01 Hoop Stress Plot 60 -
40 -
i 20 -
r
-20
-40 300 -
6 4 200 -
t 1 00 -
0-0.0 0.5 1.0 1.5 2.0 2.5 3.0 Distance fnm Nozzle Bottom
{inch)
O0 Su rfa ce S IF ID Su rface SI A v era g e S IF 0
1 2
3 4
0 perating Time {years)
Developed by:
Verif
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 3 Page 10 of 10 Engineering Report M-EP-2003-00201 1.5 I
o
.s 0.0 o
1 2
3 O perhtifg Tm
( (years)
Developed by:
Verified by:
lIDeveloped by Verified by.:
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 1 of 11 Engineering Report M-EP-2003-00201 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Bnhmadesam Verffied by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-I 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8" Degree Nozzle, Downhill Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPoint = 1.544 To place the flaw 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 "c-tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist := 1.786 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. Bihymadesam VedrIed by B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 2 of 11 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.32 ao := 0.661-0.07 od := 4.05 id := 2.728 Pint = 2.235 Years := 4 him = 1500 T :=604 aOC := 2.67-I 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F R. :=od
- 0.
2 Rid :
id Rid t:= Ro - Rid Rm :=id Timopr := Years-365-24 CFinhr := 1.417 105 Timopr Cblk.=
him Pmtblk =
50 l L
Rm Rt:=
t Qg
(
1 1.103 10 3 T+459.67 Tref+ 459.67 Co:= C0 1 0C Temperature Correction for Coefficient Alpha 75 h percentile MRP-55 Revision 1 Developed by:
J. S. Biihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 3 of 11 Engineering Report M-EP-2003-00201 Stress Input Data Input all available Nodal stress data In the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "" = ID Stress data at each Elevation (ksi)
Cloumn w2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn w3w = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (kst)
AllData :=
0 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 AXLen:= AlIData(0)
IDA11:= A11Data(')
ODAII := AllData(5)
Stress Distribution 100 un 50 0
I I
I :
I I
1344 0.86 I
I I
I~~~~~~~~~~~~~~
-50 0 0.5 I
1.5 2
2.5 3
Axial Elevation above Bottom [inch]
ID Distribution
OD Distribution Developed by:
J. S. Brlhmadesam Veifled by:
. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 4 of 11 Engineering Report M-EP-2003-00201 Observing the stress distribution select the region in the table above labeled DataAI that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region In the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function In the tool bar to paste the selection.
Data :=
0 0.483 0.87 1.18 1.428 1.627 1.786 1.919 2.051 2.183
-27.404 0.633 17.665 29.798 33.623 32.364 27.394 21.498 16.944 14.834
-24.356
-1.486 16.422 26.049 27.792 28.469 28.918 25.556 23.793 22.263
-22.209
-3.599 14.61 22.723 24.8 27.591 31.388 33.55 34.064 34.779
-20.407
-4.44 12.415 18.95 24.321 34.284 43.882 48.089 49.472 49.055
-18.978)
-5.268 9.376 14.201 26.989 45.104 63.718 66.365 67.672 63.377 )
AxI := Data(0)
(3)
()
MD: Data ID: Data(
TQ := Data(4)
QT := Data(2)
OD := Data(5)
RID := regress(Axl, ID, 3)
RQT := regress(Axl, QT, 3)
ROD:= regress(Axl, OD, 3)
RMD := regress(Axl, MD, 3)
RTO := regress(Axl, TQ, 3)
Developed by:
- 1. S. Bihmadesam Verified by:
. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLICntr :=
Refpoint-CO if Val Refpoint if Val = 2 Refpoint + c otherwise Flaw center Location above Nozzle Bottom UTip := FLCntr+ Co InCstrs.avg :=
ULStrs.Dist - UTip 20 No User Input is required beyond this Point 2Sat Aug 09 10:59:39 Developed by:
J. S. Bnhmadesam AM euWj Verified by:
B. C. Gray
Entergy Operations Inc.
Central EngineeringPrg....
Appendix "C"; Attachment 4 Page 6 of 11 PPLengh 0.082 Engineering Report M-EP-2003-00 241 Q
C s
._c LT 0.2 0
1.5 OPerating Time 2.5
{years) 3.5 4
Q:
,C l4 V3 o
1.5 2
OPerating Time 2.5
{years}
3 3.5 4
Developed by:
a S. Shfiadesm Venfedby:
B. C. Gray
l Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 7 of 11 Engineering Report M-EP-2003-002-01 100 0
c 5-
.J 3
co 80 60.
Stress Intensity Factors 40 t 20 o I 0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developedby:
J. S. Brlhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 8 of 11 Influence Coefficients - Flaw 1.1 0.9
'A v
0 U
0 U
A) r-:
4-0.8 0.7 0.6 0.5 0.4
~
Engineering Report M-EP-2003-002-01 Verified by B.,C Gray 0.3 0.2 0.1 o I 0.5 l
l.5 2
2 Operating time {years}
2.5 3
3.5 4
a" - Tip -- Uniform "a" - Tip -- Linear
"a" - Tip -- Quadratic I"a" - Tip -- Cubic "c" - Tip -- Uniform c' - Tip -- Linear
"c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by:
J. S. Brlhmadesam
Entergy Operations Inc Central Engineering Programs CGRsambi(k 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 4 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k, 6) 14.996 14.886 14.89 14.895 14.899 14.903 14.907 14.912 14.916 14.92 14.925 14.929 14.933 14.938 14.942 14.946 CGRsambi(k, 5) 12.571 12.495 12.499 12.504 12.509 12.513 12.518 12.522 12.527 12.531 12.536 12.541 12.545 12.55 12.554 12.559 Developed by:
J. S. Blihmadesam Verfled by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 4 Page 10 of 11 Engineering Report M-EP-2003-002-01 60 4 0 a
20 0
-2 0
-4 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Axial Distance From N ozzle Bottom (inch)
A A
A Verified by.
B. C. Gray r
CM tD 0.12 -
z 0
i 0
. 0.08 -
0.06 -
0.04 i
0 I
2 O p e ra tin g T ime
{y e a rs}
3 4
Developed by:
J. S. Brihmadesam
Entergy Operations Inc.
Centra I Engineering Programs 0.12 -
I I
U 2 0.08 -
i, D 0 0 4 -
0.0 0 -
Appendix "C"; Attachment 4 Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
3 4
O perating Time (years) 19 -
V;
'hit 17 -
i 1 3 -
11 l
S F S u r fa c P
FD t
o i 0
2 0 p ra tin g T im e (years)I 3
4 A
A H
Verified by.
S. C. Gray f
A Developed by.
J. S. BSimadesam