ML032320180
| ML032320180 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear, Waterford  |
| Issue date: | 08/14/2003 |
| From: | Alexion T Office of Nuclear Reactor Regulation |
| To: | Entergy Operations |
| References | |
| TAC MB8927, TAC MB9542, TAC MB9644, TAC MB9882, TAC MB9883 | |
| Download: ML032320180 (138) | |
Text
NRC FORM 658 U.S. NUCLEAR REGULATORY COMMISSION (9.1l99 TRANSMITTAL OF MEETING HANDOUT MATERIALS FOR IMMEDIATE PLACEMENT IN THE PUBLIC DOMAIN This form is to be filled out (typed or hand-pinted) by the person who announced the meeting (ie., the person who issued the meeting notice). The completed form, and the attached copy of meeting handout materials, will be sent to the Document Control Desk on the same day of the meeting; under no circumstances will this be done later than the working day after the meeting.
Do not Include proprietary materials.
DATE OF MEETING The attached document(s), which was/were handed out in this meeting, is/are to be placed 08/14/2003 In the public domain as soon as possible. The minutes of the meeting will be issued In the near future. Following are administrative details regarding this meeting:
Docket Number(s) 50-368 and 50-382 Plant/Facility Name Arkansas Nuclear One, Unit 2 and Waterford 3 TAC Number(s) (if available)
MB8927, MB9542, MB9644, MB9882, MB9883 Reference Meeting Notice 08108/03 (ML032200089)
Purpose of Meeting (copy from meeting notice)
EOI will discuss its May 8, June 11, and July 1, 2003, relaxation requests from NRC's vessel head Inspection Order.
NAME OF PERSON WHO ISSUED MEETING NOTICE TITLE Tom Alexion Project Manager OFFICE Nuclear Reactor Regulation DIVISION Division of Licensing Project Management BRANCH Project Directorate IV Distribution of this form and attachments:
Docket File/Central File PUBLIC NRC~~~~~~~~~~~
FOM 6..
.9 PNE ON.EYCE P.E
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NRC FORM SW8 (91S99)
PRINTED ON RECYCLED PAPER This form was designed using InForms
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ANO-2 and W3 NDE Order Relaxations Entergy Operations, Inc.
Date - August 14, 2003 1
Introduction~~~~~
Bill James 2
Purpose of Meeting n Comprehensively review Entergy's RVH issues n Review Entergy's current relaxation approach and basis for compliance with the Order n Provide technical review of supporting analysis for relaxation options n Reach mutual agreement on our deliverables and timing 3
l Overview William Sims 4
Challenges for Order Compliance nANO-2 BMV hardship n Vent Line - Volumetric examination will not provide leakage assessment n CEDM/ICI - Cannot perform full volumetric examination due to nozzle configurations.
5
I Approach for Order Compliance n Vent Line q ANO LFECT & wetted surface ECT q W3 - BMV & wetted surface ECT n
CEDM q ANO LFECT & supplemental visual q W3 - BMV q Volumetric examination of accessible areas q Deterministic analysis of flaw growth from unexamined area q Probabilistic analysis for areas not examined n
ICI q BMV q Volumetric examination of accessible areas q Deterministic analysis of flaw growth from unexamined area q Probabilistic analysis for areas not examined 6
Vent Line Configuration & Examination S
Cannot do leakage assessment with ultrasonics N Manual ECT Wetted surface of J-weld and automated exam of nozzle.
ANO-2 only - Low frequency ECT of the vessel OD Relaxation: AN02 - BMV, Combination UT and ETC 7
CEDM Inspection Approach ANO-2 Combination of Supplementary and BMV inspection W3 Bare Metal Inspection Volumetric nsp. of nozzle/J-weld UT through wall of nozzle Weld fusion line and Triple Point Riverbed Low Freq ECT Vessel Inspection Leakage/degradation assessment on vessel OD and annulus region Relaxation: AN02 - BMV, Threaded blind zone 8
ANO-2 CEDM Refuel Outage 15 -
Ultrasonic Results Weld Extends into blind zone rile Channl G.te C-Scan 8-Scan A-Sca Tools flosplay Seti
\\~ ~~~~ ~~~~~~~~~io 4t.0 s: 088 1:.08 1 80
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CEDM Ultrasonic Free Span Results ANO-2 UT data reveals 1
many nozzles span on down q 46% CEDMs span q 1 1% CEDMs free span 23% CEDMs 0.20" have no free hill side
- with no free with 0-.10 "
with 0.1 1 -
q 7% CEDMs with 0.21 -0.30" Remaining greater than 0.30" or no data Downhill 10 CO+
Plot of Free Span Length O&)W1tC WE Free Span Length Blue=0.0 Red= 0.01 thru 0.10 Green= 0.11 thru 0.20 q Orange= -. 21 thru
/
/
0.30 q No color indicates
/l 7i 3 i40 either greater than 5o l3 0.30, or no data f
Adm3 available.
ICI Inspection Approach ANO-2/W3 Bare Metal Inspection Volumetric nsp. of nozzle/J-weld UT through wall of nozzle q Triple Point Cf Riverbed (Leakage) ection Relaxation:
Counterbore and nozzle end blind zone, 13 Co&'
ANO-2 ICI Refuel Outage 15 Results
- Ultrasonic U
Minimal free
- _Ifl§o H,.l I F1i1 Chnel te C-S0, a-S-as S-Sear Teals soolaj ettiog 1
- 51.
010 I0P.
- F 4-001.1:.490 1-0
-0.a 3.0
-0 0 ~ta01 length detectable F
I l
I
-10 I.0 O 00.
0 1.0 4...
0 0
. I I
.0 C w:010 000 0 1 5 1 0. i m l
-l.
Ill 14 r o1
W3 ICI Pictures q Free length on upper hillside 15
Deterministic Analysis Jai Brihmadesam 16
Purpose of Deterministic Fracture Mechanics CEDMs ICIs Free span length \\
UT Blind zone in counterbore region Zone not subject to PWSCC due to compressive stress field f
UT Blind zone below weld zone Define minimum free span length for at least 1 cycle of flaw growth for l.D. and O.D. part-through wall flaws and through wall flaws.
Define portion of the CEDM nozzle end not susceptible to PWSCC
........ _... A Define minimum free span length for at least 1 cycle of flaw growth for.D. part-through wall flaws.
Define area of counterbore for at least 1 cycle of flaw growth for.D. part-through wall flaws.
17
Postulated Flaws-CEDMs Flaws configurations considered: through wall, I.D. part through wall, and O.D. part through wall (as shown below)
/
l
~~~~flaw 7
///
1 >s Flaw growth, Cr.
(
)'
4 l
~~
along nozzle length
/
l
'O-Flw growth a throt D
! X Cove
~~~~~~~~~nozzle thickoess Flaws evaluated at uphill, downhill, and mid-plane locations Initial flaw depth (ao)-for part through wall flaws-and length (2co)-for all flaws-based on NDE detection limits 18
Postulated Flaws-ICIs Flaw' growuhl, el, thpoumt~h 4 I.D. part-through nozzle thic k n i-wall flaws considered at downhill nozzle end and uphill just below the ao counterbore.
Flaw growth. c, dlng nozzle length Initial edge flaw
_ LcO ok length (co),
co
~counterbore flaw length (2co), and a0 depth (aO) based on MPO!21AW fllw.`,"A+-' oa hrtlrnNDE detection limits 19
Deterministic Fracture Mechanics Analyses Finite Element Model:
Model geometry based on evaluation of both NDE (UT) data and design drawings/ Waterford under evaluation Highest yield strength nozzle in each nozzle group (for example, 0°, 8.80, 28.80, 49.60) was evaluated.
Temperature-dependent stress-strain curve for wrought tube material, and elastic-perfectly-plastic stress strain curve for weld material Model uses a 3-D solid (brick) mesh with four elements representing the tube thickness and approximately 0.125-inch spacing along the tube height on the downhill side.
20
Deterministic Fracture Mechanics Analyses Finite Element Stress Analysis:
Model combines stresses obtained from analyses covering Fabrication + Hydro
+ Normal Operating Residual Stresses (through wall distribution) at all nodal points from the bottom of the nozzle to the top of the attaching J-weld.
l_________
Method to quantify residual
/one I
stresses similar to model used for BWRVIP-14 and 59, benchmarked with experimental residual stress determination on core shrouds and core shroud supports and independently verified by BCL under contract with the NRC.
Stresses in these Regions Used for Analysis 21
Deterministic Fracture Mechanics Analyses Fracture Mechanics (General Approach)
Through wall stress distribution along the tube length determined by averaging the stress on the flaw as the flaw grows in depth and length.
Choice of flaw location based on definition of a reference line (e.g., the location of the UT blind zone) with particular location of flaw defined as user input. (Flaw tips or flaw center based on location.)
Stress profile for initial flaw based on an average profile at three (3) locations on the flaw-the lower tip, center of the flaw, and the upper tip.
The distance between the upper flaw tip and the weld bottom is divided into twenty (20) equal segments to establish stress profiles 22
Deterministic Fracture Mechanics Analyses Fracture Mechanics (General Approach)-continued As the flaw grows, the stress profile imposed on the flaw is re-averaged to account for the new flaw position. This averaging method was determined to be more conservative than a force-averaging technique.
Flaw growth based on EPRI MRP curve at the 75th percentile Flaw growth in the depth and length dimensions computed independently using the different flaw influence coefficients (at the "a-tip" and "c-tip" of the flaw)
Time increment for flaw growth is approximately 20-24 hours of operating time. At the end of each increment, the flaw size is updated.
Based on the new flaw size, the flaw influence coefficients and stress coefficients are determined.
23
I p Deterministic Fracture Mechanics Analyses n Fracture Mechanics Models Surface Flaws:
- Based on NASA model (SC04) covering a range from a very thick-wall cylinder (R/t = 1.0) to a flat plate (R/t = 300).
- Depth-to-half length aspect ratio (a/c) of the flaw is variable from 0.2 to 1.0
- Flaw depth-to-thickness ratio (a/t) is variable from 0.0 to 1.0 Through wall Flaws:
- Based on ASME Pressure Vessels and Piping (PVP) paper for through wall axial cracks in pipes and cylinders (thick-wall solution) 24
Determinisic Fracture Mechanics Analyses n Comparison of Conventional & Entergy Approaches for Flaw Evaluation Flaw Type Feature Conventional Approach Entergy Approach Surface Flaws Stress Distribution fixed at initial flaw Variable distribution along length of (ID & OD) location tube & flaw face pressurized Part Through wall Cylinder Fixed "R/t" ratio of 4.0 Variable "IR/t" ratio from 1 to 300 Geometry Flaw Fixed aspect ratio; "a/c" = 0.33 Variable aspect ratio; "a/c" from 0.2 Geometry to 1.0 Flaw Growth Only growth in depth direction Growth both in the depth and length evaluated directions evaluated independently Through wall Stress Uniform tension @ initial flaw Variable along length; both Axial Flaws location membrane and bending components considered; flaw face pressurized Model Center cracked panel without Thick cylinder with correction for I P 8
correction factors flaw/tube geometry 25
Vl CEDM Summary Results for ANO-2 n ID flaws do not grow significantly for all nozzle groups n OD and Through-wall flaws uphill and mid-plane locations for all nozzle groups do not grow significantly n Only concern is for downhill locations q Small angle nozzles flaw grow within one cycle Large angle nozzles weld extends into blind zone 26
CEDI Summary Results for ANO-2 Only area of concern is the lower hillside
(+/- 450CircumferencE Downhill 27
Probabilistic Analysis Pete Riccardella 28
Probability of Leakage n Analysis based on prior MRP developed technology n Weibull analysis of plant inspection data q Population = 30 plants that have performed non-visual NDE or visual exams that have found leakage or cracking q 12 had leaks or significant cracking q Includes both Nozzle and Weld Metal Cracking n Plants w/ multiple affected nozzles extrapolated back to predict time to first leak or crack 29
All inspection data adjiusted to 600 F (
= 50 kcaL/mole) 0.90 0.63 0.50
-4 59 8o
-4=
cc i..
PX4 a,
J; 0.20 0.10 0.05 I
I 0.02 0.01 10 IEDYS 100 JU
Effect of Inspections on Leakage n Primary Goal of MRP PFM is to ensure that inspections protect against nozzle ejection n However, effect of inspections on leakage probability (Weibull hazard rate) generated as by-product of analyses n Results indicate that reasonable assurance against leakage maintained, dependent on inspection coverage (80% assumed) 31
Leakage Probability (w/o NDE) 1 a_
0.9 0.8 u 0.7
.5 3 0.4 A
2 0 3 ------------
/
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/
- ~ ~ *Mont;
/
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~~~~~~~~~~Leak s
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.- I I-cI-
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Probability of Detection Assumptions for NDE n Non-Destructive Examinations (NDE) q POD = f(crack depth) per EPRI-TR-1020741 q 80% Coverage Assumed n POD Curve Compared to Vendor Inspection Demonstrations 1Dimitrijevic, V. and Ammirato, F., "Use of Nondestructive Evaluation Data to Improve Analysis of Reactor Pressure Vessel Integrity, " EPRI Report TR-102074, Yankee Atomic Electric Co. March 1993 33
POD Curve for NDE (Illustrating Comparison to Vendor Demonstrations)
Probability of Detection Curve Used in MRPER Algorithm Defected 90%
75%
z 60%
-'--FULLV Curve from Ref.1 06 x Vendor 1
=
45%
0 Vendor 2 30%
15%
Not Detected 0%
IX 030 X
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 Flaw Size (in) 34
Effect of NDE on Leakage Probability 2.OOE-01 1.80E-01 1.60E-01 1.40E-01 t
1.20E-01 No Insp.
1.OOE-01 10%
FULLV@ 2-yr Interval FULLV @ 4-yr Interval 0
-- /FULLV
@ 8-yr Interval 3 8.OE-02
° 6.OOE-02 4.OOE-02 2.OOE-02 O.OOE+00 0
5 10 15 20 25 30 35 40 EDYs 35 C) (D
Proposed Probabilistic Approach for ANO-2 and W-3 Order Relaxaion n Conduct Plant Specific Probability of Leakage Analysis n Include effect of proposed inspection n Evaluate inspection zone limitations in terms of reduced examination coverage n Being performed on CEDMs/ Expected to be conservative for ICls n Expect only minor effect on probability of leakage due to limited inspections 36
Entergy Operations Inc.
a CentralEngineeringPrograms Appendix C; Attachment yy Page 1 of 15 Engineering Report M-EP-2003-002-00 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesom Verified by: B. C. Gray Note : Only for use when RQ;td/t Is between 2.0 and 5.0 (Thickwall Cylinder)
Refrences:
- 1) ASME PVP paper PVP-350, Page 143; 1997 (Fracture Mechanics Model)
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8.8"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 MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first nput is to locate the Reference Line (eg. top of the Blind Zone). The throughwall flaw "Upper ip" Is located at the Reference line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Oput is the Upper Limit for the evaluation, which Is the bottom of the fillet weld leg. This is showni 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)
IDeveloped by:
Verified by:
I Entergy Operations Inc.
Central Engineerng Pmograms Appendix C; Attachment yy Page 2 of 15 Engineering Report M-EP-2003-0020 Input Data :
L :=.794 od:= 4.05 id:= 2.728 Pnt := 2.235 Years:= 4 1iurn:= 1500 T := 604 v := 0.307 aoc:= 2.67 10 12 Qg:= 31.0 Tref := 617 Initial Flaw Length TW axial Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Poissons ratio @ 600 F Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth MRP)
Reference Temperature for normalizing Data deg. F
[
-Qg r
1 I
Co = e 1.103.-
3 T+4 59.6 7 T+459.67)J Tinopr:= Years 365.24 od 2
R; = id 2
t:= Ro-Ri Rm:= R +
2 CFinhr := 1.417-105 Tinopr k Jim Pmtblk:= l-50"m I
L 2
Developed by:
Verified by:
Entergy Operations Inc.
Central Engineerng Programs Appendix C; Attachment yy Page 3 of 15 Engineering Report M-EP-2003-0020 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 (ks)
Column 5W = OD Stress data at each Elevation (ksl)
DataAll:= -
0
- 5 1 2 3
~~~~~~4
~
5
- 0.
0
-27.4
-24.36
-22.21
-20.41
-18.98 1i 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 1-0 1.92 21.5 25.56 33.55 48.09 66.36 8
f 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
.. 1'kj Fej ijct
-PP AIlAxl:= DataAIllI (I)
AIIID= DataAIl (5)
AIIOD= DataAl Developed by:
Verified by:
[Developed by Verifedby I
Entergy Operations Inc.
Central Engineering Programs Appendix C; Attachment yy Page 4 of 15 Engineering Report M-EP-2003-002-00 C)
'I) 0 0.5 1
1.5 2
2.5 Axial Distance above Bottom [inch]
ID Distribution OD distribution 3
Observing the stress distribution select the region in the table above labeled DataAle that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0
-27:
404 -24356
!222
-0: M4 7 -18 978
-g. ^ ^ ^ W
-IL=
Data:=
1M8 M
2.79 4 2:723
. 5 4.20
.t.--.
104 1.78 7..
. 1 1.e 88,3. 8 37 1 8 )
(5)~
l) 4'm zigLF.C l 2&f)
F2 1jyL AN & C I (o)
Axl := Data ID Data l 2 4S IA-m-1 OD:=) Data5 R D ress( a t ROD:= regress(Axl, OD, 3)
RID:= regress(AxI, ID, 3)
Developed by:
Verified by:
lIDeveloped by:
Verified by: I C17
Entergy Operations Inc.
Central Engineenng Programs Appendix C; Attachment yy Page 5 of 15 Engineering Report M-EP-2003-002-0 FLCntr:= BZ - I Flaw Center above Nozzle Bottom IncStrs avg:
ULStrs.Dist - BZ 20 No User Input required beyond this Point Calculation to develop Stress Profiles for Analysis Hoop Stress Profile In the axial direction of the tube for ID and OD locations N:= 20 Loc,:= FLCnt - L Number of locations for stress profiles i:=..N + 3 Incr. :=
I ifi < 4 IncStrs.avg otherwise Loci:= Loc i-I + Incri SID:= RID + RID LoC + RID,-(Lo 2 + RID (Loci)3 i
3 4
lj 6;
SOD1:= ROD + ROD Loc. + ROD (Loci) + ROD (Loci)3 3
4 1
5 6
Developed by:
Verified by:
IDeveloped by.
Verifed by. l
Entergy Operations Inc.
Central Engineenng Programs Appendix C; Attachment yy Page 6 of 15 Engineering Report M-EP-2003-002-00 Development of Elevation-Averaged stresses at 20 elevations along the tube for use In Fracture Mechanics Model j:=..N 5id SIDj + SID jl + SIDj+2 3
SodJ =
SODj + SODj+1 + SODj+2 3
if j=l Sodj (j + 1) + SODj+2 otherwise j +2 Sidj *(i + 1) + SIDj+2 j+2 otherwise 5 od. + SidP 1 =
J J + ph Sod. - Sid.
Obi 2
Stress Distributions for use In Fracture Mechanics Analysis Membrane Stress Bending Stress OD Stress ID Stress (TM =
0 I
3 4
.-6y 7
8 a
z1
2 3
15 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 38.086 V.
I, art C :
M8i r4.
r,.
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 =
3 0,
4"'
f3'
-'0f 0
18.023 23.172 26.475 28.858 30.719 32.256 33.58 34.757 35.83 36.826 37.766 38.662 39.526 40.365 41.185 Sid =
0 gx3 Mt0 E12 0
25.096 27.036 28.176 28.914 29.42 29.779 30.039 30.226 30.361 30A53 30.513 30.546 30.555 30.545 30.518 lDeveloped by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix C; Attachment yy Page 7 of 15 Engineering Report M-EP-2003-002-00 PrOPLength := ULStrsDist - (LCntr + I)
PropLeng*t 0.242 Calculations : Recursive calculations to estimate flaw growth Recursive loop for Entergy Model Twcpwscc:
i-0 10PI NCB 00 Cb4 k
[while i Ilim l1 Im.appld -
Gml am2 am3 a 3 am4 a 4 0 m5 0m6 G6 0m9 Gml Om GM,,
if Ii
- if 0<
i5 io+ IcStrs.avg if 10 + IncStrs avg < Ii S Io + 2 fInCSt5.Savg if 10 + 2 IncStrs.avg < I S 10+ 3 IncStrs.avg if 10 + 3 fInCStrs.avg < li S 10 + 4 fIncStrs.avg if 10+
4 fIncStrs.avg <1 li 10+ 5-InCStrs.avg if 10+
5 fIncstrs.avg < i 1 lo+ 6 lInCstrs.avg if 10 + 6 fIncStrs.avg < I S 10 + 7 nCStrs.avg if 1 + 7 Incstrs.avg < ij S 10 + 8Incstrs.avg if 10+ 8Incstrs.avg I S 10 + 9 fInCStrs.avg if 10 + 9-Incstrs.avg < I* S 0 + 10IncStrs.avg if L + 10-Incet..,
<1. S L + I ncct..,,
Developed by:
Verified by1 IDeveloped by.
Verfifedby. I
Entergy Operations Inc.
Appendix C; Attachment yy Engineering Report Central Engineering Programs Page 8 of 15 M-EP-2003-002-00 12 U
I'6 1
U CYm13 if Io + ll InCStrs.avg < IS 10+ 12fInCstrs.avg am 14 ifI 0 + 12-IncStrs.avg < I 10+
3 -fncStrs.avg am15 if 10 + 13InCstrs.avg < i1S 10+ 14fIncstrs.avg (m 16 if 10 + 14fIncStrsavg < i 1 l + 15-InCstrs.avg am 17 if 10 + 15InCstrsavg < i 5 10 + 16fIncStrs.avg Om18 if 10+ I6-Incstrsavg < I 5 Io + 17-InCStrs.avg Cm19 if 10+
7-fncstrs.avg < i< 10+ 18-InCStrs.avg oM20 otherwise ab.appld b I if I S 10 Ob2 if 10 < li
+ InCSrsavg Ob3 if 10 + ICStrs.avg < i S1 + 2CStrs.avg b 4 if 10 + 2IncStrs.avg < I 510 + 3-InCStrS.avg Ob if I0 + 3-ncstrs.avg < I 1 + 4ncSts.avg b 6 if I0 + 4IncSts.avg < S I0+ 50 IncStrs.avg ab7 if 1 0 + 5-Incstrs.avg < 1 5 lo +
IncStS.avg a b8 if I0 + 6IncStrs.avg < i< 5Ilo+ 7 ncStrs.avg rb if 10 + 7Incstrs.avg < i 10 + 8 IncStrs.avg Ob 0 if lo + 8-IncStrs.avg < i< Sto + 9InCSts.avg Ob7 if 10+ 9-Incstrs.avg < i 10 + 0 IncSts.avg Ob 12 if I + 10- IncStmavg < i S 10 + I -InCSts.avg Ob1 if 10+ 1l-IncStrs.avg < I 5 I
+ 121ncSts.avg Ob 14 if I0+ 12 IncSrs.avg < I 50 +13-InCSfsavg Ob if 10+ 13 IcStrs.avg < 1 10 + 14-IncStrs.avg Ob 16 if 10 + 14-IncStrs avg <
I +15-IncSts avg Cyb1 if 10 + 15Incsts.avg <
I 1
+16 IncSt;.avg Gb12 if 10 + 16-InCStrs.avg < I S lo + 17 lncSts.avg b 9if 10 + 17-Incsrs.avg < I 1 + 18InCstrs.avg Developed by.
Verified by.
Entergy Operations Inc.
Central Engineering Prograns Appendix C; Attachment yy Page 9 of 15 Engineering Report M-EP-2003-002-00 lOb2. otherwise
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outpu,(i 1) 365.24 nftmnt.
+-;1.:
w fL i,,aft "z r-7
--- r ej-dc I-
,:-
37 CV2-
1-1!;(
L-Developed by:
Verified by:
lIDeveloped by.
Veified by I
Entergy Operations Inc.
Central Engineering Programs Appendix C; Attachment yy Page 10 of 15 Engineering Report M-EP-2003-002-00 r _
- r~(1,2)
£1 output(i,3) i- 0 OU'Put(i,4) 1 i output(i 5)
IApp output(i 6)
' APPODi output(i 7)-
- KAPPID, outputs 8)-
Kmembrnl);
- outputo,
- 4) Kmembml D
output Io) 4-Kbend outPUt(I, 8)
- KbendD, i +
Ki Ii+
i_, + Dlengrthi_l NCBv NCBi() + Cblk output O.:=.O iim I Developed by.
Veified by I Developed by:
Verified by:
Entergy Operations Inc.
Central Engineering Programs Appendix C; Attachment yy Page 11 of 15 Engineering Report M-EP-2003-002-00 ProPLength = 0.242 Flaw Length vs. Time 1.5 TWCpwsc pwcj, 3 05 Ce 0.5 0
-0.5 0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
Entergy Model TWCPWSCC I1)
Operating Time {years}
Increase in Half Length IiI 2
C)
C)
C)
C) 1.5 0.5 0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {Years) 4 Developed by:
V
Entergy Operations Inc.
Central Engineering Programs Appendix C; Attachment yy Page 12 of 15 Engineering Report M-EP-2003-002-00 300 z
a, 200 rj) 0 U
100 vn 0
0 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {Years}
OD SIF - Entergy Model ID SIF - Entergy Model SIF Average 0
t 7
I 7
0 t
7 I
Aged by 0
C\\?
Developed by:
Ver
Entergy Operations Inc.
I Central Engineering Programs Appendix C; Attachment yy Page 13 of 15 Engineering Report M-EP-2003-002-00 TCpwsc~
Tcwc(j,6) 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 TWCp~o wPWSVCr(j,)
35.69 39.253 39.279 39.305 39.331 39.357 39.382 39.408 39.434 39.46 39.486 39.512 39.538 39.564 39.59 39.617 TWWSC
=,
" wc(j,g 8) 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 I
.A--
ILJveIo1UP Dy:
Verified by Ver.fied by:
Entergy Operations Inc.
Central Engineering Programs Appendix C; Attachment yy Page 14 of 15 Engineerir M-EP-20 H o o p S tre s s P lo t 60 4 0 Is 20
.4 0 300 -
=T I
200
,u1 2 0 0 100 0
0-1 0 1.5
- 2. 0 D is la n c e fro m N o z z le B o tto m in c h )
2.5 3.0 ng Report b03-002-00 7
0 7
t t
0 7
0
'erified by:
CgO
D S u rfa c e S IF ID S u rfa c e S IF I -
A v e ra g e S F
I 0
1 2
3 4
O p e ra tin g T im e
{y e a rs )
Developed by:
V lIDeveloped by:
Vt
Entergy Operations Inc.
Central Engineering Prgrams Appendix C; Attachment yy Page 15 of 15 Engineering Report M-EP-2003-002-00 I
I 1.0 -
5-I 0.5 -
o.o 0
1 2
3 4
0 perating Tim * (years)
Developed by:
Verified by:
I Developed by.
Veified by I
Page 1 of23 Stress Corrosion Crack Growth Analysis Throughwall flaw Developed by Central Engineering Programs, Entergy Operations Inc bevelopedby: J. S. Brihmadesam Verified by: B. C. Gray Note : Only for use when RQSd/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 1.3 inch above Nozzle Bottom Calculation
Reference:
MRP 76 th Percentile and Flaw Pressurized Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The first Ohput s to ocate the Reference Line (eg. top of the Blind Zone). The tnohwail flaw 'Upper rip Is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
BZ:= 1.3 Location of Blind Zone above nozzle bottom (inch)
The Second rZpout is the Upper Limit for the evalwtion, which is the bottom of the fillet weld leg. This s shown on the Excel spread sheet as weld bottom. Enter this dimension (measvred from nozle bottom) below.
ULStrs.Dist:= 1.786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Page 2 of23 Input Data :
L :=.794 OD:= 4.05 ID := 2.728 Pint:= 2.235 Years:= 4 1jim:= 1500 T := 604 v := 0.307 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 aoc:= 2.67 10 12 Qg := 31.0 Trf := 617 Q g -
I cI 1
C:=e1.103 103 T+459.67 Tf+459.67).a Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F Timopr := Years.365-24 OD 2
ID 2
t:= Ro-Ri Rm:= Ri + 2 CFinhr:= 1.417-105 Tiflnopr Cblk :=T r
lim Pmtblk:= I 50 1 I
L 1 =L 2
LI:= BZ I
Page 3 of23 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 (ks, Column "5" = OD Stress data at each Elevation (ksi)
DataAIl:=
tt0 1
S 2
-I 3 - - :
4 5
0 0
-27.4
-24.36
-22.21
-20.41
-18.98 91 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
d 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 2.18 14.83 22.26 34.78 49.05 63.38 AlAx:= DataAIl AIIID := DataA~l I
AIIOD := Dat (5
A111D= DataAhl A11OD= DataAlI
Page 4 of23 V
Ic/.
_,;n !
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).
(o
-27.404 -24.356 -22.209 -20.407 -18.978) 0.483 0.633 0.87 17.665 Data:= I 1.18 29.798
-1.486
-3.599
-4.44
-5.268 16.422 14.61 12.415 9.376 26.049 22.723 18.95 14.201 27.792 24.8 24.321 26.989 28.469 27.591 34.284 45.104 28.918 31.388 43.882 63.718 )
1.428 33.623 1.627 32.364 1.7 86 27.394 Axl:= Data ID:= Data S)
OD:=Data RID := regress(Axl, ID, 3)
ROD:= regress(Axl, OD,3)
Page 5 of23 FLCntr:= BZ - I Flaw Center above Nozzle Bottom ULStrs.Dist - BZ Iflcstrseavg :=
20 ULStrs.Dist - BZ InCrEdg:=
20 RIDAII:= regress(AIIAx1, AIlID, 3)
RODAII := regress(AI1Axi, AIIOD, 3)
No User Input required beyond this Point Calculation to develop Stress Profiles for Analysis Hoop Stress Profile in the axial direction of the tube for ID and OD locations N := 20 Loc0 := FLCnt - L Number of locations for stress profiles i:= I..N+ 3 Incr.:=
I if i < 4 IncStrs.avg otherwise if i<4 Incredg :=
2
Page 6 of23 I
u6 Loc. := Loc I + Incri Locl j:= 1° if i =
lLocI + Incredg otherwise SOD. = ROD + ROD4 Loci + ROD 5-(Loci)2 + ROD6.(LDci)
SID := RID3 + RD4-Loc + RID5 (Lc)2 + RID 6-(LoCi)3 SIDAII = RIDA113 + RIDAIILoCIi + RIDA115(Locli) + RIDAII (Locli)3 SODAII := RODAII + RODAII Locli + RODAjII(LoCli)2 + RODAII (Locl )3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j:= I..N SID + SID
+ +SID 2 Sid:=
-+
+2 if j 1 Sd
- (j + ) + SIDj+2
-1 2 otherwise j +2 Sodi =
Sod.all =
SOD. + SOD.j+ + SOD 2 j
j~l j+2 3
if j = I Sodj l-(j + 1) + SODj+2 otherwise j+2
=I SOD
+ SODAI j+ + SODA j
I
$1 j+2~ if jl Sid.alI:=
J SIDAII + SIDA11jI + SDAl11+2 3
if j = 1 Sid.all (j + ) + SIDAIj+2
- -I j+2 otherwise j+2 I
Sod.al
- (j + 1) + SODAIlj+2 j+2 otherwise Sod. + Sid.
. :=
J J + Pt Sod. - Sid.
j 2
Sod.ai. + id.alj
- all 2
+ PInt
Page 7 o23 Stress Distributions for use In Fracture Mechanics Analysis Membrane Stress Bending Stress OD Stress ID Stress Membrane stress (Edge Crack)
(Fm=
0 0
15.27 18.819 21.119 22.794 24.115 25.215 26.169 27.022 27.802 28.53 29.217 29.874 30.507 31.122 31.723 Ob =
0 ~
0 4.731 4.823
-4.766 4.625 4.426 4.184
-3.905
-3.594
-3.254
-2.885
-2.489
-2.066
-1.617
-1.142
-0.64 Sod =
0 8.303 11.761 14.117 15.934 17.454 18.796 20.029 21.193 22.314 23.41 24.493 25.572 26.655 27.745 28.848 Sid =
'I0 0
17.766 21 A08 23.65 25.184 26.306 27.164 27.839 28.381 28.821 29.18 29.471 29.705 29.889 30.029 30.128 am.all =
0 0
5.53 12.037 16.08 18.889 20.99 22.646 24.005 25.153 26.146 27.022 27.807 28.518 29.169 29.77 30.329 ProPLength := UStrs.Dist - (FLCntr + 1)
Propmength = 0.486
Page 8 o23 Calculations : Recursive calculations to estimate flaw growth Recursive loop for Entergy Model and Industry Model TWCpwsMc =
10+I NCB 4-Cb1k while i Ilim I m.appld +-
om if
<10 am 2 if 1
10 + LnCStrs.avg
- M3 if 10 + ICStrsavg < I S 10 + 2 InCStrs.avg
- m4 if I0 + 2Incsts.avg < i S 1 0 + 3Incst.avg am5 if 10 + 3 IncStrs.avg < Ii S 10 + 4 IncStrs.avg
- M6 if lo + 4ncStrs.avg < i S 0 5IfnCStrs.avg am7 if I0 + 5 IncStrs.avg <
1i I0 + 6IncStm.avg am8 if 0+ 6-IncStm.avg < i S 0 7nCStrs.avg 1M9 if I0+ 7InCstm.avg <
1i I0 + 8 1ncStrs.avg am 8 if I0 + 8Incstrs.avg < i 1 0 + %*ncs.avg am if 10 + 9-Incstrs.avg < li S 0 + 1fIncStrs.avg am12 if 10+ 10-IncStrs.avg < i S 10 + IflICStrs.avg am3 if 10+
I lncStrs.avg < i 1 + 12InCStrs.avg am14 if 10 + 12IncStrs.avg < 1i1*10 + 13InCStrs.avg am5 if 10 + 13fnCStrs.avg < 1i1 1 0+ 14InCStrs.avg am16 if 10+
l4 -1ncStrs.avg < I S 10+ 15InCStrs.avg am if 10 + lSlncStrs.avg < Ii S 10 + 16JflCStrs.avg am8 if 10 + l6 f1nCStrs.avg < Ii S 10 + 17fInCStrs.avg am if 10 + 17-IncStrs.avg < I S 10 + 18-IncStrs.avg
Page 9 of23 I M0omerwise Cyb.appld Obl if 1j 10 Cb2 if 10 < i< 10 + ICStrs.avg Ob3 if I0+ InCstrs.avg < 1 1 0 + 2IncSts.avg ab 4 if 1 + 2 Incstrs.avg < I 1
0 + 3InCStrsavg Cyb5 if 10 + 3 Incstrs.avg < li 510 + 4-InCStrs.avg (Fb if 1 + 4 InCStrs.avg < i I0 + 5InCStrs.avg b 7 if 10 + 5-IncSrsavg < i 10 + 6InCStrs.avg ab if 10 + 6-IncStrs.avg < li 10 + 7-IncSts.avg ab if 1 +6 IlnCStrs.avg <
i o +
IlnCStrs.avg Ob 1if I0+ 8-IncStrs.avg <
S I1 + 9IncStrs.avg Ob 11if lo+ 9IncSrs.avg < I S 10 + 0l-IncStrs.avg Ob12 if 1 + 10-Incstrs.avg < i1
+ I1IncStrs.avg sb 13if I0+ I -IncStrs.avg < i1
+ 12-IncStrs.avg Ob 14 if 1 + 12-1ncStr.avg < i I 0+ 13-InCstrs.avg Ub 15if 1 + 13-Incsts.avg < I 1+ 14-InCStrs.avg Ub 16 if 1 + 14fIncstrs.avg < i< 1 + 1fInCStrs.avg Ob17 if 10 + 15-IncStrs.avg < I 1 + 16-InCStrs.avg b 18 if I0+ 16-IncStrs.avg < I 1 + 17InCStrsavg Ob if 1 + 17 -IncStrs.avg < Ii < 10 + 1-InCStrs.avg cyb2o othierwise Xi +- 12-( - v 2)] 0.
1 16 0 t)0.
Aemi F 1-0090 + 03621 i + 0.0565.(Ai)2 _ 0.0082 (i)
+ 0.0004 (i)-
8.326 10 6(A)
Abm i
-0.0063 +.0919-Xi - 0.0168. (Xi)2 - 0.0052 (Xi) + 0.0008.(Ai)4 - 29701-100
- .(Ai)5 Aeb F 00029 + 0.0707-i - 0.0197(X)
+ 0.0034 (Ai)3 -0.0003(i
+ 8.8052-10 (i)
~~~~~Ahh F0-9961 - 0R06-IL + 012-39-(;
0021{
+ OA.007
)4 - 499391
(;
Page 10 of23
.. rr.
Kpmn a Gmappld (IC 0.)
Kpbi 0
Ob.appld (1I;)
KmembrnOD. 4(Aemi + Abm.) Kpm KmembnIjD 4-(Aem. - Abmj).Kpm KbendODi
- (Aebj + Abbi).Kpbi KbendlD;
- (Aeb - Abbj)-Kpbi KAppODi 4 KmembrnOD + KbendOD, KAPpRI 4 KmembrnID + KbendID, WHj m I.(XA i) 0.5 KAppOD + KAppR
- KApp, 2
KWH.Icnr.strs +- Om.appld'(Rldi)
Kai KApp
- 1.099 Kai 9.0 if KC,< 9.0 lKa. otherwise Dlen 4 CO(Kai - 9.0)1.16 Dlengrth, -
Dlen CFinhrCbLk if Kai 80.0
-10 I
410 CFinhrCblk otherwise outputo 4)-
NCB.
output(ij 1) 0 365.24 output(i 2)
Xi outPut(i, 3) i 1
outpu'(i,4) li output(i, 5)
- KApp, output(i 6) 4KAppODi output(i 7) 4 KAppID, T
R
\\
I I
Page 11 of23 output(i, 8)
KmembmOD.
outputs g) 4 KmembmlD.
output(i 10)
KbendOD outputo, I
- Kbend D Pu(i, 12)
WHi output(i 13)
KWH.Icnr.Strs; i
i + I Ii I1,1 + Dlengrth,_
NCBi 4-NCBi- + Cblk l
I
Page 12 o23 Recursive Loop For Edge Crack Model TWCEDGpwscc :=
i+-O LI +- LII NCB 0 +- Cblk while i 5 11im l 0m.appld 4-Om all if LI 5<LI Om.al 2 if LIO < L l S LIO+ IcrEdg Om.all if L1O + InCrEdg< L 1*Ll+ 2IncrEdg 0m.all4 if L + 2-InCrEdg < LI
- L1 0 + 3InCrEdg am.all5 if LIO+ 3-InCrEdg< LlI LIO + 4 IncrFdg Um.all6 if
+ 44 IncrEdg < LI, LO + 5 nCrEdg 0m.all7 if Ll + 5-InCrEdg < LjI 5 L1O + 6-InerEdg am.all8 if L1O + 6-IncrEdg < LI LIO + 7 InCrEdg am.all if LIO + 7 IflCrEdg < LI
+ lOIncrEdg 0m.all12 if L
+ 10IncrEdg < L i L
+ ll IncrEdg am.all13 if L
+
fIncrEdg < L i <LI + 12. ICrEdg ym.all 4 if LI 0 + 12-InCrEdg < LI i <
0+ 13-nCrEdg 0m.all 5 if LI+ 13-IlnCrEdg< LlI L1 0 + 14-InCrEdg ym.all16 if LI + 14-IncrEdg < Li S LI + 15-IncrEdg Om.all17 if L
+ 15-InCrEdg < LIi S LI + 16-nCrEdg Om.all1 if LI 0 + 16lfnCrEdg < L i L
+ 17. lCrEdg Gm.all19 if L
+ 17-inCrEdg < L i L
+ 18-InClEdg Gm.alI otherwise b 4 ULStrs.Dist I
I
Page 13 of23 I T TTT I
TT1 r
LI.
Z. -
0.99 if-2 1.0 b
otherwise b
Fab +- 1.12- 0.231 (Z;) + 10.55. (Z) 2 - 21.72.(Zi)3 + 30.39.(Z i)4 Kedg.Crk. -
appldj iY if (mappld'J4i;)
0 (Jnmappld(x Lji)
- Fab otherwise KA 4-Kedg.CrkL 1.099 i
I Ka 19-° if KA S5 9.0 l KA otherwise I
Dien CO-(Ka, - 9.0)1.16 Dlengrth 4-Dien CFinhrCblk if Ka; S 80.0 410 10 CF"u.,CbIk otherwise outputoO) - i NCB.
output.
(iI1) 365-24 P(i, 2)
L 0
output(i 3) 4-Dlengrthi output(i 4)
Kedg.Crk output(i, 5)
l +
i-i ngrth NCB; i NCB il + Cblk output
Page 14 of23 Pressurized Cylindrical Shell with a Fixed End Containing an axial throughwall Crack: Yashi &
Erdogan; Murakami Problem set 9.38 Wmura =
By
-0 I
1 ~I~
2 ' "~-
O 1
1 2.933 1
1 1.1 0.151 2
1 1.5 0.346 3
1 2
0.572 4
1 10 1.286 5
2 1
5.754 6
2 1.1 0.284 7
2 1.5 0.839 8
2 2
1.34 9
2 10 1.645 iG 3
1 9.164 111 3
1.1 0.49 3
1.5 1.5
[13 3
2 2.015 4
3 10 2.067 15 10 1
43.555 16 1 0 1.1 2.853
.7 10 1.5 4.703 8
10 2
4.912 i1 101 10 4.923 A :=rMFmura (C)
C:
W~m=r (2)
Fm= Mffmura Mmem := augment(AC)
Rff := regress(Mmem, Fm, 3)
F(A,C):= inte4RMF, Mmem, Fm (C)]
F(10, 10) = 4.928 I
I
Page 15 of23 TWCMura:=
i1 +_ LL 0
2 NCB0 4-Cblk
((while i lim Cm.appld Cym.all am all2 am.all smi4
- m. all Cym all6 smi6 Cym.alI7 G~m.all, am.all am.all am.all am.all Cm.all Cym.all14 Cm.all15 Cm.all1 6 Cm.a11 17 Cym.al 18 Cym.al 19 am.a1 C 4-2.087 - FLCntr 7
C if LI *LI li 0o if LI 0<LI <LI + IncrEdg if Lo +IncrEdg< Li Li+ 2IncrEdg if LI + 2IncrEdg< Li<L+
3 24 ncrEdg if LI 0 + 3IncrEdg< L i< L 0 + 4InCrEdg if LI + 40IncrEdgI< Li L+
5IncrEdg if L + IncrEdg< Li< LI + 6ncrEdg if LI + 6IncrEdg< Li< LI + 7ncrEdg if Lo + 7IncrEdg0< Li L+
8InCrEdg if LI + IfncrEdg< Li< LI + 9-InCrEdg if LI + 9IncrEdg < LIi< Ll + 1ficrEdg if L0+ 10IncrEdg< Li LI0+ IncrEdg if L 0+ I -IncrEdg < L S
<LI0+ 12-IncrEdg if L + 12-IncrEdg< L <L 0 + 13Incddg
- if L 0+ 13-IncrEdg < L S
<LI0+ 14-IncrEdg if L
+ 14IncrEdg< L <LI + 15-InrEdg if L
+ 15+IncrEdg< Ls <L
+ 16IncEdg if L
+ 16IncrEdg< LI <LI + ITfInCrEdg if L
+ 17IncrEdg< Li <LI + 18IncrEdg
,otherwise 1
l l I~~~~~
_I
Page 16 23 AT4--
FM 4-F(Z AT)
KMura +- m.appld ( L)
- 5FM KA. 4-KMura-1.099 1
I Ka, -
9.0 if KA S 9.0 KA otherwise Then. 4-co.(Kai - 9.0)1.16 Dlengrth, 4-Dlen1CFinhrCblk if Ka S < 80-0 410
- CFih.Cblk otherwise output, 0) 4-i NCB; output(i 1) 365.24
°U'Pu'(i, 2)4-LI 1
LI output(i, 3) 4 Dlengrth output(i 4)
KMura Output(i, ) F M i + i+ I Llj L L 1 + Dlengrth_
NCB;.NCBi1
+ Cblk output j := 1.. Ilim
Pag ProPLength = 0.486 Flaw Length vs. Time 1.5 I
TwC
.a TWCPWSCC(j, 3)
'7 TWCEDGp PW
)
2 Mura(j,2) c: -- - -
3 0.5 0 !
-0.5 0 le 17 of23 i~~~~~~~~~
C'~~~-'Z-0.5 1
1.5 2
2.5 3
3.5 4
4.5 TWCPWSCC I )
Operating Time {years}
Entergy Model Edge Crack Model Erdogan &Yashi Clamped Tube Model i
Page 500 450 400 350 a
Cr U-U
._~
)
300 250 200 1 8 of 23 7
7 7
7 7
7 X 1
/,,
e 150 100 50 0 0 0.5 1
1.5 2
2.5 3
3.5 4
Operating Time {Years}
OD SIF - Entergy Model ID SIF - Entergy Model SIF Conventional approach {Constant Stress Model}
SIF Conventional approach ( Increasing Stress Model)
Entergy Model - Average used for Flaw Growth Edge Crack Erdogan-Yashi clamped Tube Model I
Page 19 o23 TWCpwscc
=
'(j, 6) -
23.407 23.417 23.428 23.438 23.448 23.459 23.469 TWCEDGpwscc
=
(j,2) 1.324-10 -3 2.64810 -3 3.972-10 -3 5.296-10 -3 6.62-10 -3 7.944-10 -3 9.268-10 -3 TWCpwsocc.n T CP (j.7) -
29.92 29.93 29.941 29.951 29.961 29.971 29.981 TWCpwsc 27.884 27.895 27.906 27.917 27.928 27.94 27.951 I
I
Page 20 of23 23.48 0.011 29.992 7 27.962 23.49 0.012 30.002 27.973 23.5 0.013 30.012 27.984 23.511 0.015 30.022 27.996 23.521 0.016 30.032 28.007 23.532 0.017 30.043 28.018 23.542 0.019 30.053 28.029 23.552 0.02 30.063 28.041 23.563 0.021 30.073 28.052
Pagewe 21 of23 III~
Hoop Stress Plot ID Hoop Stress 60 -
ODHoopStress 40Top of 40 -1o MMnd Zole
Page 22 of23 r
I e 20-05 I
0- -40 8ooo of NeC I
0.0 0.5 1.0 1.5 2.0 25 3.0 Distance from Nozzle Bottom inch}
ilK.
I._
Page 23 o23 0.
OC0 1
-2.009 2
6.13 3 20.789 22.133 5 23.542 6 25.021 SOD= 7 26.57 8 28.192 9
29.891 10 31.667 11 33.525 12 35.465 3 37.491 4 39.605 15 41.809 I
-I
Entergy Operations Inc Centra I Engineering Programs 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: Y. 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, "O" Degree Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rmit" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 65-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 necessmr to evaluate the stress dstribution on the flaw both for the initial flow and for a growing flaw. This Is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured pward from the nozzle end.
Refp0 int = 1.544 To place the flow with repsect to the reference point the flaw tips and center can be located as follows:
- 1) The Upper 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 Developed by:
J. S. Bdhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.3966 ao := 0.0661 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Pfnt = 2.235 Years := 4 Ilim := 1500 T := 604 a0C := 2.67 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2d id Rid t
Ro-Rid t
Rm=Rid+ +
Timopr:= Years-365-24 CFirdhr = 1.417-105 Timopr Cblk 11im Pmtblk =
0 L
co:= -
Rm t
_ [ Qg (i
- 1. 103-C 3 tT+3459.67 Co := C01
.a0c Temperature Correction for Coefficient Alpha 75 percentile MRP-55 Revision 1 Developedby:
J. S. Bnhmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data In the table below. The column designations are as follows:
Column "Ol = 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 (ks)
Column 4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (kso AllData :=
.t 0 X D=-
1 0
1 2
3 i
4-5 0
0
-27.4
-24.36
-22.21
-20.41
-18.98 0.48 0.63
-1 A9
-3.6
-4.44
-5.27
-2 0.87 17.66 16.42 14.61 12A1 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 1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.091 66.36 8X 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:= A (l)ata()
IDAII:= AIIData(i)
ODA11:= AlIData()
Stress Distribution 100
-, IDAI A OD-WW D,
l 50 0
-50 0 0.5 1
1.5 2
2.5 AXLen Axial Elevation above Bottom [inch]
3 Developed by:
J. S. n7hmadesam Verfied by B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003002-01 Observing the stress distribution select the region In the table above labeled DataA that represents the region of Interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection In the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equar' sign (Shift-Colon) then Insert the same to the rfight of the Mathcad Equals sign below (paste symbo.
Data :=
0 0.483 0.87 1.18 1.428 1.627 1.786 1.919 2.051
-27.404 0.633 17.665 29.798 33.623 32.364 27.394 21.498 16.944
-24.356
-1.486 16.422 26.049 27.792 28.469 28.918 25.556 23.793
-22.209
-3.599 14.61 22.723 24.8 27.591 31.388 33.55 34.064
-20.407
-4.44 12.415 18.95 24.321 34.284 43.882 48.089 49.472
-18.978)
-5.268 9.376 14.201 26.989 45.104 63.718 66.365 67.672 Axi := Data<°)
MD:= Data(3)
ID := Data(l)
TQ := Data(4)
QT = Data(2)
OD:= Data(5)
RID:= regress(Axl,ID,3)
RQT:= regress(Axl,QT,3)
ROD:= regress(Axl,OD, 3)
RMD:= regress(Axl, MD,3) 1LLStrs.Dist = 1.786 UpperAi nozzle be RTQ := regress(Axl,TQ,3) dal Extent for Stress Distribution to be used in the Analysis (Axial distance above 3ttom)
FLcntr =
Refpoi 0
-c 0 if Val I
Refpoint if Val = 2 Refpoint + c0 otherwise Flaw center Location Location above Nozzle Bottom UTip := FLCntr +co InCstrs.avg = ULStrs.Dist - UTip 20 Developed by.
J. S. Bdhmadesam Vefried by:-
B. C Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles In the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locations for stress profiles Loco := FLcntr - L i:= i..N+3 Incri :=
co if i < 4 InCStrs.avg otherwise Loci Loci-j + Incri SIDi RID + RID4*Loci + RID (Loci) 2 + RID (Loc;)3 SQTi RQT3 + RQT 4-Loci + RQT.(Loc;)2 + RQT6(Loc;)3 SMDi= RMD + RMD 4Loci + RMD 5 (Loc;)2 +[RMD 6(Loc,)31 STQ: RTQ3 + RTQ4 LoCi + RTQ.(Loc,) 2 + RTQ6*(Loc;)3 SOD; ROD3 + ROD4*Loci + ROD.(Loci)2 + ROD6.(Loci) 3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use In Fracture Mechanics Model j := i..N Deveiopedby.
Verffied by:
J. S. Brihmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Sidj SIDj + SIDj+1 + SIDj+2 if j = 1 3
sqt. :
Sid
- (j + 1) + SIDj+2 j+2 SQTj + SQTj+1 + SQTj+2 3
Sqt (
i(j + 1) + SQTJ+2 j+2 if j =
otherwise otherwise Smd =
J SMDj + SMDj+l + SMDj+2 if 3
Smd
- (j + ) + SMDj+2 Ji otherwise j+2 Stq :
STQj + STQj+l + STQj+2 if
=
3 Stq.
(j + 1) + STQj+2 otherwise j+2 Sod.j SODj + SODj+j + SQDj+2 3
5odj j + 1) + SOD3j+2 J-1 if j =
otherwise I
j+2 Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution)
U0 := 0.000 u1 := 0.25 U2 := 0.50 u3 := 0.75 u4 := 1.00 Y := stack(U0,uIu 2,u 3,u 4 )
SIG1 := stack(SOd,St.
,Smd.,sQ,Sid.I SIG 2 := stack(Sod, StW. Smd. Sqt. SidJ Developed by:
- 1. S. Bnhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-00201
\\
I
'I I
. I 1/
2 z
2/
SIG3 := stack ( Sod Stq 3' Smd3 Sqt3 Sid3)
SIG5 := stack( Sod5, Stq5 Smd5 Sqt5' Sid5)
SIG 7 = stack(Sod7 stq7' Smd7 Sqty Sid7)
SIG9 := stack( od9 Stq, Smd Sqt)Sid)
SIG II := stack (Sodli, Stqll, smdl, Sqtl 1, Sid 11)
SIG13 := stack (Sod 13 ' Stq13 ' Smd13' Sqt13 ' Sid 13)
SIG 15 := stack(Sod 15 Stq 15 Smd' 5 Sqt15 Sid1 5)
SIG1 7 := stack(Sod17 tq17 ' Smd17 ' Sqt 7 ' Sid 17)
SIG 19 := stack( Sod 19 ' Stq 9 Smd 9 Sqt19 'Sid 19)
SIG4 stack( Sod 4Stq 4Smd4 qt4 Sid4)
SIG6 stack( Sod6i Stq6 ' Smd6' Sqt6 ' Sid6)
SIG8 stack( Sod8 s tq8'Smd8' Sq% Sid8)
SIG 1 0 := stack (Sodio, Stq 10' Smdio Sqt10 s Sid10)
SIG 12 stack(Sod1 2 'Stq 12 Smdci 12 qt12 id 12)
SIG 14 =stack(Sod 14, tq14 ' Smd 14 'Sqt 14 ' Sid14)
SIG 1 6 :=stack( Sod 16 'S tq 16 ' Smd 16 'Sqt16 Scid1 6)
SIG18
= stack( Sod 18 ' Stq18 ' Smd 18 'Sqt 8 Sid18)
SIG20 := stack( Sod20 '
Stq20 '
Smd 20 ' qt 0 id20)
Regression of Throughwall Stress distribution to obtain Stress Coefficients throughwall using a Third Order polynomial ODRGI := regress(Y,SIG1,3)
ODRG2 := regress(Y, SIG2, 3)
Developed by:
J. S. Bdhmadesam Vediedby:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-200300201 ODRG3 := regress(Y, SIG3, 3)
ODRG5 := regress(Y,SIG 5,3)
ODRG7 := regress( Y,SIG7,3)
ODRG9 := regress(Y,SIG 9,3)
ODRG 1 := regress(Y,SIG1 1,3)
ODRG13 := regress(Y,SIG1 3,3)
ODRG1 5 := regress(Y,SIG 15,3)
ODRG1 7 := regress(Y,SIG 17,3)
ODRGI 9 := regress(YSIG1 9,3)
ODRG4 := regress(Y, SIG4, 3)
ODRG 6 := regress(Y, SIG6, 3)
ODRG8 := regress(Y, SIG8, 3)
ODRG1 o:= regress(Y,SIG 1 0,3)
ODRG1 2 := regress(Y,SIG 1 2,3)
ODRG1 4 := regress(Y,SIG 1 4,3)
ODRG 1 6 := regress(Y, SIG 1 6,3)
ODRG1 8 := regress(Y,SIG18,3)
ODRG2 0 := regress(Y, SIG2 0, 3)
Stress Distribution in the tube. Stress Influence coefficients obtained from nhid order polynomial curve fit to the throughwall stress distribution PrOPLength = ULStrs.Dist - FLCntr -Co PrOPLength = 0044 Developed by:
- 1. S. Brihmadesam Veifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Data Files for Flaw Shape Factors from NASA (NASA-TM-I 1707-SC04 Model)
(NO INPUT Required)
Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw In Cyinder Jsb :=
0 2
0 1.000 0.200 0.00 0
1.000 0.200 0.200 1.000 0.200 0.500 3
1.000 0.200 0.800 4
1.000 0.200 1.000 1.000 0.400 0.000 5
1.000 0.400 0.200 6
1.000 0.400 0.500 7
1.000 0.400 0.800 9
1.000 0.400 1.000 10 1.000 1.000 10 1.000 1.000 0.200 12 1.000 1.000 0.500 13 1.000 1.000 0.800 41 1.000 1.000 1.000 5
2.000 0.200 0.000 15 2.000 0.200 0.200 2.00 0.200 0.500 18 2.000 0.200 0.800 19 2.000 0.200 1.000 10 2.000 0.400 0.000 21 2.000 0.400 0.200 2
2.000 0.400 0.500 23 2.000 0.400 0.800 2
2.000 0.400 1.000 25 2.000 1.000 0.000 26 2.000 1.000 0.200 2.000 1.000 0.500 8_
2.000 1.000 0.800 9
2.000 1.000 1.000 27 4.000 0.200 0.000 31 4.000 0.200 0.200 20 4.000 0.200 0.500 31 4.000 0.200 0.800 32 4.000 0.200 1.000 Developed by:
J. S. Bihmadesam Verfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-00201 5r 4.000 0.400 0.000 35 4.000 0.400 0.200 36 4.000 0.400 0.500 38 4.000 0.400 0.800 38 4.000 0.400 1.000 40 4.000 1.000 0.000 41 4.000 1.000 0.200 42 4.000 1.000 0.500 42 4.000 1.000 0.800 4
4.000 1.000 1.000 10.000 0.200 0.000 10.000 0.200 0.200 7
10.000 0.200 0.500 48=
10.000 0.200 0.800 9
10.000 0.200 1.000 48 10.000 0.400 0.000 51s 10.000 0.400 0.200 50 10.000 0.400 0.500 3
10.000 0.400 0.800 52 10.000 0.400 0.00 54 10.000 0.400 1.000 5
10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 1
300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 300.000 0.200 1.000 300.000 0.400 0.000 66 300.000 0.400 0.200 300.000 0.400 0.500 8
300.000 0.400 0.800 68 300.000 0.400 1.000 09 300.000 1.000 0.000 70 300.000 1.000 0.200 72 300.000 1.000 0.500 73 300.000 1.000 0.800 300.000 1.000 1.000 Developed by:
J. S. Bdhmadesam Vet ried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Sambi :=
0 1
2 3
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 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 OA9 1.148 0.202 0.076 0.039 1
1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 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 8
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 0
1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 4
2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 6
1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 8
1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 9
1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 0
1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 2.51 1.178 0.782 0.596 1.16 0.242 0.097 0.051 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 5
1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 6
f 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 7
1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 I
fn 4
fl%
^
M AO coo 4 S04 A
A 404
^f 4 Developed by:
- 1. S. Bfihmadesam Vented by:
E. C. Gray
Entergy Operations Inc Central EngineeringPrograms Engineering Report M-EP-2003-002-01 OVI IC.U;o I1.U3 U.IS U.O00 1.1011 U. I I
U. I 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41-D 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 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 9
2.921 1.323 0.859 0.645 1.715 0.020.169 0.092 D
0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 7
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 1
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 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 1244 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(0)
X := Jsb)
Y := Jsb(2) au:= Sambi(°)
CU := Sambi(4) aL := Sambi(l)
CL := Sambi(5) aQ := Sambi(2)
Q
- =
Sa mbi(6)
-(3) aC := Sambi cc:= Sambi(73 Developed by:
J. S. Bitadesam Verfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-00201 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 X 1 faij(WXY)~y
)
faU(4,4,.8) = 1.741 Check Calculation Linear Term MaL:= augment(W,X,Y)
VaL := aL RaL := regress(MaL, VaL, n)
W) faL(W, X, Y) := interp RaLMaL, VaL X
-~~~.y
)
faL(4,.4,.S) = 0.919 Check Calculation Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Quadratic Term MNaQ augment(W,X,Y)
VaQ aQ RaQ := regress(MaQ, VaQ, n) faQ(WX,Y) := interP[RaQMaQ, VaQ(X faQ(4,.4,.8) = 0.656 Cubic Term Check Calculation MaC:= augment(W,X,Y)
VaC := aC RaC := regress(MaC, VaC, n) faC(W, X,Y) := interp[RaC MaC, VaC, X faC(4,.4,-8) = 0.524 Check Calculation Developed by:
J. S. Bdhmadesam Verified by:
S. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 "C" Tip Coefficients Uniform Tern Mcu := augment(W, X, Y)
VCU := cU RCu := regress(MCu,VCUn) eWu fcU(W, X, Y):= interp RC,McU sVcU, x I
- ~,y
)-
fCU(4,4,.8) = 1.371 Check Calculation Linear Term MCL := augment(W, X, Y)
VCL := CL RCL := regress(McL, VcL, n) fw) fCL(W,X,Y) := interp RLMcLVcL X
~
Y) fcL(2,.4,. 8) = 0.319 Check Calculation Developed by:
J. S. Sfrhmadesam Veified by:
B. C Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Quadratic Term McQ := augment(W,X, Y)
VCQ := CQ RcQ := regress(MCQ,VcQ,n) fcQ(WXY):
(W'Y1
,it X
fCQ(4,.4,.8) = 0.126 Check Calculation Cubic Tern Mc := augment(W,X,Y)
VCC := Cc RCC := regress(Mcc,VcC,n)
WW fc (W. X, Y) := interp cC, McC, VcC X
fCC(4,4,.8) = 0.068 Check Calculation Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Calculations: Recursive calculations to estimate flaw growth.
Recursive Loop for Calculation of PWSCC Crack Growth Entergy Model CGRsambi:=
ao <- aO CO (- CO NCBo Cblk while j < Ilim 0 +- ODRG1 if cj < co ODRG2 if co < cj < co + InCStrs.avg ODRG3 if co+ IncstrS.avg < Cj < Co + 2Incstrs.avg ODRG4 if co + 2Incstrsavg < j < CO + 3InCStrs.avg ODRG5 if co + 3-InCstrs.avg < j < Co + 4InCstrs.avg ODRG63 if co + 4IncStrs.avg < cj < c0 + 5-InCstrs.avg ODRG73 if Co + 5 InCStrs.avg < Cj < Co + 6InCStrs.avg ODRG8 3 if co + 6InCStrs.avg < Cj < C0 + 7-InCstrs.avg ODRG9 if Co + 7InCStrs.avg < j < CO + S-Incsts.avg ODRG1 03 if c + s.fncStrs.avg < j < co + 9fInStrsavg ODRG11 3 if co + 9-InCStrsavg < Cj < co + 10IncStrs.avg ODRG1 2 3 if co+ iolIncStrs.avg < cj < co + II-IncStrs avg ODRG1 33 if co + ll-lncstrs.avg < cj < Co + 12-IncStrs.avg
- ODRG14, if Co + 12-lncstrs.avg < cj < co + 13-Incsts.avg Developed by:
J. S. Bdhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Engineering Report Central Engineering Programs M-EP-2003-002-01 J
ODRG153 if Co + 13-Incstrs.avg < cj < Co + 14-Incstrs.avg ODRG16 3 if Co + 14-InCStrS.avg < Cj < Co + 15-IncStrs.avg ODRG17 3 if cO + 15InCstrs.avg < Cj < co + 16-Incstrs.avg ODRG18 3 if co + 16 InCstrs.avg < Cj < co + 17Incstrs.avg ODRG193 if Co + l7InCstrs.avg < Cj < co+ 18-InCStrs.avg ODRG2 0 otherwise 3
1-F ODRG1 if cj o
ODRG2 if co < cj 5 co + InCStrs.avg ODRG3 if co + IncStrs.avg < cj < C + 2-Incstrs.avg ODRG4 if co + 2-Incstrs.avg < j < co + 3-IncStrs.avg ODRG5 if co + 34fCStrs avg < cj < CO + 4InCstrS.avg ODRG64 if Co + 4 InCStrs.avg < cj < Co + 5InCstrs.avg ODRG7 if co + 5 InCStrs.avg < cj < C + 6InCstrs.avg ODRG 84 if Co + 6-Incstrs.avg < j < CO + 7fInCStrs avg ODRGg if o + 7-InCStrS avg < j < o + 8 IncStrs.avg ODRG104 if co + 8-Incstrs.avg < cj < CO + 9-Incstrs.avg ODRG1 4 if co + 9InCStrs.avg < cj < CO +
°InCstrs.avg ODRG124 if Co + 9IflnCstrs.avg < Cj 5 co + II-Incstrs.avg ODRG134 if co +
I -lncstrs.avg < Cj < Co + 12-IncstrS.avg ODRG144 if Co + 12-InCstrs.avg < j < C + 13-Incs.avg ODRG154 if co + 13 IncStrs.avg < cj < CO + 14InCstrS.avg
£'
Tr~
I..
T Developed by:
J. S. Blihmadesam Vei fNed by:
B. C. Gray
Entergy Operations Inc Engineering Report Central EngineeringPrograms M-EP-2003-00201 JLIKLT1 64 lT Co + 14-fCStrS.avg < Cj s cO + lifcStrs.avg ODRG 174 if Co + 15InCStrsavg < Cj s Co + 164nCStrsavg ODRG 18 4 if Co+ 16-lnCstrS.avg < Cj s CO + 17-InCStrs.avg ODRG1 94 if Co+
7-lncstrs.avg < j s co + 18-IncStrs.avg ODRG2 0 otherwise 02 ODRG1 if j CO ODRG2 if co < j < Co + InCStrs.avg ODRG 3 if co+ IncStrs.avg < Cj s co+ 2Incstrs.avg ODRG4 if cO + 2-Incstrs.avg < Cj s Co + 3-InCstrs.avg ODRG 5 if co + 3InCStrs.avg < Cj s CO + 4-Incstrs.avg ODRG65 if co + 4InCStrsavg < Cj s co + 5Incstrs.avg ODRG7 if co + 5Incstrs.avg < Cj s cO + 6fInCstrs.avg ODRG85 if co + 6Incstrs.avg < Cj s Co + 7-InStrs.avg ODRG9 if co + 7IncStrs.avg < Cj s Co + 8-InCstrS.avg ODRGIO if co + S-Incstrs.avg < Cj s cO + 9IncStrsavg ODRG1 1 5 if co + 9InCStrs.avg < cj 5 co + 1O.IncStrs.avg
°DRG1 2 5 if co+ O-IncStrs.avg < cj s co + l-InCStrs.avg ODRG1 35 if co + 11-InCstrS.avg < Cj < CO + 12-InCstrs.avg ODRG14 5 if co+ 12-Incstrs.avg < Cj 5 cO + 13-InStrs.avg ODRG1 5 5 if Co + 13-InCStrs.avg < Cj s Co + 14-InCstrs.avg ODRG1 6 if Co + l4IlnCstrs.avg < Cj s Co + l5-InCstrs.avg ODRG1 7 5 if co + 15fInCstrs.avg < Cj s cO + 16fIncstrs.avg Developed by:
J. S. Bdhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Y3*-
ODRG1 8 5 if co+ 16 lncStrs.avg < Cj < co+ 17IncStrs.avg ODRG1 9 if co+ 17-Incstrs.avg < j < c0 +
8-IncStrs.avg ODRG20 otherwise ODRGI if Cj < Co ODRG2 if co < j
- Co + InCStrs.avg ODRG3 if co+ Incstrs.avg < Cj < Co + 24 lCStrs.avg ODRG46 if co + 2-InCStrs.avg < j < co + 3-IncStrs avg ODRG5 6 if co + 3fIncStrs.avg < cj < Co + 4-InCstrs.avg ODRG6 if co+ 4IlnCstrs.avg < Cj - co+ 5. lcStrs.avg ODRG76 if co+ 5-InCStrsavg < j < co + 6IncStrs.avg ODRG8 6 if Co + 6-InCstrS.avg < Cj < Co + 7-Incstrs.avg ODRG96 if co + 7fInCStrsavg < j < co + SIncstrs.avg ODRGO6 ODRG 1 6 ODRG1 2 ODRG1 3 ODRG1 3 6 ODRG1 4 6
ODRG1 6 O D RG1 76 ODRG1 8 6 ODRG18 if co + 8I nestrs.avg < Cj < co + 9InCStrs.avg if co + 9Incstrs.avg < cj < co + 1OlncSts.avg if co+ lOIncstrs.avg < cj < co+
-InCStrs.avg if Co + I-InCstrS.avg < Cj < Co + l2InCStrs.avg if Co+
2-InCstrs.avg < Cj < Co + 13InCStrs.avg if Co + l3-InCstrs.avg < Cj < Co+ 14InCStrS.avg if Co + 4-Incstrs.avg < cj < co+ 15IncStrs.avg if Co+ 15-InCstrs.avg < Cj < co + 16IncStrs.avg if co+ 16-Incst.ravg < j < co + 17IncStrs.avg if n+ 17-llc..-- -
< C; < C +
-Inc,.
Developed by:
J. S. Bldhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 I -
6
-u i
--- birs.avg - -J -
-- ---- brs.avg ODRG2 0 otherwise 6
40F o0 41 +-
+
0.25 aj+
2 0.25 aj' 2 + 03 (0.25* aj) 0.5-ajA°.S-a;2 o.5-aj)3 42 -0+<- +
+C2-
)
0f3-t t )
44 -OO+O ( 0.75 a
+
44Fo0+
y t )+
2 0.75 aj 2 + 0 3 (0.75 aj 3
'2
+--)
+
3-(-
X0 0.0 xi 0.25 x2o0.5 x3 0.75 X4-F1.0 X - stack(xOxIx 2,x 3,x 4 )
ST<- stack(4Oftl,42,43,44)
GOO - RG3 + PInt a 1 0 *- RG 4 020 - RG5 030 - RG6 aj ATJ +- ajt Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Engineering Report Central EngineeringPrograms M-EP-2003-002-01 (auj
- taUttSAj,Alj)
J Gal - faL (RtARjATJ)
Gaqj faQ (RtJAR ATJ)
Gacj 4faC(RtAR ATj)
GCuj fcu(RtARjATj)
GClj fcL(Rt'ARi'ATi) j Gcq 4-fcQ(RtARj, ATj)
GCCjF fCC (Rt, ARj, ATj)
(j 1.65 Qj v lI + 1.464-I-if cj aj (j 1.65 1 + 1.464-I-otherwise aj)
Kaj <4-KQ* J Gauj + ao Ga i + (y2o-Gaqj + 30-Gacj)
K~.
(29
.(aOO.Gcu + ao-Gclj + 520Gcq. + u30G
)
Ka-Kaj 1.099 i
i Ky Kc 1.099 Ka 9.0 if Ka
- 9.0 Ka otherwise K
4-9.o if K, < 9.0 K Kw otherwise Da C(Ka 9
1.16 D
In-.F-.
. 1..
if K-. <zoo Developed by:
J. S. Bnhrnadesam Veified by.
B. C. Gray
Entergy Operations Inc Engineering Report Central Engineering Programs agj
- aj - mnr 01K
-- --ul.
4-l
-CFinhr-Cblk otherwise D C-Co.(Ky - 9.0)1.16 DC j(
D CCFinhr-Cblk if Kyj < 80.0 4-1o6 '-CFinhr-Cbl otherwise output(j,0) i output(j, )
aj OUtput(j, 2 )
cj - CO outPut(j,3) 4 Dagj OUtpUt(j,4)
- Dcgj OUtPUt(j, 5)
Ka oUtPUt(j, 6)
KCi NCBj OUtPUt(j,7)- v365-24 output~j, )
Gauj output(j, 9)
Gal output(j, 10) - Gaq output(j, II)
Gacj outPUt(j, 12)
Gcu OutPUt(j, 13)
Gc output(j, 14)
G OUtPUt(j, 1)
Gcc jv j~~~~~~l aj +- aj-1 + Dag;_I Developed by:
J. S. Blhmadesam Verfifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Cj - Cji- + Dcgj.l aj t if a t
aj otherwise NCBj - NCBj-i + Cblk output Developed by:
J. S. Bidhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Recursive Loop for Industry Model ff4 = 4.0 and a/c=3 The R4 lower Limit for Original Raju-Newman model and aspect ratio a/2c was ftxed at 6)
CGRBa Banm = Ii
-0 aO - ao CO 0 4-CO NCBo - Cblk while j < Ilim 004-ODRG13 o 1 ODRG1 024-ODRG1 0Y3 - ODRG6 40*- 00 41- 0 + CYY 0.25 aj) t )
0(o.25-aj 2
+0^2. (-+0.5.aj
~~~+ C2 t
t2 -- Go+l I-(t.5aj')
~24-00+01k)
(0.25. j-0 (o.5-aj)3
+03 (o.75 aj 3
+ 3K~ t )
+- 00+0 1{
07aj) 2 43Fo+a1 -
t
+o~tt
)
t4 +-
c+
15 r 02-2+ CF3' (.O aj)3
~44-00+f1-t 77t
+021 t7 ) +Of3
~)
40 - 0.0 x-0.25 X 2 4- 0.5 x3 - 0.75 x 4 4-.0 Developed by:
J. S. Bnhmadesam Verifed by:
B. C. Gray
Entergy Operations Inc Engineering Report Central Engineering Programs M-EP-2003-002-O1 X +- stack(x x x2,x 3,x 4 )
ST*v stack(0 142,43 44)
- regress(X, ST, 3)
C0o - RG3 01*O-RG4 020 - RG5 030 - RG6 ARj -
Cj ATJ +- aj t
Gau - faU(4,.3,ATj)
Gal - faL (4,.3, ATj)
Gaqj 4-faQ(4,.3,ATj)
Gacj - faC(4,3, ATj) 1a.~
65 Qj l
+ 464-if cj aj
+ 1.464-I otherwise (i.A0.5 Ka. - (-:
(rOO Gau + 1 OGal + y20 Gaq + 30Gacj)
Kaj 4 Kaj 1.099 Ka 9.o if Ka < 9.0 K., otherwise Da C(Kaj
- 9.0)1.16 Developed by:
J. S. Bnhmadesam Venfied by:
B. C. Gray
Entergy Operations Inc Engineering Report Central EngneeringPrograms M-EP-2003-002-01
)ag; Da mFihr( bik i Ka. < 80-0 4-lo 1 0 CFirCblk otherwise Dcgj Dagj*3 output(j, 0) 4-j output(j, )4 aj outpUt(j,2) 4 Cj - CO OUtPut(j, 3)
Dag oUtpUt(j, 4)
Dcgj output(j, 5)
Ka.
NCBj OUtPUt('7)- 365-24 oUtpUt(j, 8)
Gau J
output(j,9)
Gal.
output(j, 10)
Gaq output(j, II)
Gacj j4-j+1 aj - aji + Dagj Cj 4-Cj-i + Dcg 1 aj4-t if aj 2 t aj otherwise NCBj +- NCBj-I + Cb1k output k
O.. im Developed by:
Verifed by:
- 1. S. Bdhmadesam B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Flaw Growth in Depth Direction E
4-4)
I2, 0~
0.6 0.4 0.2 A
v 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model Conventional Model 4
C c:
I 0.8 0.6 0.4 0.2 0 0 0.5 1
1.5 2
2.5 3
3.5 4
Operating Tine {years}
Entergy-CEP Model Conventional Model Developedby:
J. S. Bnhmadesam Vedfied by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 0
0 U.
>1 ct~'
c-v:
80 60 40 20 fA 0
0.5 1
1.5 2
2.
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model Conventional Model Depth Point 5
3 3.5 4
Verified~~
by B. C.
Gray~~~~~.
C l~~~~
Developed by' J. S. Brihmadesam
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw v)
L 0.8
.2a 0
E 0.7 v
0.6
._Q 00 U
0.5 Q
0 0
0.4
/
A I
4 Verified by B. C. Gray Cur 0O0 0.5 1
1.5 2
2.5 3
3.5 Operating time {years}
"a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Srihmadesam
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002-01 CGRbi (k, 8) 1.158 1.158 1.158 1.158 1.157 1.157 1.157 1.156 1.156 1.156 1.156 1.155 1.155 1.155 1.154 1.154 CGRsambi(k, 6) 22.27 23.876 23.887 23.898 23.909 23.92 23.931 23.942 23.953 23.963 23.974 23.985 23.996 24.985 24.997 25.008 CGRtsmbi(k, 5) 18.751 20.044 20.052 20.061 20.07 20.078 20.086 20.095 20.103 20.111 20.12 20.128 20.136 20.93 20.939 20.947 Developed by:
- 1. S. Bdhmadesam Veried by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs 60 -
40 -
I
-20 Engineering Report M-EP-2003-002-01 0.0 0.5 1.0 1.5 2.0 2.5 3.0 D istance from N ozzle Bottom finches}
.'0 4-I 2
so 0.1 0.0 I
E. n.E te rg M
de Industry M odel l - -----
//
0 3
4 O perating Time (years)
Verified by B C. Gray A
Developed by.
J. S. Brllimadesam
Entergy Operations Inc Central Engineering Programs Engineering Report M-EP-2003-002O1 Developed by:
J. S. Bnrhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 1 of 30 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 ntensity 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:- "Rlt" - between 1.0 and 300.0 Note: Used the Metric fonn of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required Input Is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). ThIs reference point s necessar to evaluate the stress distribution on the flaw both for the nitial flow and for a groing flow.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Refp0int = 1.544 To place the flaw with repsect to the reference point, the flow tps and center can be located as follows:
- 1) The Upper "c-tip" located at the reference point (Enter 1)
- 2) The Center of the flow at the reference point (Enter 2)
- 3) The lower "c-fip)" located at the reference point (Enter 3).
Val := 1 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld leg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist = 205 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by:
J. S. SBihmadesam Vedried by.-
B. C. Gray
'I' Entergy Operations Ina Central Enghwering Programs Apendix C; Attachment yy Page 2 of 30 Engineering Report M-EP-2003-002-01 Input Data :-
L :=.35 ao := 0.035 od := 4.05 id := 2.728 Pint = 2.235 Years := 4
'jim = 1500 T := 604 aOc := 2.67 12 Qg := 31.0 Tref := 617 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2d id Rid := 2 t = Ro - Rid Rm:= Rid +2 Tihopr := Years-365-24 CFinhr := 1.417-105 Timopr Cblk
-= m nim Pmtblk :=50 L
co:= 2 Rrn Rt :=-
[
Qg (1
I
.103* i T
Tref+459.671I CO1 K=
.aoc Temperature Correction for Coefficient Alpha Co:= C01 75 t percentile MRP-55 Revision 1 Developed by:
J. S. BrIhmadesam Verified by:
B. C. Gray
Entergy Operations Ina Central EngieerngPrograms Apendix C; Attachment yy Page 3 of 30 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (kso Cloumn "2" = Quarter Thickness Stress data at each Elevation (kso Cloumn 3" = Mid Thickness Stress data at each Elevation (kso Column "4" = Three quarter Thickness Stress data at each Elevation (ksl)
Column 5' = OD Stress data at each Elevation ks)
AllData :=
0-
-l / 0 l i_
_e_=_
l 1
-2 3
4 5=
0-0
-28.32
-18.3
-12.16
-6.2
-0.02 I1 -
0.35
-18.79
-12.49
-6.61
-1.37 3.65 0.63
-17.84
-10.52
-4.41
-0.48 2.08
-..I; 0.85
-20.52
-12.97
-5.9
-0.87
-1.54 4'1 1.03
--19.66
-11.83
-5.29 0.23 1.46 1.18
-17.2
-10.59
-0.52 16.33 21.02 6.-
1.29
-8.02
-2.2 10.46 32.66 37.29 7,
1.44 4.78 9.56 24.9 38.18 54.09 8
1.59 13.25 18.57 35.28 52.81 66.52 9
1.74 16 22.02 39.19 62.95 75 10 1.89 15.86 23.14 40.23 64.33 74.87 11 2.04 12.63 23.76 41.26 58.67 66.78 Pmo~
F s,7
-d-L AXLen:= AlIData(0)
IDAII:= AllData(l)
Stress Distribution ODAI := AllData (5) a t
W 100 _
50 -
0
-s0 0 0.5 ID Distribution OD Distribution 1
1.5 2
2.5 3
Axial Elevation above Bottom [inch]
3.5 Developedby.
J. S. Bhmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 4 of 30 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 ::
fl)~~~~~~~
035' f794g ;i 57% 6
- 1~3665 0.67 ~8 18lob
~-04Z7=~2>
1
=
~2~Q~.
3265 7-8
=1w42
=14-3n38
-~
540t ri:
17 1601694
.7~1 18955.784 j;;-D AA AxI := Data(0)
MD := Data 3)
ID := Data(l)
TQ := Data(4)
QT := Dat(2)
OD := Data(5)
RID := regress(Axl, ID, 3)
RMD := regress(Axl, MD,3)
RQT *. regress(Ax1QT, 3),
ROD =regress(AxI,OD,3)
RTO := regress(Axl, TQ, )
=~~~~~
Developed by:
J. S. Bnhmadesam Verixfed by:
B. C. Gray J/,d lflGtq
(,84 t
-cog e x S c
)
I/
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 5 of 30 Engineering Report M-EP-2003-00201 FLcntr:=
o if Val = i Flaw center Location above Nozzle Bottom if Val = 2
+ co otherwise UTip := FLcntr + Co InCstrs.avg =
ULStrs.Dist - UTip 20 No User Input is required beyond this Point Calculation to develop Stress Profiles for Analysis Number of locations for stress profiles N := 20 Loco := FLCntr - L i:= 1..N+3 Incri := Co if i < 4 IncStrs.avg otherwise Loci := Loci-, + Incri SIDi = RID + RID 4Loci + RID.(Loci) + RID (Loci) 3 Developed by:
- 1. S. Bldhmadesam Veified by:
B. C. Gray
Entergy Operations Inc.
Central Egieerng Programs Apendix C; Attachment yy Page 6 of 30 Engineering Report M-EP-2003-002-01 SQTi 1RQT3 + RQT4-Loci + RQT' (Loci) 2 + RQT. (Loci) 3 SMDi= RMD3 + RMD 4Loci + RMD.(Locj)2 + RMD (Loc;) 3 STQ; RTQ + RTQ 4-Loci + RTQ.(Loci)2 + RTQ. (Loci)3 Di:= ROD 3+ ROD 4-Loci + ROD *(Loc;) +ROD6*(Loc;)3 j:=.. N Sidj =
Smdj SIDj + SIDj+i + SlDj+2 3
3
-I-.
f=j
- M,;.
oth1+
wise 5qt. :
SQTj + SQTj+i + SQTj+2 if
~~~~~If 3
J7 e.,
.c
+4.1j_
J =
1-_..! _ _
SMDj t+SMDj+' + SMDj+2 3:f 3
e
.=
r,,-,<,
s sY,5 oinewise STQj + STQj+-+/-+ STQj+2 f
3 T.=._
slj 1_1
I--,
__ I
4_
Sod =
J ODy+ SQ~jTiz+/-:SOD>1
'~~FTJTTY+1,rSOMj+
wotherwise Developed by:
J. S. Bdhrmadesam Verified by:
. C. Gray
Entergy Operations Inc.
Central Engineering Progrnms Apendix C; Attachment yy Page 7 of 30 Engineering Report M-EP-2003-002-01 Stress Distribution for ID Flaws (i.e. ID to OD Stress distribution)
U0 := 0.000 U1 := 0.25 U2 := 0.50 U3 := 0.75 U4 =.00 Y := stack(u0 u 1,u 2 1u3,u 4)
SIG1
= stack(Sid, ISqt Smd, Stq, Sod )
SIG3 = stack( Sid3' Sqt3' Smd3' Stq3, Sod3)
SIG5 = stack( Sid, Sqt5 Smd5, Stq5, Sod5)
SIG7 = tack ( Sid qt7
'S Smd7 Stq7 Sod7)
SIG9 := stack(Sidg Sqt9 ' SmdyStq>Sod9)
SIG II := stack (Sidil, Sqtll sSmdll s Stqll sSod 11)
SIG1 3 = stack(Sid1 3 'Sqt 1 3 Smd13 ' Stq13 ' Sod13)
SIG 1 5 := stack(Sid 5 'Sqt 15 Smd 5 tq,5,Sod 15)
SIG1 7 = stack(Sid 17 'Sqt] 7 smdl7 Stq 7 ' Sod17)
SIG 2 = stack(Sid 2 Sqt2 ' Smd2 Stq2 ' Sod2 )
SIG4 = stack(Sid4,Sqt4,Smd4 Stq4Sod4)
SIG6 = stack(Sid6' Sqt6 Smd 6 Stq 6' Sod6)
SIG8 = stack( Sid8, Sqt8, Smd8 Stq8 Sod8)
SIG1 0 = stack ( Sidlo, Sqt1 0' Smd10'Stq 10 sod o)
SIG 1 2 = stack ( Sid 12 ' Sqt12 ' Smd12 ' Stq12 ' Sod12 )
SIG1 4 = tack ( Sid14 'Sqt 14 ' Smd 14 'tq 14 ' od 14)
SIG 1 6 = stack( Sid 16 ' Sqt16 ' Smd16 ' tq16 ' Sod16 )
SIG 18 := stack( Sid 18 S qtt 8 ' Smd 8 'Stq 18 ' Sod18 )
Developed by:
J. S. Bnhmadesam Venfled by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 8 of 30 Engineering Report M-EP-2003-00201 SIG19 := stack(Sid 19 Sqtl92 smd9 Stqlg, Sod )
SIG20 = tack(Sid 0, Sqto0 Smd2 0, Stq20 ' Sod20)
Regression of Throughwall Stress distribution to obtain Stress coefficients throughwall using a Third Order polynomial IDRG1 regress(Y,SIG,3)
IDRG3 regress(Y,SIG 3,3)
IDRG5 regress(Y, SIG 5, 3)
IDRG7 regress(Y, SIG 7,3)
IDRG9 regress(Y, SIG9, 3)
IDRG 1i regress(YSIG Ii3)
IDRG1 3 regress(Y,SIG1 3,3)
IDRG 15 regress(Y,SIG 1 5,3)
IDRG1 7 regress(Y,SIG17,3)
IDRG1 9 regress(Y, SIG1 9, 3)
IDRG2 regress(Y, SIG2, 3)
IDRG4 regress(Y, SIG4,3)
IDRG6 regress(Y,SIG6,3)
IDRG8 regress(Y, SIG8,3)
IDRG1 o:= regress(YSIG1 0,3)
IDRG1 2 regress(YSIG1 2,3)
IDRG1 4 regress(Y,SIG14,3)
IDRG1 6 regress(Y,SIG 1 6,3)
IDRG1 8 regress(YSIG1g,3)
IDRG2 0 regress(YSIG2 0,3)
Stress Distribution in the tube. Stress nfluence coefficients obtained from thid order polynomial curve fit to the throughwall stress distribution Developed by:
J. S. Bnhrnadesam Vedrifed by.
B. C. Gray
Entergy Operations Inc.
Central EngineeringPrograms Apendix C; Attachment yy Page 9 of 30 Engineering Report M-EP-2003-00201 Propkengf := ULStrs.Dist - UTip PrmPeng
= 0.506 Data Files for Flaw Shape Factors from NASA SC04 Model (NO INPUT Required)
Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw In Cyinder Jsb :=
0l
^f
---^l
-1 2
0 1.000 0.200 0.000 1.000 0.200 0.2 2
1.000 0.200 0.500 3
1.000 0.200 0.800 4
1.000 0.200 1.000 4
1.000 0.400 0.000
-5 1.000 0.400 0.000 7
1.000 0.400 0.500 6
1.000 0.400 0.800 78 1.000 0.400 0.500 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 0.500
- 13 1.000 1.000 0.800 14 1.000 1.000 1.000 15 2.000 0.200 0.000 16 2.000 0.200 0.200 17 2.000 0.200 0.500 18 2.000 0.200 0.800 19 2.000 0.200 1.000 20 2.000 0.400 0.000 21 2.000 0.400 0.200 22 2.000 0.400 0.500 21 I000
. f00 000 CGlU.A4 R
P /
Developed by:
J. S. Bihmadesam Verified by:
B. C. Gray
Entergy Operations Inc, Central EngineeringPrograms Apendix C; Attachment yy Page 10 of 30 Engineering Report M-EP-2003-00201 r
£.uuu U.'
I u.oJ 2.000 0.400 1.000 2.000 1.000 0.000 2.000 1.000 0.200 2.000 1.000 0.500 8
i2.000 1.000 0.800 9-t 2.000 1.000 1.000 4.000 0.200 0.000 4.000 0.200 0.200 4.000 0.200 0.500 3§3d 4.000 0.200 0.800 4.000 0.200 1.000
'35 4.000 0.400 0.000 4.000 0.400 0.200 4.000 0.400 0.500
'38 4.000 0.400 0.800 4.000 0.400 1.000 0
4.000 1.000 0.000 4.000 1.000 0.200 42 4.000 1.000 0.500 43 4.000 1.000 0.800 q1~t 4.000 1.000 1.000 10.000 0.200 0.000 idly10.000 0.200 0.200
_7.
10.000 0.200 0.500 10.000 0.200 0.800 10.000 0.200 1.000 10.000 0.400 0.000 10.000 0.400 0.200 (isT 10.000 0.400 0.500 10.000 0.400 0.800 10.000 0.400 1.000 10.000 1.000 0.000 10.000 1.000 0.200 7
10.000 1.000 0.500 10.000 1.000 0.800 10.000 1.000 1.000 (3~
300.000 0.200 0.000 M
300.000 0.200 0.200 t>
300.000 0.200 0.500
§3 300.000 0.200 0.800
>4 300.000 0.200 1.000 65 300.000 0.400 0.000 t I Developed by:
J. S. Bnhmadesam 300.000 0.400 0.200 Verifed by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 11 of 30 Engineering Report M-EP-2003-002-01 67 300.000 0.400 0.500 6
300.000 0.400 0.800 69 300.000 0.400 1.000 300.000 1.000 0.000 71 300.000 1.000 0.200 721 300.000 1.000 0.500 73 300.000 1.000 0.800 74 300.0001 1.000 1.000 I: a evv L Ls.
e -:h C:
6fi"C-I,; _-f7 AC-1i~
jx
Sambi :=
Oal 23
=
4 S5L-6-
70-
- 0 1.076 0.693 0.531 0.434 0.608 0.083 0.023 0.009
.1 1.056 0.647 0.495 0.408 0.615 0.085 0.027 0.013 2
1.395 0.767 0.557 0.448 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 0.646 0.504 0.421 0.745 0.119 0.041 0.02 7-1.149 0.694 0.529 0.435 0.916 0.181 0.073 0.04 8
1.6 0.889 0.642 0.51 1.334 0.307 0.132 0.073
,9;-
2.087 1.093 0.761 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 11 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 1.116 0.2 0.078 0.041 13 1.07 0.73 0.623 0.523 1.132 0.218 0.095 0.051 14 1.128 0.75 0.675 0.556 1.131 0.229 0.11 0.06 15 1.049 0.673 0.519 0.427 0.6 0.078 0.021 0.008 16 1.091 0.661 0.502 0.413 0.614 0.083 0.025 0.012 17 1.384 0.764 0.556 0.446 0.817 0.15 0.058 0.031 18 2.059 1.033 0.708 0.545 1.3 0.291 0.123 0.067 19 2.739 1.301 0.858 0.643 1.783 0.421 0.18 0.099 20 1.075 0.674 0.527 0.436 0.73 0.072 0.044 0.021 21 1.045 0.659 0.511 0.425 0.76 0.122 0.043 0.021 22 1.16 0.71 0.536 0.441 0.919 0.197 0.064 0.034 Developed by:
J. S. Blihmadesam Verified by B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 12 of 30 Engineering Report M-EP-2003-002-01 t3 1.51 0.854 0.623 0.498 1.231 0.271 0.114 0.062 1.876 0.995 0.71 0.555 1.519 0.317 0.161 0.089 2
1.037 0.732 0.594 0.505 1.132 0.192 0.07 0.035 6
1.003 0.707 0.577 0.493 1.113 0.19 0.071 0.036 1.023 0.714 0.58 0.495 1.155 0.207 0.08 0.042 8E 1.129 0.774 0.619 0.521 1.286 0.247 0.098 0.052
'A9.
1.242 0.84 0.661 0.549 1.416 0.285 0.115 0.061 1.003 0.649 0.511 0.43 0.577 0.07 0.015 0.005 E
1.097 0.666 0.511 0.426 0.606 0.079 0.023 0.01 E2 1.405 0.776 0.567 0.46 0.797 0.141 0.054 0.028 1.959 0.996 0.692 0.542 1.201 0.262 0.108 0.059 7
2.461 1.197 0.808 0.619 1.586 0.37 0.154 0.085 1.024 0.668 0.528 0.451 0.737 0.11 0.033 0.015 1.057 0.666 0.52 0.439 0.77 0.123 0.042 0.021 1.193 0.715 0.545 0.454 0.924 0.174 0.068 0.036 1.443 0.828 0.614 0.509 1.219 0.263 0.109 0.059 1.665 0.934 0.681 0.565 1.487 0.339 0.143 0.078 1.005 0.72 0.597 0.518 1.119 0.188 0.068 0.034 4Tp
-y 1.009 0.713 0.588 0.511 1.128 0.194 0.072 0.037 1.041 0.726 0.594 0.515 1.191 0.214 0.082 0.043 1.105 0.768 0.623 0.536 1.316 0.248 0.097 0.05 1.162 0.81 0.653 0.558 1.428 0.277 0.109 0.055 t45~
0.973 0.635 0.499 0.446 0.579 0.07 0.016 0.005 1.115 0.673 0.514 0.438 0.607 0.079 0.023 0.01 1.427 0.783 0.571 0.462 0.791 0.138 0.052 0.027 1.872 0.96 0.671 0.529 1.179 0.253 0.104 0.056 2.23 1.108 0.757 0.594 1.548 0.356 0.149 0.081 0.992 0.656 0.52 0.443 0.733 0.109 0.032 0.014 1.072 0.672 0.523 0.441 0.777 0.125 0.043 0.021 1.217 0.723 0.549 0.456 0.936 0.176 0.069 0.036 1.393 0.806 0.601 0.493 1.219 0.259 0.106 0.056 1.521 0.875 0.647 0.528 1.469 0.328 0.135 0.071 0.994 0.715 0.59 0.518 1.114 0.187 0.068 0.035 1.015 0.715 0.588 0.512 1.14 0.197 0.074 0.038 1.05 0.729 0.596 0.515 1.219 0.221 0.085 0.044 1.09 0.76 0.618 0.532 1.348 0.255 0.099 0.051 1.118 0.788 0.639 0.55 1.456 0.282 0.109 0.056 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07
§;5~
0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 Developed by:
J. S. Bdhmadesam Veriffed by:
B. C. Gray
Entergy Operations Inca Central EngineeringPrograms Apendix C; Attachment yy Page 13 of 30 Engineering Report M-EP-2003-002-01 Lei A.+
1.0951 0.677 0.727 0.791 0.838 0.431 0.446 0.473 0.496 0.782 0.946 1.201 1.413 0.127 0.18_
0.253_
0.31 I
0.022 0.037 0.054 0.066 1.4381 l
W := Jsb(O)
X := Jsb(1)
Y := Jsb(2) au:= Sambi(o)
CU := Sambi 4)
.(I) aL := Sambi (5)
CL :=Sambi aQ := Sambi(2) cQ := Sambi(6) aC := Sambi(3)
CC := Sambi(7) n:=
3 if Rt<4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W, X, Y)
VaU:= aU RaU := regress(Mau, VaUn) faU(WXY):= interp RaUMaUVaU X I fau(W,,Y))
faU(4,.4,.8) = 1.424 Check Calculation Linear Term MaL := augment(W,X,Y)
VaL := aL RaL := regress(MaL, VaL bn)
Developed by:b J. S. Bnhmadesam Vedied by:
R C Gray
Entergy Operations Inc.
Central EngineeringProgratms Apendix C; Attachment yy Page 14 of 30 Engineering Report M-EP-2003-002-01 W)-
faL(W,X,Y) := interp RaLMaLVaL X
Y )-
faL(4,.4,.8) = 0.827 Check Calculation Quadratic Term MaQ:= augment(W, X, Y)
VaQ := aQ RaQ:= regress(MaQ,VaQ,n) faQ(W, X, Y) :=
WY~
y)-
faQ(4,.4,.8) = 0.614 Cubic Term Check Calculation MaC:= augment(W,X,Y)
VaC := aC RaC := regress(Mac, VaC n) faC(W,X,Y):= interp RaC MaC, VaC X I faC(4,.4,.8) = 0.502 Check Calculation
'C" Tip Coefficients Uniform Term McU := augment(W,X,Y)
VcU:= cU RCU := regress(Mcu, VcU, n)
Developed by:
J. S. Brfhmadesam Veried by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 15 of 30 Engineering Report M-EP-2003-002-41 fcu(W,X,Y):
Wli I
Iy)_
fCU(4, A,.8) = 1.222 Check Calculation Linear Term MCL := augment(W,X,Y)
V& L-CL RCL := regress(McL, VcL, n) fcL(W, X, Y) = interP[RCL, McL, VcL, X I fCL (2,.4,-)
= 0.282 Check Calculation Quadratic Term McQ:= augment(W,X,Y)
VCQ :=CQ RcQ := regress(McQ,VcQ, n)
{WR]
fcQ (W, X, Y) := interp RQ, McQ, VcQ, X
- ~
~
,Y) fcQ(4,.4,.S) = 0.11 Check Calculation Cubic Term McC := augment(W,X,Y)
VCC := c RcC := regress(McCVcCn)
Developed by:
- 1. S. Bnhmadesam Veified by:
B. C. Gray
Entergy Operations Inc I
Central EngteerngPrograns Apendix C; Attachment yy Page 16 of 30 Engineering Report M-EP-2003-002-01 fcC(W,X,Y) = interp{RcCMCCVcC{X I1 fcc(4,4,.S) = 0.059 Check Calculation Calculations : Recursive calculations to estimate flaw growth Recursive Loop for Calculation of PWSCC Crack Growth CGRsambi =
j*-0 ao-ao cO c aO NCBo - Cblk while j < lim
- o0-IDRG3 if Cj Co IDRG2 if CO < Cj co + ICStrs.avg 3
ID RG33 if C + IflCSfrs avg < Cj < CO + 2dflCSfs avg IDRG4 if co + 2Incsrs.avg < j CO + 3InCStrs.avg IDRG5 if CO + 3Incst savg < Cj
- C0 + 4ifCStrs.avg IDRG6 if O + 4-Inctrs.avg < Cj S cO + 5-lncstrs.avg 3
IDRG7 if CO + 5-nCstrs.avg < j < CO + 6InCStrs.avg 3
IDRG8 if CO + 6-Incstrs.avg < cj S CO +
Inc trs.avg IDRGg 3if C C+ 7dincst s.avg < cj CO + 6-fCStrs.avg IDRG1 03 if cO+ 8lncstrs.avg < j < cO + 9lncStrs.avg 3
c,vtj.
A-,~sli/7 ci' ers C,,4 cv'Df I>v 10 M
Developed by:
J. S. Bn'imadesam Vefried by:
B. C. Gray
Entergy Operations Inc.
I Ctral Enginering Programs Developedby:
J. S. Bnhmadesam Apendix C; Attachment yy Page 17 of 30 IDRG113 if cO + 9lncstrs.avg < cj*< Co + 10flncstrs.avg 123ifco+ 1 Icsrsavg<
ec+
-nsrav IDRG1 2 if co+ 10 InCstr.avg < cj < co + 1I Incstrs.avg IDRG12 if eo+il*IDCStS avg < Ci < Co + l4 lCstrs.avg I63 if co +
InCsts.avg < Cj c
CO + 1 InCstrs.avg IDRG 17 if co + I32 lCStrs.avg < cj < co + 1 InCStrs avg 3
IDRG 1 3 if cO+ 1lncstrs.avg < Ci < co+ 1 4 lncStrs.avg IDRG16 if co + 1 Incstrs.avg < j < Co + 1'IfnCStrs.avg IDRG 17 if o + 16dflcs.avg < Cj co+ l6 IlcStrs.avg IDRG3S if co + Infls c +
<7d c
+CstrS.avg IDRG2 0 i otherwise IDRGI if cj < co 4
4 IDRG 4 if co + 4 flCs avg < Cj S Co + 5 nctI.avgnc 4
IDRG7 if o + Inctrs avg < Cj 5 co +
fInCStrs.avg -
4 8DR 64 if CO
+ 2Incs
< Cj S co +
ncStrs.avg IDRGg if co + Incrsavg 4DR~lo i
ncStrs.avg < j < CO + 9. fCstrs.avg IDRG6 if co +
IncStrS.avg < Cj S co + 7I lncstrs avg 4
IDRG2 CifO
+co+ Incrs avg < cj *< o+
+ IcStsav aj v
-4 I D R G 1if C + S ~ l ~ str ~ a v < j *5 c o + 7
- fl.1.
v IDRGj if c + 9flCStrs.avg ncj~
O Strsav 4
IDRG 1 2 if co + 1 ilt~ag<
j
- co + Intrs av A~~~'tr~v y
Engineering Report M-EP-2003-002-01 za..6--'
4 S
{5 0;
g5 L ~ 4 ThC g
4!
VerIfed by B. C. Gray
EnteiWy Operations Inc.
Central Engineering Prognm Apendix C; Attachment yy Page 18 of 30 Engineering Report M-EP-2003-002-01 02 zDRwGj 3 ifc cO+ 1 flCs avg-< C e CO + l24 lCStrs.avgt IDRG1 4 if CO +FI2-Ilns.avg
< Cj < CO+ 13-IncS 14 0
S~agtrs.avg IDRG1 5 - if C + 13 IncS avg < cj c 0+ 14 IncSfsavjt I DRG164 if 4O+ I44 lCStrs avg < Cj < CO + 154flcstIs.avg 4
IDRG17 4 if CO + 154flCstr avg < cj < O + I6-lncSrsavg 4
IDRG14 'if O-+
-1nsr.v
< Co+ 1-Instrsg 4
-IDRGI if C + 1-IncSk avg <
j < co + 1 incStrs.ag IDRG1 if cj S C0
/
.184 c
o n~tsag tr a,
IDRG4 if Co + Inc 1C ncStrsgs avg j
TDRG6 if Co + 4IflCStavg. < cj C O + ICst s aig IDRG7 if co + ICst s avg< Cj < Co + 34flCStis.avg 4
if~~~~~~~~7 IDRGg if Co + 3IflCstrsavg< C S eo + 4dflCStrs0av ID-RGgsi O+7Ict--ag 4fcj rSc-n iag TDRG3 if CO + -Icstrs avg < CJ < CO + -flncst.avg 5
-DRG4 if co + 9Incstr avg < Cj < CO + InCSrs.ag T 8if CO + 106IfCtrs.avg < Cj S CO + iflctrs avg.
.5 5JRG 1
if C+ 394fic Mj.a
< j*C +1 rls ag 5J IDRG1 2
~fC + 1OfCStr.ag < Cj CO +- 11ftrs.avg 5
.DlRG
.1-7 CcIA i
Developedby:
J. S. Slihwdesam Verified by:
S. C. Gray
Entergy Operations Inc.
Central Egineering Programs Apendix C; Attachment yy Page 19 of 30 Engineering Report M-EP-2003.002-01 IUDKIUpW5 It Coo+ 12flCs-rs*yg <Cj C0 +l13-lncStrs.avg3 IDRGj5 jf Co +I3flnCstrs avg <-Cj <C6 + 14 Iflcstrs ayig IDRG - -if
+
1--<I
---j S 6+ 14.Inc IDj3RG 176 if cS+ 4lflCstr.avg<
+ 16Ilcstrs.avg IDRG18 i co+ 16SflCstri.avg < Cj < co+ 174flcstgsavg 5
IDRG1 9 ifCoC+167-ncstrs.avg < Cj < cO + 1IncSrstav IDRG.
95 ag c
[DRG2 0 otherwisei 205 1-I
-17.1--
1 -- -
-4
~IDR~~if~o +5IDCSL yg~SC~i~~'C&+G If-tr avg W
-1 C~
~
~
~
~
~~~-
}~~~~~~r jiFiT c0T 114 Stis.avg. *j C0+i2dfls;
1 t co,+n C+I
~D =i 2ic-+/-3 w~~--
Srg~j*C*idCfsv Developed by:
J. S. Bnhradesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engieering Programs Apendix C; Attachment yy Page 20 of 30 Engineering Report M-EP-2003-002-01
~DRG9' f3W rO~
l~.nc<~sc+1ncH
(*
fSrv 40 00 r-, r-,7FR, tV-t I <- 0
+4 I -.
j + 2-(
0.25.aj) 2 t
)
+0(0.25 aj3
-)I
'StrC clrM LA J ;,J
~
VI 4v LA/fl
~~~vV LAS~~~~~~~~~
42+- Go+ CY(I -o0.5.aj)Ct )
0 5.aj 2
(o.5 aj 3
+ 02-
+0(3.
~3 +-co+ 01. C0.75a-(O 7s.aj" 2 3 t
)f2Lt
)
+03- 0.75-aj)3 t
)
(l.O a t.O-aj2 1z.0-aj) 44+- Go +f Or
)+
2 t
)
+3-t t )
Xo +-- 0.25 xi +- 0.25 X2 - 0.5 X3 - 0.75 X4F
+-1.0 X - stack(x 0, x1,x 2, x3, x4 )
"eS
'i" C;
'Q CIA -7:
w$
CA A kv)'
k it VI f~n soh ST - stack(40X,1ST2,43 4)
RG +- regress(X, ST, 3) 000- RG 3 j73
( 0 RG4 (Y20 +- RG5 plt
tA vc-,
tz Q
,I
". 0 " vv-,-
em
,,,I J'j
-f-( kc "'. f'.' V'YCMA.")'d 1-1)
Developed by:
J. S. Bflhmadesam Verified by:
B. C. Gray
Entergy Operations In, Cenral E1ieedugProrams C
A A'
Ga Gac Gac Gi Gqj llGCUj Kaj*
I~ l+is Kaj I
Deve/oped by:
J. S. Bdesade Apendix C; Attachment yy Pag 21 f 30 Engineering Report AN-EP-2003-002-01
'30 <- KU6
,R 3
SR i
T j
o.
iTj Y ajs
- CcO4 h
j _ t Huj +- faU (Rt, ARj ATj aIj +- faL (RtARjATj) g4 ij f-(R t A R jA 'J)
'T4 c;
-faC(RtARj,ATj)
F fcU(RtARjATj) fCL(Rt, ARj,ATj)
L &
)
aepfcz-'5 1 +
I 464 (a. )i.jS aj I + 1.464.
1.5Otherwise
- Q(,) ( OO'Gauj + a I
o Ga + 20 G G )
/
\\nS t I.
k
'((YOO'G,
+ aO.Gci + ' 2 0 'Gcqj + 30.Gccj) t..G 4-CCW f
- CJL, USA A 1 4'.
d*r1-4,.
'ck-61 )
r-; ~^ ->M u4 LdrL LTIA f-d I+
A Ka otherwise Verifled by.
S. C Gray
c!tla Inc
-_- rogrm 7;9.
ApendixC; AttachMen PaQ 22 o ent Y
,,~9.0 dse
),-
"Od edl M
fry /X 1.16 1 -
d-a KJ
- Cblk Otheri4se J
cL j, ha zmzwe Eliiern e1
-9.0)
I, Ad A^,
+
C._C,&
vx.t S, "
r "A
M/.C,,
(,
:
c " at-de-
'IC.- lfl'h
A
C,-_-V-_+
4 -1o 10.
outpukj 0 0) f-j OUtpukij 1) ~_ '
I OUtk, 2) <- Cj- - C'o Ili l tuPt(i, 3) f-Da i,
U0PUkj 7)
Nce.
36s.24 UtP jk, ) < GIu
~~~~~~I.-
.4e/opd j
S
- 13) < G.ci VerIedby C. Gras
Entergy Operations Inca Central Engineering Programs Apendix C; Attachment yy Page 23 of 30 Engineering Report M-EP-2003-00201 OUtpUt(j, 14)
- Gcqj oUtpUt(j, 5) - Gccj j
j+ I aj - aj-. + Dagj_
Cj - cj-, + Dcg. 1 aj-It if aj > t aj otherwise NCBj - NCBj-j + Cblk output k := o.. im Developed by J. S. Blihmadesam Veried by:
B. C. Gray
Entergy Operations Inc.
Central Engteenng Programs Apendix C; Attachment yy Page 24 of 30 Engineering Report M-EP-2003-002-01 PropLength = 0.506 Flaw Growth in Depth Direction I
I I
I I
I I
0.6 I,-
-0 0.4 -
0.2 -
l 1
l l
l l
n -
0 0.5 1
1.5 2
2.5 Operating Time {years}
3 3.5 4
2 0
1.5 0.5 0
I I
I I
I:
-0.5
-1 0 0.5 I
1.5 2
Operating Time 2.5
{years}
3 3.5 4
Developed by:
J. S. Brihmadesam Vendred bya B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 25 of 30 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 80 1-ut CU 0n i
IP 4)9 on U,
60 _
40 _
I I
I I
I I
I I
I I
I I
I I
20 _
o 0.5 1
1.5 2
2.5 Operating Time {years}
3 3.5 4
Depth Point
.Surface Point Developed by:
J. S. Bnhrmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 26 of 30 Engineering Report M-EP-2003-002-01 1.1 0.9 0.8 En 0
ei) 0 5
.E cI) 00 0.7 0.6 0.5 0.4 Influence Coefficients - Flaw
. ~
~~~~.---
0.3 0.2 0.1 0
I 0
0.5 I
1.5 2
2.5 Operating time {years}
3 3.5 4
"a" - Tip -- Uniform I.'.....a" - Tip -- Linear a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic l"c" - Tip -- Cubic Developed by:
J. S. Brihmadesam
Entergy Operations Ina Central Engineering Programs CGRsab (k, 8) 1 1
I
'I 3
,1, I
11 I
I I
I I
1 Apendix C; Attachment yy Page 27 of 30 Engineering Report M-EP-2003-002-01 b (k, 6) 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 0.163 CGabi(k )
0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 0.111 Developed by:
J. S. Bnhmadesam Vered by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs 8 0 -
60 -
40 2 0 -
I 0 - -40 Apendix C; Attachment yy Page 28 of 30 Engineering Report M-EP-2003-002-01 1.0 1.5 2.0 A x ia I D is t n c e F ro m N o z z le B o ttom
{in c h 0.05 -
0.04 -
r 0.0 3 -
0.02 -
0.0 1 -
0 2~~~~
0 1
0 p e ra tin g T im e (y e a rs }
3 4
Ver-ified by
. C. Gray C e~7o Developed by.
J. S. Brihmadesam
Entergy Operations Inc.
Central Engineering Programs Apendix C; Attachment yy Page 29 of 30 Engineering Report M-EP-2003-002-01 0.5 Z'
0.3 co -03
-0.
0.1.
I c
0.55 0.14 i
-O 1 ti
- 0. 3 u
0.12
-O.5 0.16 -
z in 0 1 5 o O.1 4-I I O.1 3 -
=
I re O.1 2 -
0 1 1
-1 0
2 O perating Tim e (years}
3 4
S IF D ep th Point S IF Su rface P o in t 0
2 0
1 2
O Pe retin g T im e (years) 3 4
Verified by:
B. C. Gray Developed by.
J. S. Brihmadesam
Entergy Operations Inc.
Central EngineeringProgrants Apendix C; Attachment yy Page 30 of 30 Engineering Report M-EP-2003-002-01 Developed by:
J. S. Bnhmadesam