ML032790027
| ML032790027 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 08/26/2003 |
| From: | Entergy Operations |
| To: | Document Control Desk, Office of Nuclear Reactor Regulation |
| References | |
| CNRO-2003-00033 M-EP-2003-002, Rev. 1 | |
| Download: ML032790027 (95) | |
Text
Engineering Report: M-EP-2003-0002 Rev. 00 Appendix A Appendix A This Appendix contains design information, UT analysis data and an evaluation to determine the best-estimate as-built configuration.
This Appendix has five (5) Attachments.
Design Input Sheet for Fracture Mechanics Evaluation of CEDM nozzles below the Attachment J-weld
{ANO Unit 2 and WSES Unit 3}
Item Source Input Used Concurrence' Length from bottom of nozzle to Drawing M-2001 -C2-23 1.25 inches Site Desi Engine ng top of thread relief counterbore revision 4 (CE drawing E-ANO: Jamie GoBell (includes I inch thread length plus 234-760-2) ANO-2 WSES3:
V4 inch thread relief counterbore)
E-74170-112-01 WSES-3 Maximum Chamfer Dimension Same Drawing as above 0.094 inches Site Design Engineer g.
along the axis of the nozzle, ANO: Jamie GoBell gin vh V
?
including 1/32" tolerance WSES3__
NDE Dead Zone Ronnie Swain's Notes of 0.300 Site Quality Prograrns/NDE 4/23/03 attached to e-mail of ANO:_
4/23/03 WSES3:
Residual Stress Distribution DEI calculations:
Nodal stresses below J-DEI Calculations were performed for Westinghouse C-7736-00-5 ANO-2 weld under contract to Westinghouse for ANO-2 and C-7736-00-4 WSES-3 WSES3 RVHP evaluations. Westinghouse {OEM}
provided design input. Westinghouse and DEI have Appendix "B" qualified QA program and these calculations were performed under the applicable program. This provides reasonable assurance that the results are applicable.
PWSCC Crack Growth rate EPRI-MRP 55 revision 1.
Seventy-fifth Percentile EPRI report based on information provided by all Curve utilities and the analyses for the report was performed under EPRI QA program. The report was reviewed by Utility peer group MRP} for correctness, completeness and applicability. The information is reasonable for use for ANO-2 and WSES-3 application.
Nozzle Dimensions (ID and OD)
Drawing M-2001-C2-23 OD = 4.05"; ID - 2.719" Site Desig Enginee n revision 4 (E drawing B-OD = 4.05"; I 2.719" ANO: Jamie GoBell 234-760-2) ANO-2 WSE3:
E-74170-112-01 WSES-3 CD C2 X o:m o to, '
>D r\\3 :'Z I
n 1: Concurrence is only requiredfor items that have a signature block. The Residual Stress results and PWSCC crack growth rate report have been provided under approved QA programs and there is reasonable assurance of the result's accuracy. Hencefor these two items specific concurrence is not required.
Engineering Report: M-EP-2003-002 Rev. 01 Appendix A; Attachment 2 NDE Dead Zone Design Input June 6, 2003 Design Input to Engineering Report M-EP-2003-002:
At the request of Entergy, Westinghouse reviewed UT data for 10 penetrations taken from the 2R1 5 ANO-2 reactor head inspection. This inspection was performed with a 7010 ultrasonic end-effector, using 0.250" diameter, 24mm PCS Time-of-Flight-Diffraction ultrasonic transducers. The penetrations were chosen by their location on the head, in order to provide a representative sample of the entire head. The analysis was performed in order to determine the ultrasonic dead band located immediately above the threaded region of the CEDM nozzles. This review determined the dead band to be 0.200".
Ronald V. Swain UT Level IlIl Waterford 3 SES
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 3 Page I of 2 To support the crack growth rate evaluation for the portion of thc CEDM nozzle that extends below the J-groove weld on thc ANO-2 and W-3 heads, the length of this portion of thc nozzle is required. Because this length varies with the nozzle location, an Exccl spreadsheet was developed to calculate the various parameters ofthe nozzle 3-groove weld configuration.
To describe thc geonctry, the following nomenclature is used: The location of the nozzle relative to the curvature of the head is identified by the angle in degrees between thr vertical centerline of the head, and a line created by the radius of curvature of the bottom surface ofthe cladding where it intersects with the centerline of the nozzle The nozzte locations included in the crack groNit rate evaluation are identified as the following:
ANO-2 Waterford-3 Nozzle location I Penetration No.
8.S0 1 2,3.4.5 Nozzle location Penetration No.
00 1
7.8' 2, 3 2g.1' 36, 3 38, 39, 40, 41 42 43 28.8' 49.60
- 30. 3. 32, 33, 34.
70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80.8s1 4M'7 88,89.90,91 The point location around the OD of the nozzle is identified by the azimuth angle with the 7cro degrce azimuthl location be ing te point futhest from the vertical centerline of the head, whtich is also the lowest point that the i-groove weld attaches to the nozzle (the "low-Itillside"). The length of the portion of thc nozzle that extends down below the J-groove weld is calculated at the zcro degiec azimuth for each ofthc nozl locations evaluated.
The length, l, of the portion of the nozzle that extends down below the J-groove weld is defined as the vertical distance from the point where the surface of the cladding would intersect vith the outsidc sgrfaqv of the nozzle at the zero degree azimuth location dowin to the bottom of the nozzle (see attached sketch).
Using ANO drawings NI-2001-C2-23, M-2001 -C2-26, MI-2001 -C-32, M-200 1 C2-55, and Nt-200 -C2-107, and Waterford drawings 1564-506, 1564-1036, and 15644086, the length I,1 was calculated as shown in the following table:
ANO-2 Waterford-3 Nozzle location _
1, (inches)
Nozzle location
- i. inces) 0' 2.50 0O 2.88 8.80 2,49
- 7.
288 28.80 2.48 29.10 2.86 49.60 2.48 497° 2.92 Verified by:
/3asnieGollJpJ Waterford-3 L
NAru1ayj I6/4,01 Nara Rab Dt
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 3 Page 2 of 2
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 1 of 7 ANO-2 UT Data Measurements UT data obtained during last Refueling Outage (April 2002)
Data from review of Zero degree UT Scan
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 2 of 7 CEDM Dlimensions taken from the n degree UT data on the ANO-2 RPY Head DZMi U k11 Dead Zone to Bottom of Filet Dead Zone to Ton of J-I 0.32"'
1:24' On nozzle # 1, the dead zone is aot visible on this data, so the accuracy of these dimensions are questionable.
2 3
4 5
Low HS.
High HS Low HS High HS Low HS High HS Low HS High HS Low US High HS Low HS Hig HS Low HS High HS Low HS High HS
, 0.24"'
0.84" 0f16" 0.92" 1.24" 1.R8" 0.18" 0.80" 1.20" 1.84" 1.24" 1.92' 032" 1.00"5 1,24" 1.96" 6
0.44" 1.32" 0,32" 1.24"'
7 1.40" 2.36" 1.52" 2.36" 1.44" 2,28" B
9 10 0.20'"
1.12" 0.48" 1.44" 1.52" 2.48" Low HS 0.12".
1.60" High HS 1.68" 2.68" On nozzle-#10, the dead zone is not visible on this data, so the acturacy of these dimensions are questionable.
11 Low HS HighHS 0.16" 1.64" 1.52' 2-76" 12 Low HS 0.i1' 1.36i"
13 Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 3 of 7 High HS 1.52" 2.801 On nozzle #12, the dead 'tdne is not visible on his data, so the accuracy of these dimensions are questionable.
Low HS 0.16" 1.56" High HS 1.68"
.2-80"'
On nozzle # 13, the dead zone is not visible on this data, so the accuracy of these dinensions are questionable.
Low HS 0.0"'
1.08" High HS 1.40" 2.48"'
On nozzle #14, the dead zone is nqt visible on this data, so the accuracy of these dimensions are questionable.
14 15 16 17 Low HS High HS Low US
-ligh S Low HS High HS Low HS Iligh HS Low ES High HS Iow HS High HS 0.16" 1.X2"
- 0. 12" 1.84" 1.44" 3.04" 1.60" 3.08" 0.08" 1.80"'
0.24" 1.76" 1.44" 3.04" 1.48" 3.08" 18 19 0.16" 1.76" 1.52" 3.16" 20 0.48" 1.88s 1.52" 3.08" 21 Low IIS 0.24" 1.44" High HS 1.92" 2.92" On nozzle #2 1, the dead zone is not visible on this data, so the accuracy of those dimensions are questionable.
22 23 Low IS High HS Low HS 1-lgh HS Low HS High HS 0.12" 2.32" 1.48X' 3.56" 0.0" 2.36" 1.32" 3.56" 24 0.12" 2.28" 1.32" 3.32"
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 4 of 7 25 26 27 28 29 30 Low HS
-High HS Low HS High HS Low HS
-igh 1S, HighHS Low ITS High I-TS Low HS igh S LOW HS High HS Low ITS 1-igh HS Low HS High HS Low HS High HS Low HS High HS Low HS High'HS 0.28" 2.44" 0.08" 2.44" 2.52"'
0.24" 2.36".
- 0.16"'
2.56" 0.16" 2.48" 0.20" 2.56" 0.16" 2,601-0.0" 2.24" 0.20"
- 2. 12" 0.16" 2.76" 0,04" 2.48" 1.72" 3.64" 1.36" 3.56" 1.48" 3.76" 1.60" 3.84) 1.56" 3.60' 1.36" 3.76" 31 1.32" 3.56" 32 1.24" 3.64" 1.40" 3.72" 33 34 1.08" 3.68" 35 1,40' 3.88" 36 1.60"
. 3.80" 37 38 l,ow -1S 0.24" I-igh HS 2.68" No A-Scan data present for nozzle #37 1.52" 4.00" Low wS High HS Low HS Iligh lS OO" 3.16" 0.0>
- 2. 8 1.20" 4.32`'
39 1.08"I 4.16"
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 5 of 7 40 Low HS High HS 0.0" 2.60" 1.04" 4.04" 41 Low HS High HS 0"
2.84" 1.00"'
4.24" 42 row I-IS F-li gh 1 S 0.0"5 2.72" I'.0jag 4.04" 43 Low HS High HS 0.0" 7? (probe I ift-oft 1.36" 4.28" 44 45 Low ES High US Low HS Higll HS 0.08" 3.20" 0.0" 3.00" 1.32" 4.40" 1.12" 4.24' 46 Low HS High HS 0.0"'
2.92" 1.08" 4.40" 47 Low HS High HS 0.0" 3.16" 1.04" 4.28" 48 CD BLANK NO DATA AVAILABLE 49 CD BLANK/ NO DATA AVAILABLE 50 CD BLANK/ NO DATA AVAILABLE 51 52 Low I-IS High I-IS Low HS High HS 0.0" 2.961 1.04" 4.56" 0.0" 3.40" 1.16" 4.60" 53 FAULTY CD/ NO DATA AVAILABLE 54 55 Lows I1.S High HS Low ES High ES Low HS I lIgh :tS Low HS 0.0" 3.16" 3.28"
.0.0" 3.36" 0.0" 1,04" 4.64"'
1.12' 4.72" 56 1.40" 4.76" 57 1.16"
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 6 of 7 High HS
,'Low HS Hgh HS 3.28" 58 0.16" 3.60" 59 60 Low HS High HS Low HS High HS
.0.08' 3.44t" 4.64" 1.12">
4.88" 1.12' 4.68"'
0.96" 4.64" 1.28" 4.92" 0.08" 3.40 61 Low.1S High HS 0.0"7
- 3. 64" 62 Low HS_
0.0" High HS 3.84" On nozzle #62, the dead zone is not visible on this accuracy of these dimensions are questionable 1.00" 5.12' data, so the 1.16" 5.08" 63
.Low HS High HS 0.04" 3.76' 64 65 66 67
.Low ES High TS Low HS High HS.
Low HS High HS Low IIS High I1S Low HS High ES Low HS High HS Low S1-S High HS Low HS High HS 0.04"
? (probe lift-off) 0.0"1 3.76".
0.0" 3.72" 0.08" 3.92" 0.0" 3.84" 0,0
- 3. Wl 1.00" 4.88" 0.96" 5.08" 1.00" 4.96" 1.56" 5,44't 68 1.52" 5.32" 69 1.36" 5.20" 70 71 1.44" 6.52" 1.32" 6.52" 0.0" 5.04"
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 4 Page 7 of 7 72 Low HS 1-igh ITS 0JT 5.o8r 1.32" 6.52" 73 Tow HS
-Iigh HS 0.0" 5.00" 1.20' 6.44"
.A42 18" 6.28"1 74 75 Low HS High HS Low US 1-ugh -IS 0'
5.12" 5.00"
. 1.20" 6.40" 76 Low HS High HS 0.06" 4-.6411 1.60" 6.52" 77 Low T-IS 0.0" 1.52" High HS 5.20" 6.44" On nozzle #77, the dead zone is not visible on this data, so the accuracy of these dimensions are questionable 78 79 Low HS High I-IS Low HS Hi gh HS 0.05" 5.16"'
1.4R" 6.68" 0,0" 4.96" 1.64" 6.52" 80 Low HS High -IS 0.0" 4.96" 1.44" 6.52" Low -S High HS C"
5.08" 1.56"'
6.48"
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 5 Page I of6 Analysis of UT information and Information from Design Drawings
- 1) Comparison of Freespan length to develop as-built nozzle configuration for Finite Element Model.
- 2) Development of nozzle dimension and fillet weld profile.
Analysis sequence:
- 1) Using design drawing information and blind zone elevation of 1.544 inch, determine design based freespan length.
- 2) Compare the as-designed freespan length with UT measured freespan length at both the downhill and uphill locations.
- 3) Record the differences.
- 4) Based on an evaluation of the differences, develop nozzle dimension and expected fillet weld profile.
- 5) Develop nozzle configuration for FEA model.
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 5 Page 2 of 6 Design Analysis Information uO Nozzle
_U_
As Designed Length All HS 1.21 Bottom 0.56 Top 1.77 II
-'~~~~~~
.1-Il,..
I.
As Designed Bottom Low HS 0.54 High HS 1.17 As Designed Top Low HS 1.73 High HS 2.41 As Designed Length Low HS 1.19 High HS 1.24 As Designed Bottom Low HS 0.44 High HS 2.69 As Designed Top Low HS 1.64 High HS 4.09 As Designed Length Low HS 1.19 High HS 1.40 As~~~~~~~~~~~~~~~~~~~~~~~~~~~_
Deige
__.__o.N..zz....l.....
As Designed Bottom As Designed Top As Designed Length Low HS High HS Low HS High HS Low HS High HS 0.21 5.05 1.51 6.75 1.30 1.71
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 5 Page 3 of 6 Comparison of UT and design Data 0.00 Nozzle Bottom Top l
Length I Measured Diff Measured Diff Measured Diff Nozzle 114 1
All HS 0.32 0.24 1.24 0.53 0.92 0.29 8.8° Nozzle 1
Bottom l
Top l
Length
_ Measured Diff Measured Diff Measured Diff Nozzle 2
Low HS 0.24 0.30 1.20 0.53 0.96 0.23 High HS 0.84 0.33 1.84 0.57 1.00 0.24 Nozzle 3
Low HS 0.16 0.38 1.24 0.49 1.08 0.11 High HS 0.92 0.25 1.88 0.53 0.96 0.28 Nozzle 4
Low HS 0.18 0.36 1.24 0.49 1.06 0.13 High HS 0.80 0.37 1.92 0.49 1.12 0.12 Nozzle 5
Low HS 0.32 0.22 1.24 0.49 0.92 0.27 High HS 1.00 0.17 1.96 0.45 0.96 0.28
- 1) Note the differences between the bottom and top locations (Diff Column); They are consistent but the differences are 0.33 inch at bottom (both downhill & uphill) and 0.53 inch at the top (both downhill & uphill). This indicates that the nozzle may be shorter.
- 2) The average between the differences is about 0.4 inch, hence a nozzle that is shorter by 0.4 inches would minimize the differences between the as-designed and UT measurements.
- 3) The measurement for weld length (diff. in Length column) is small and random; indicating that the weld profile is close to the as-designed condition.
- 4)
A nozzle configuration with a shorter (2.08 inches vs. 2.48 inches) by 0.4 inch with an as-designed weld profile provides the best estimate for the as-built configuration of these two nozzle groups.
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 5 Page 4 of 6 Evaluation of the 28.80 Nozzle Group:
28.80 Nozzle 1
Bottom l
Top T
Length Measured Diff Measured Diff j Measured Diff Nozzle Low 30 HS 0.16
-0.28 1.36
-0.28 1.20 0.01 High HS 2.48
-0.21 3.76
-0.33 1.28
-0.12 Nozzle Low 31 HS 0.20
-0.24 1.32
-0.32 1.12
-0.07 High HS 2.56
-0.13 3.56
-0.53 1.00
-0.40 Nozzle Low 32 HS 0.16
-0.28 1.24
-0.40 1.08
-0.11 High HS 2.60
-0.09 3.64
-0.45 1.04
-0.36 Nozzle Low 33 HS 0.00
-0.44 1.40
-0.24 1.40 0.21 High HS 2.24
-0.45 3.72
-0.37 1.48 0.08 Nozzle Low 34 HS 0.20
-0.24 1.08
-0.56 0.88
-0.31 High HS 2.12
-0.57 3.68
-0.41 1.56 0.16 Nozzle Low 35 HS 0.16
-0.28 1.40
-0.24 1.24 0.05 High HS 2.76 0.07 3.88
-0.21 1.12
-0.28 Nozzle Low 36 HS 0.04
-0.40 1.60
-0.04 1.56 0.37 High HS 2.48
-0.21 3.80
-0.29 1.32
-0.08 Nozzle Low 37 HS 0.24
-0.20 1.52
-0.12 1.28 0.09 High HS 2.68
-0.01 4.00
-0.09 1.32
-0.08
- 1) Differences between the bottom and top locations are varied.
- 2)
At the downhill (low HS) location the differences between the bottom and top are significant.
- 3)
At the uphill (High HS) location the differences are not very significant.
- 4) This indicates that the weld profile at the down hill location are different from that at the uphill location.
- 5) Experience from another CE fabricated RV head indicated that the Fillet weld at the downhill location had a larger radius than specified ( as found vs. 3/16 as-specified).
- 6)
The weld size at the uphill location is close to the as-designed condition.
- 7) The nozzle lengths appear to be close to the as-designed value of 2.48 inches.
- 8)
A nozzle configuration having a as-designed length, as-designed weld profile at the uphill location, and a larger fillet radius at the downhill location will minimize the observed differences between the as-designed and UT (as-measured) data.
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 5 Page 5 of 6 49.60 Nozzle Group 49.60 Nozzle 1
Bottom Top
[
Length l Measured Diff l Measured Diff Measured Diff Nozzle 70 Low HS 0.00
-0.21 1.44
-0.07 1.44 0.14 High HS 5.04
-0.01 6.52
-0.23 1.48
-0.23 Nozzle 71 Low HS 0.00
-0.21 1.32
-0.19 1.32 0.02 High HS 5.04
-0.01 6.52
-0.23 1.48
-0.23 Nozzle 72 Low HS 0.00
-0.21 1.32
-0.19 1.32 0.02 High HS 5.08 0.03 6.52
-0.23 1.44
-0.27 Nozzle 73 Low HS 0.00
-0.21 1.20
-0.31 1.20
-0.10 High HS 5.00
-0.05 6.44
-0.31 1.44
-0.27 Nozzle 74 Low HS 0.00
-0.21 1.20
-0.31 1.20
-0.10 High HS 5.12 0.07 6.28
-0.47 1.16
-0.55 Nozzle 75 Low HS 0.00
-0.21 1.20
-0.31 1.20
-0.10 High HS 5.00
-0.05 6.40
-0.35 1.40
-0.31 Nozzle 76 Low HS 0.00
-0.21 1.60 0.09 1.60 0.30 High HS 4.64
-0.41 6.52
-0.23 1.88 0.17 Nozzle 77 Low HS High HS Nozzle 78 Low HS 0.00
-0.21 1.48
-0.03 1.48 0.18 High HS 5.16 0.11 6.68
-0.07 1.52
-0.19 Nozzle 79 Low HS 0.00
-0.21 1.64 0.13 1.64 0.34 High HS 4.96
-0.09 6.52
-0.23 1.56
-0.15 Nozzle 80 Low HS 0.00
-0.21 1.44
-0.07 1.44 0.14 High HS 4.96
-0.09 6.52
-0.23 1.56
-0.15 Nozzle 81 Low HS 0.00
-0.21 1.56 0.05 1.56 0.26 High HS 5.08 0.03 6.48
-0.27 1.40
-0.31 1 ) Observations are similar to that fro the 28.80 nozzle group. Therefore a similar nozzle configuration would exist.
- 2)
The estimated as-built nozzle configuration for this group is similar to that for the 28.80 nozzle group.
- 3)
Using this approach it is demonstrated that the weld bottom at the downhill location would fall 0.18 inch below the dead zone for this group of nozzles.
- 4)
Sketches in the following pages show the estimated as-built configurations for the 28.80 nozzle group and the 49.60 nozzle group.
Engineering Report M-EP-2003-002-01 Appendix A; Attachment 5 Page 6 of 6 Sketches for Estimated As-Built configuration for the 28.8° and 49.60 nozzle Groups ANO 2 -49.6 Degree CEDM Nozzle ANO 2 -28.8 Degree CEDM Nozzle Sketches showing estimated as-built configurations. The blue lines show the estimated as-built profiles for the weld (fillet cap) at the downhill locatrion.
C 114
Engineering Report M-EP-2003-002-01 Appendix B Appendix B Explanation of Mathcad worksheet used in the deterministic Fracture Mechanics Analyses.
This Appendix has three (3) Attachments.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page of 23 ID Surface Flaws Entergy Operations Inc.
Central Eflginefing Program,,s 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 Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"8.8" Degree Nozzle, "0" Degree Azimuth, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "R Itt -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1 The correction is applied in the determination of the crack extension to obtain the value in inch/hr ID Surface Flaw General information containing the Component Identification for analysis. Note the information for Nozzle group, Location, and Elevation at which the analysis is being performed. This information is not critical to the analyses; it is general information but it is important for cataloging the analyses files.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 2 of 23 The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flow.
This is defined as the reference point Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
Rtel Pojint := 1.544 ro place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper c-tip" located at the reference point (Enter )
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower Vc-tip" located at the reference point (Enter 3).
Val :=
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.
[ 1Strs.Dist := 2.05 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Three critical information are required in the three entries on page one.
1 ) the first entry required {Refpoint} is the "Reference Location"; this entry defines the reference line (e.g. the blind zone elevation) with respect to the nozzle bottom.
- 2) The second entry {Val} defines the location of the Crack. In the current analysis a value of two (2) is selected. This value locates the center of the flaw at the reference line described above.
- 3) The third required input is the upper limit, elevation above nozzle bottom, to be used for the stress distribution that will be used in the analyses. This location for the current analyses is chosen to be slightly above the bottom of the weld such that the appropriate stress profiles are incorporated into the analyses.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 3 of 23 Input Data
- 1.
.35 Initial Flaw Length ao 0.03 Initial Flaw Depth od 4.05 Tube OD id 2.728 Tube ID Pint := 2235 Design Operating Pressure (internal)
Years := 4 Number of Operating Years Ilii, := 1500 Iteration limit for Crack Growth loop T := 604 Estimate of Operating Temperature Qtlc :=2.67 1-12 Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Q g 31.0 Thermal activation Energy for Crack Growth {MRP)
T re : 617 Reference Temperature for normalizing Data deg. F
- 1) General Input data for tube and flaw geometry. In addition other parameters required for the analyses are defined. These inputs remain unchanged for this set of analyses.
- 2) The input for internal pressure PIlnt is used to add the internal pressure to the flaw face.
- 3) The operating time Years is set to four (4) such that proper analysis for one cycle of operation is obtained.
- 4) The iteration limit ILim is prescribed as a large number (1500) such that small time increments for crack growth are used in the crack growth analysis.
- 5) The remainder of the inputs are for crack growth model, which is based on MRP-55 at the seventy-fifth percentile.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 4 of 23 od RO Rid:= id2
(
- = Ro - Rid R1l := Rtido t Timopr := Yars-365-24 Cljlr:= 1 417-105 Timlp him
': iln L
Co
=
Rill C 0
(
I I
T Co I1., 10-3 T+159.,
"ret+159.671 CO[ I= C' U
OC Temperature Correction for Coefficient Alpha CO:= CoI 75 th percentile MRP-55 Revision 1 General calculations to develop the constants needed for the analyses.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 5 of 23 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "o" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1' = ID Stress data at each Elevation (ksi)
Cloumn 2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column 4" = Three quarter Thickness Stress data at each Elevation ksi)
Column "5' = OD Stress data at each Elevation ksi)
AIII)ata :=
I _ ~~~~~~~~~~~~~1E111 111 0
-28.32
-18.3
-12.16
-6.2
-002 0.35
-18.79
-1249
-661
-1.37 3 65 0 63
-17.84
-1052
-441
-0.48 2.08 085
-20.52
-12 97
-5 9
-0.87
-1 54 103
-19.66
-11 83
-529 0.23 1 46 1 18
-17.2
-10 59
-0 52 16.33 21 02 1.29
-8.02
-2.2 10.46 32.66 37 29 1.44 4.78 9.56 24.9 38.18 54 09 1,59 13.25 18.57 35.28 52.81 66 52 1 74 16 2202 39.19 62.95 75 1 89 15.86 23,14 40.23 64.33 74 87 204 12.63 23 76 41.26 58.67 66 78 AXI.el:= AlIII)alao° IlDAI := Alll)att l Stress Distribution (l)All := A\\lI)ata >i
-4(
I) of.5 l
1.5 2
25 3
3 5 Axial Elevation above Bottom linchi ID Distrihution
)OD Distribution
- 1) the nodal stress data is imported from an Excel spread sheet provided by Dominion Engineering. The appropriate data set in the spread sheet is provided in the import command in Mathcad. It is important not to import the node number column.
- 2) The data imported is plotted for the ID and OD distribution along the length of the nozzle.
- 3) The plot presents all the nodal stress data imported. This plot is used to define the region of interest for analysis and to select the sub-set of stress distribution data pertinent to the analysis.
(-IS
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 6 of 23 Observing the stress distribution select the region in the table above labeled DataAj, 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.
(
0
-28 324 -18 299 -12 16 -6.201
-0.021 )
Data :=
0 35
-18 794 -12,495
-6.607
-1.366 0 63
-17,838 -15 1 8 -4.407 -0.477 0.854 -20. 5 1 7 -12.968 -5.902 -0 874 I 034 -19.663 -1 1.831
-5288 0 227 178 -17 203 -10.587 -0.515 16.326 I 293 023
-2.205 10461 32.658 1442 4,778 9.557 24,903 38.1 77 1,591 13252 18569 35278 52808 1s74 16.001 22.017 39 194 62.945 1.889 15.857 23.14 40.235 64.335 2.038 12.629 23.76 4 1.263 58.673 3.655 2.08
-1.36 1 46 2 1.019 37.2 89 54.089 66.5 17 75.00 1 74.874 66.777) k Axi := Datao)
NtD := Data')
ID := Data I)
TQ:= Data(4)
QT:= Data(~)
OD:= Data(5)
RID := regress(AxIID,3)
RQ,- := regress(AxI, QT 3)
ROD:= regress(Axl,OD,3)
RNID := regress(Ax1,M/lD.3)
R-0-( := regress(Axl,TQ, 3)
- 1) Shows the incorporation of the selected data into a Data matrix that will be used in the analysis.
- 2) The definiton of the axial distribution at the five locations through the wall thickness are defined.
- 3) A third-order polynomial regression is performed at each of the five through-wall locations to define the curve used to develop the through-wall distributions.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 7 of 23 Hi ntr :=
Co it Val =
Flaw center Location above Nozzle Bottom Ret'Pjrt i Val = 2 Reljoint + c others ise I'i := H~-Cntr+ co lCSts.a-
=
UI'Strs.Dist -
rip 20
- 1) defines the upper tip of the flaw based on reference line and flaw location (Val) inputs provided in the first sheet.
- 2) Determination of segment length above the initial crack upper tip location.
Twenty (20) segments are used.
N :=2o Number of locations for stress profiles Loco := FLCntr L
i:=.. N +
Incr =
co if i < 4 I1llCStrs.axNg otherwise Loci := Loci-, + Incri
- 1) Setting of the iterative loop to develop the through-wall stress distribution.
- 2) Initialization of the loop to define axial elevation and segment length required to obtain the through-wall stress profiles at defined locations.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 8 of 23 SIDi = RID + RID Loci + RID (Loci)' + RID (Loci) 3 3
45 6
SQTi RQT + RQTI 0L'ci + RQT (oci)
+ RQT (Loci) 3 S1 4
56 SMDi= RNID + RNID *-oci + R..1D (Locj) + RN-ID (Loci)3 3
4 6
STQi:= RTQ + RTfQ TLocj + RTQ (LoCi)
+ RTQ6 4Loci)
SOD = ROD + ROD Loci + ROD (Loci) + ROD (Loci)3 3
~4 6
Determination of stresses at the five locations through the thickness and at defined elevations. This structure develops the matrix for the through-wall stress distributions for the defined locations that will be used in the moving average method for developing the stress profiles.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 9 of 23
.. N Sid.
Smd J.=
SID, + SIDj+j + SIDj+2 ifj=
sqtj =
SQTi + SQTj+l + SQTj+
3 SI (i + ) + SQTJ+-
j + 2 Sid
- (j + ) + SIDj+2
-,i.
--.; c,
" LIl I I I % t5:
j+2 SMDJ + SMDJ+ + Sll)j+,
it'jf Sid (j + I) + SNMDi+-
.1-I otherwise j +2
_) if j =
- otherwise
-7 it' j =I otherwise Stq.=
STQ + TQ1~+1 I-STQ +
3 Stq (j + l)+ STQ+2 j + 2 i=
SOD + SODj+' + SODj+2
- f,*
Sod
- (j + I) + SODj+2 otherwise j+2 Loop structure to perform the calculations for stress profiles at the defined locations along the nozzle height.
- 1) All five locations through the thickness are similar.
- 2) The first conditional statement defines the average stress at the initial flaw location, which is the average of the stress at the lower tip, the flaw center, and the upper tip. These stresses are used to calculate the applied stress for the initial flaw.
- 3) The second conditional statement performs the moving average at each segment location. Thus the moving average accounts for the changing stress field as the crack progresses towards the bottom of the weld. In the current analyses the stress field increases in magnitude as the crack progresses towards the weld bottom.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 10 of 23 11 0
- = 10 01 0
- =
Uooo LIl := 0.25 L12 := 0.50 U3 := 0.75 Y := stack (uLO. L IL.2
.1134)
SIG
= stack(Si Sqt Sld* Stq Sod )
SIG,)
SIG3 stack(Sid3 Sqt3 SIld 3 Stq3 Sod3)
SG :
SI67:= stack (Sid sqt Smd5Stq 5
S(5)
S1G6 SIG7 stack Sid7 Sqt7 Sind7 Stq7Sod)
S[So)S8 SIG9 stack (Sid S q19 Smd,)Stq 5 Sod
)
S[G161 SIG II stack (S Id S~t Sllll I'S qI ISod u)
S['12=
SIC13 =stackSid Sqt SndSKIS ack'S SIGS stack( Sid. Sqt, sid,' Stq2. Sod )
stack( Sjd Sqt
- d *Stq4 Sd 4) stack(Sid 6Sl 6Snd 6 St.
od6 )
stack (Sid8 ' Sqts Snids stqs Sods)
= stack (Sid SqtIO SnlldW Sl1O'Sod 0)
= stack(Sid 1 Sqt2 Silld<lStq< Sod12)
= stack(Sid
- Sqt 1. Sminil StqltStod J)
SIG 5 := stack ( Sid 5,Sqt 1Smd
' Stq sod,_)
SqG16 = stack(Sid 1
6Sqt16 Sid 16 '
stq16 Sod 16)
SI1 7
= stack(Sid,Sqt Sind 7'stq, Sod 7)
SIG 18
= tack(Sid,.,Sqt Smfnd.Stqjs.SodI)
SIG 9 := stack(Sid sqt9 Stndl 9 Stq19 Sod,))
S1G20= stack(Sid20 Sqt 2 Snd20 Stq2 od20)
Setting of a column matrix for the stresses at each segment for the five through-wall location.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page I I of 23 IDRG 1 regress(Y, SIC I 3)
IDRCG3 regress(Y, S1CG3.3)
IDRG 5 reoress(YSIG5,3)
IDRG7 regress(Y,SIG 7,3)
IDR 9 := egress(YSIG9.3)
IDRII regress Y, SIC D3)
IDR 13 regress(Y, SIG 3,3)
IDRG15 regress (SIG 5 *3)
IDRG1 7 regless(Y, SIG17 3)
IDRG := regress( Y, SICJ 9, 3)
- 1DRG, regress (Y, SIGJ2
)
IDRG 4 regress(Y, SI1 4.3)
IDRG6 regress(
. 163)
IDRG8 regress(YSIG 8 3) 1DR G10 regress(Y, SI, 0 3) 1DRG 12 regress(YsIG 12.3)
IDRG 14 regress(Y,SIG 1 4.3)
IDRG 16 egrcss(YS G16 3)
IDRG 18 regress(YSICs18 3)
IDRG,2 0 regress(Y, SIG 20 3)
Third-order polynomial regression to determine the coefficients that describe the stress distribution through the wall at the defined locations.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 12 of 23 SICF Coefficient Determination Jsb :=
0 1
2 0
1.000 0.200 0.000 1
1.000 0.200 0.200 2
1.000 0.200 0.500 3
1.000 0.200 0.800 4
1_000 0.200 1.000 5
1.000 0.400 0000 6
1.000 0.400 0.200 7
1.000 0.400 0.500 8
1.000 0.400 0.800 9
1.000 0.400 1.000 10:
1.000 1.000 0.000 11 1.000 1.000 0.200 12 1.000 1.000 0.500 13 1.000 1.000 0.800 14 1.000 1.000 1.000
.1 2 2.000 0.200 0.000 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 Partial data table for the SICF determination.
- 1) Column 0 is the Rm/t ratio.
- 2) Column 1 is the a/c ratio (crack aspect ratio)
- 3) Column 2 is the a/t ratio (normalized crack depth)
This table in conjunction with the table in the following page together is used to determine the particular SICF
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 13 of 23
- mbi :=
0 1
2 3
4 5
6 7
0 1.076 0693 0.531 0.434 0.608 0.083 0.023 0.009 1
t056 0.647 0.495 0.408 0.615 0.085 0.027 0.013 2
1.395 0.767 0.557 0.446 0.871 0.171 0.069 0.038 3
253 1.174 0.772 0.58 1.554 0.363 0.155 0.085 4
3846 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 0556 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 1.09 0.661 0.502 0.413 0.614 0.083 0025 0.012 Partial table of the influence coefficients (SICF) as described below:
- 1) Column 0 is the uniform coefficient for the a-tip.
- 2) Column 1 is the linear coefficient for the a-tip.
- 3) Column 2 is the quadratic coefficient for the a-tip.
- 4) Column 3 is the cubic coefficient for the a-tip.
- 5) Column 4 is the uniform coefficient for the c-tip.
- 6) Column 5 is the linear coefficient for the c-tip.
- 7) Column 6 is the quadratic coefficient for the c-tip.
- 8) Column 7 is the cubic coefficient for the c-tip.
Both tables, (labeled Jsb and sambi), have the same number of rows.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 14 of 23 sh(O)
X =Jsb()
Y := Jsb(`)
a, : Sambi(P) at, Sarnbi~')
aQ Sambi(l) aC Sambi(3) cl:
Sambi(I) cL Sambi(5 CQ Sambi6S
)
n:=
3 if Rt*40 l 2 otherwvise "a-Tip" Uniform Term MIat: aL, tl I(VNX.Y)
Vatl all.
Rau regrcss(Mat I al a )
f tj(\\AXY) := interp RaU, Nia. VaL;* X ratj(4, 4, 8) = 1424 Check Calculation Programming steps shown for determining the SICF.
1 ) First is the definition of the column matrix defined with respect to the tables above.
- 2) Second is the conditional statement that defines the polynomial order based on cylinder property (Rm/t ratio). For thick cylinder the polynomial order is cubic (3) whereas for thin cylinder it is quadratic (2).
- 3) Third the Mau statement assembles the matrix required for regression and interpolation for the uniform a-tip SICF.
- 4) Fourth the Rau statement performs the nonlinear regression on the assembled matrix to determine the regression coefficients needed for the interpolation routine. This is for the uniform a-tip term.
- 5) Fifth the fau statement defines the interpolation function. This is for the uniform a-tip term.
- 6) Sixth the fu(4,.4,.8) statement is the check calculation for Rm/t = 4, a/c =
0.4 and a/t = 0.8. The calculated value of 1.424 compares favorably with the text value of 1.443.
- 7) Similar structure is followed for all the other SICF entries.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 15 of 23 Recursive Loop for Calculation of PWSCC Crack Growth C~GJRsaiiubi :
-v 0
at <- ao CO -- C0 NCBO0 Cblk NvNhile j c [,it,,
Start of the recursive loop showing the loop initialization.
- 1) Index "j" is set to zero (0).
- 2) Initial crack depth and half length are defined.
- 3) The Time for corrosion interval is initialized.
- 4) The internal loop for each corrosion time span is initiated.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 16 of 23 a
I-JDRG3 if ci CO IDRGC2 if co < j co+ IncStrs aog IDRGi3 if c0 + IcStrs avg < Cj co + 2 lCStrs axa DR43 ~C 0 + 2*IlC~1l.S.axg c c; K co + 3 lflCStrs ag 3
IDRG5 if co + 2J CtlcStrs acj c
CO + 4 InlcSts.avg IRCJ 63 if C0 + 4.IrlCtrs avr c C1 c c0 + 5 T1C~ti.s axo 3
L t
IDRG37 if co + 3. lnCStrs ag < 9 co + 6 IncStrs.avg IDRG3 if co+
( ICStrs.avg
< cj < co +
f rlncStrs avg IDRG9 if co + 7 fl`cStrs.sasg < Ci
- co + 8 ICStrs.avg 73 IDRC 1 i
C+ 7-I~~rv < C 1
- CO +9ilCStr.axrg IDRGJ I no if co + 8 Ictr';s avg < c < o + 9 IcStrs-.aN-g
-5 Partial statement showing assignment of the uniform stress coefficient. The assignment considers all twenty (20) segments. Similar assignment statements cover the other three stress coefficients (viz. linear - a,, quadratic-C2, and cubic (53). The assignment is based on the current flaw upper c-tip location. The conditional statement is based on current location cj" as compared to the upper and lower limit for each segment.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 17 of 23
(-C O0 1-o+
I.
t251 )
t)
+(32
+
(
225-aj) 17i2 <- (I + 6a](
0.5. a t)
O075.a;)
I
+/- (2
)
+
I+ CT2
- 0. 75.ajy)
+cs205a~~a+
43 <-(To+
I (
(( 75ai3
+3 3
(33~~~~
4<- 0 +
/(I3. ~
t
)
Using the stress coefficients for the through-wall stress distribution, this step determines the stress distribution across the crack face in the depth direction.
The crack depth is divided into five equal segments. The stress distribution across the crack face is calculated for each current crack location.
X0 <l 0.0 X *-
0.215 x1 05 X3<- 075 X4 _ o X - stack(,
x x2, x 3 4)
ST - stk(4 1 l2'43 44)
Developing the appropriate matrix and performing a third-order polynomial regression to determine the stress coefficients for the stress distribution across the crack face. These stress coefficients are used in the SIF dteremination.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 18 of 23 o <-
RGJ + PInt CT0 RG 4 Go RG 5 l l30
- K"6 Assignment of the stress coefficients. The stress coefficient for the uniform term 00 contains the coefficient for the uniform stress (operating+residual) and the addition of the internal pressure (Pint). This is the step where the internal pressure is added to the calculation. This step ensures that the crack faces are pressurized.
ci AT-a1
--1 t GZrl < f (Rt?*AR; SAT.;)
Gal C faL(Rt ARj AT.)
G
<q G
faQ R AR.;XAT.;)
GcNJ. j -
faC,( Rt. A ARj A Tj)
GVCUi <- f, t (Rt v ARj AT;)
Gal c f<ELc(RtARi.AT)
Gcqi fCQ(RtARj ATj)
G Cej
- fC(Rt, AEi v ATi)
Step showing calculation of current crack aspect ratio (a/c), the current crack normalized depth (a/t) and the function call {G,,; e.g.(
ji )} for the eight SICF associated with the current crack dimensions.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 19 of 23 1.65 Q
l
<-A I
s.464-if I
+ 1.464{An othernise Determination of the crack shape factor depending on the current crack aspect ratio.
K~a
~~j
.y (C7( Gau + Gi10 (a i + 20(3
+6 Glac)
K, <
'aL~j + a I O'C'a.,) + ()0 lCaq.j + 0 30C KC.jv Kaj 099
.5 K
-K J 099 Determination of the SIF at the two crack tips (a-tip and c-tip) in English units and conversion to metric units.
KU.
~ i Ka <9.0 K l totherwise Conditional statement to test for the threshold value for the SIF. This is needed for PWSCC crack growth analysis. Done for both the a-tip and c-tip. Only the a-tip is shown.
Da+
Co.(K~ 9.O) 1.16 Calculation of the crack growth rate {da/dt} in metric units (m/sec). Shown for the a-tip but sthe same calculation is performed for the c-tip.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 20 of 23 D
D
'CF lCblk if c < 0o ag1i
- a.
inhir hk K
<8.
.1 j
- 4. l 0 1 inhr Cbik otherwise Calculation for crack growth in one time block. This block for the current analysis is about twenty-four hours (24 hrs.). The crack growth is in English units (inch) because the conversion factor {CFinhr} is used. The first statement is set when the SIF is below the upper asymptote and the second statement is used when the SIF is greater than the upper asymptote. When the SIF is greater than the upper asymptote, the SIF independent crack growth is about 0.5 inch per year.
Oiltpttj.0) <
3i OLltplllt( j.)
i OlltPllt(j C
Co OuPtput o 5)-
Ka.- c OUtpUt(j 3) -
Dag Ot}Ut(tJ D) <-D Ha OUtpUt(j 6)
KCJ NCB j nUtput(j 7) <-,6) 3165-24 Typical output statements within the recursive loop showing the storing of variables that are required for loop operation and those of interest in displaying the time dependent trend.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 21 of 23 aj -a
+ Dag
~i<--
J
+ DC9j i
vt if t X-L l ai otherwise NC'Bj - NCBj-1 + CMik oLutptlt The recursive loop is incremented and the required variables (crack depth, crack length, and the time variable are updated for the start of the next recursive loop operation. The last statement is a dummy statement to terminate the recursive loop.
ProPLcngth 0.506 Flaw GroNtth in Deplh Direction I
I I
I I
I I
0.6 0.1 -
0.2 -
I I
I I
I I
I o -
o
- 0. 5 1
1.5 2
2.5 Operating Time {years) 3 3.5 4
Typical Mathcad graphical display used to evaluate the important parameters.
The PropLength in the upper left corner is used to ascertain the growth to the weld.
This number is calculated internally before the recursive loop is started. This is the difference between the weld bottom location (ULstrs.Djst) and the Crack Upper Tip location (UTip).
CGRsanbi( k S) 1 1
1 1
1 1
1 1
1 1
1 1
l Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 22 of 23 CGRsambi CGRsamhi k6) 0-163 0111 0-163 0.111 0-163 0.111 0163 0.111 0163 0111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 0.163 0.111 Typical numerical output in tabular form used to ensure proper functioning of the model.
0.5 013 5.0 3
.0.5
,.,.K.................
~~~~~~.
0 1
2 Operating T Imle (years)
Typical Axum graphics for use in the report.
3 4
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 1 Page 23 of 23 End of the Mathcad worksheet Description
Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Programs Page 1 of 30 M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis - OD SurfaceFlaw beveloped by Central Engineering Programs, Entergy Operations Inc levelopedby: J. S. Brihmadesanl Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-11707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"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:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
OD Surface Flaw The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Note :- The two differences between this model and the ID surface flaw model are:
- 1) Use of SICF tables from Referencel for External flaws (pages 9 - 12).
- 2) The stress distribution is from the OD to the ID (pages 6 - 8).
These differences are noted (in bold red print) at the appropriate locations.
The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPo in t := 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "c-tip" located at the reference point (Enter 3).
Val :=
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Input Data :-
Appendix B; Attachment 2 Page 2 of 30 Engineering Report M-EP-2003-002-01 L := 0.3966 ao := 0.0661 od := 4.05 id := 2.728 Initial Flaw Length Initial Flaw Depth Tube OD Tube ID PInt := 2.235 Years := 4 Iim := 1500 T := 604 aoc := 2.67 10- 12 Qg := 31.0 Tref := 617 Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od Ro := 2 id Ri t:= Ro - Rid t
Rm : Rid + -
Timopr := Years-365*24 CFinhr := 1.417 105 Timopr Cblk :=-
Iim Prntblk =
50 L
C0 2
Rm Rt 1.103 lo 3
+49.67 Tref+459.67 T
C I := e A
1xoC Temperature Correction for Coefficient Alpha Co = Col Stress Input Data 75 th percentile MRP-55 Revision 1 Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 3 of 30 Engineering Report M-EP-2003-002-01 Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minumum to maximum recorded on data sheet(inches)
Column "1" = ID Stress data at each Elevation (ksi)
Column "2" = Quarter Thickness Stress data at each Elevation (ksi)
Column "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three Quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
01 0
-27.4
-24.36
-22.21
-20.41
-18.98
- 1 0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4
1.43 33.62 27.79 24.8 24.32 26.99 5
1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67
-9 2.18 14.83 22.26 34.78 49.05 63.38 AXLen:= AllData(0)
IDA11 := AData(')
0DA11 := AData(5)
Stress Distribution
=
IDAIJ CA C,
ODAll 3-.
ci
-50 0 0.5 1
1.5 2
2.5 AXLen Axial Elevation above Bottom [inch]
3 Observina the stress distribution select the reaion in the table above labeled DataAI, that represents the Developed by.,
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programns Appendix B; Attachment 2 Page 4 of 30 Engineering Report M-EP-2003-002-01 region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data" statement below and delete it from the edit menu. Type "Data and the Mathcad "equal" sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).
0
-27.404 -24.356 -22.209 -20.407
-18.978 )
Data :=
0.483 0.633
-1.486
-3.599
-4.44
-5.268 0.87 17.665 16.422 14.61 12.415 9.376 1.18 29.798 26.049 22.723 18.95 14.201 1.428 33.623 27.792 24.8 24.321 26.989 1.627 32.364 28.469 27.591 34.284 45.104 1.786 27.394 28.918 31.388 43.882 63.718 1.919 21.498 25.556 33.55 48.089 66.365 K2.051 16.944 23.793 34.064 49.472 67.672 )
Axl := Data(°)
MD:= Data3)
ID := Data(l)
TQ := Data)
QT := Data(2)
OD: Data (5)
RID := regress(Axi, ID,3)
RQT := regress(Axl,QT,3)
ROD := regress(Axl, OD, 3)
RMD := regress(Axi,MD,3)
ULStrsDist = 1.786 Upper A>
nozzle bc RTQ := regress(Axl,TQ,3)
Jial Extent for Stress Distribution to be used in the Analysis (Axial distance above Atom)
FLCntr =
RefPoint -c 0
if Val =
RefPo in t if Val = 2 Refp0 int + c0 otherwise Flaw center Location Location above Nozzle Bottom UTip := FLCntr + CO IflcStrs.avg ULStrs.Dist - UTip 20 Developed by:
J. S. Brihmadesam Verified by:
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Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 5 of 30 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-1 + Incr; SDi: RID + RID Loci + RID.(Loci)'+ RID (Loc i) 3 SQTi RQT + RQT Loci + RQT (Loci)2 + RQT (Loci)3 SMDi RMD + RMD 4 Loci + RMD.(Loci) + I RMD (Loci) 3 STQi := RTQ + RTQ -Loci + RTQ (Loci) 2 + RTQ6 (Loci) 3 SODi ROD + ROD Loci + ROD.(Loci) 2+ ROD (Loci) 3 Development of Elevation-Averaged stresses at 20 elevations along the tube for use in Fracture Mechanics Model j :=.. N l S1Di + S1Di+1 + SIDj+2 I SQTj + SQTi+1 + SQT1+2 Developed by.
J. S. Brihmadesam Verified by; B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 6 of 30 Engineering Report M-EP-2003-002-01 Siid. =
J Sijd (j + 1) + SIDj+2 j+2 it j =
otherwise Sqt. :=
3 Sqt (i + ) + SQTj+2 j+2 it J =
otherwise
-2 if j=
otherwise S
J SMDj + SMDj+l + SMDj+2 if j = 1 3
stqj =
Smd
.(j + I) + SMDj+2 j+2 STQj + STQj+j + STQjd 3
Stq I(j + ) + STQj+2 j+2 otherwise Sod, =
.3 SODj + SODj+ + SODj+2 i 3
ij Sod
- (j + 1) + SODj+2 i-I otherwise j+2 Note the Change here to develop stress distribution form OD to ID Elevation-Averaged Hoop Stress Distribution for OD Flaws (i.e. OD to ID Stress distribution)
U0 := 0.000 U I := 0.25 U2 := 0.50 u3 := 0.75 u4 = 1.00 Y := stack(u 0,uI,u 2,u 3,u 4)
SIGI := stack(Sod, Stq,, Smd sqt, I Sid )
SIG2
= stack ( Sod2 Stq 2 Smd2 S Sqt2y Sid2)
Developed by; J. S. Brihmadesam Verified by:
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Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 7 of 30 Engineering Report M-EP-2003-002-01 SIG3 = stack (Sod3 5stq3,Smd3 Sqt3 S id3)
SIG 5 := stack( Sod 5 Stq5'Smd5 Sqt5, Sid5)
SIG 7 = stack (Sod 7 Stq7 'Smd7 Sqt7 Sid7)
SIG9 := stack (Sod 9 Stq9, Smd Sqt' Sid9)
SIG I := stack ( Sod,,'Stqj l Smd, C Sqtl Sid 1)
SIG 1 3
= stack(Sod 3'stq13 Smd1 3 9sqt 1 3' id 3 )
SIG 4 = stack(Sod4 5Stq4' Smd4 Sqt4 Sid4)
SIG 6 = stack( Sod6 5stq'6 5smd6 Sqt6' Sid6)
SIG8
= stack(Sod 8 Stq8 Smd8 ' Sqt8 Sid8 )
SIG I
= stack(S od1 Stq10, smd1r Sqt10 Sid10)
SIG 1 2
= stack (Sod 1 2 ' stq 12 'Smd 1 2' Sqt12 ' id 12 )
SIG14 = stack(Sod 4'Stq 14 'Smd14 ' Sqt14 ' Sid14)
SIG15 = stack(Sod 5Stq15 Smd 15 ' qt15' id15)
SIG16 = stack(Sod 6'stq 6'Smd6 qt
'Sid16)
SIG17 = stack(Sod stq17 ' Smd 17 ' sqt 17' Sid17)
SIG19 := stack(Sod Stq19 Smd19 ' Sqt 19 ' Sid19)
SIG 1 8 = stack(Sod 8 Stq 18 ' Smd 8 Sqt1 8 ' Sid18 )
SIG 20 := stack( Sod20 ' stq20 ' Smd20 ' qt2 o' Sid20)
Regression of Throughwall Stress distribution to obtain Stress Coefficients throughwall using a Third Order polynomial ODRG I :=regress(Y,SIGI,3)
_ ~~~~~~~~,..
ODRG2 := regress(Y, SIG 2,3)
Developed by.
J. S. Brihmadesam Verified by:
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Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 8 of 30 Engineering Report M-EP-2003-002-01
)DKR(i3 := regress( Y, S(j 3, 3)
ODRG5 := regress(Y, SIG 5,3)
ODRG7 := regress(Y, SIG7, 3)
ODRG9 := regress(Y, SIG9, 3)
ODRG1 1 := regress(Y, SIG 1 3)
ODRG1 3 := regress(Y,SIG 1 3,3)
ODRG1 5 regress(Y,SIG 15,3)
ODRG1 7 := regress(YSIG 1 7,3)
ODRG 1 9 := regress(Y,SIG 1 9,3)
UDRU 4 := regress Y,S1(j4, 3)
ODRG6 regress(Y,SIG 6,3)
ODRG8 := regress(Y, SIG 8,3)
ODRGIo : regress(Y,SIG 1 0,3)
ODRG1 2 := regress(YSIG12,3)
ODRG1 4 := regress(YSIG1 4,3)
ODRG1 6 := regress(YSIG] 6,3)
ODRG 18 := regress(YSIG, 8,3)
ODRG2 0 := regress(Y, SIG 2 0, 3)
Stress Distribution in the tube. Stress influence coefficients obtained from thrid order polynomial curve fit to the throughwall stress distribution ProPLength = ULStrs.Dist - FLCntr - CO ProPLength = 0242 Data Files for Flaw Shape Factors from NASA (NASA-TM-111707-SC04 Model)
{NO INPUT Required)
Developed by:
J. S. Bribmadesam Veifled by B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 9 of 30 Engineering Report M-EP-2003-002-01 Data Tables for External falws from Reference I Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=
0 2.
0 1.000 0.200 0.000
- 1 1.000 0.200 0.200
'2 1.000 0.200 0.500
- 3.
1.000 0.200 0.800 4
1.000 0.200 1.000 5
1.000 0.400 0.000 060 1.000 0.400 0.200 7
1.000 0.400 0.500 8
1.000 0.400 0.800 9:
1.000 0.400 1.000 10 1.000 1.000 0.000 11 1.000 1.000 0.200
- 12 1.000 1.000 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 23 2.000 0.400 0.800
<24 2.000 0.400 1.000 w2.5.
2.000 1.000 0.000 2.000 1.000 0.200 2.000 1.000 0.500 2.000 1.000 0.800 t9.
2.000 1.000 1.000 4.000 0.200 0.000 31' 4.000 0.200 0.200
-34;2 4.000 0.200 0.500
_3 4.000 0.200 0.800 e34 4.000 0.200 1.000 935 4.000 0.400 0.000
-5 4000.0
.0 Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix B; Attachment 2 Page IO of 30 Engineering Report M-EP-2003-002-01 1361 4.000 0.400 0.200 37 4.000 0.400 0.500 38 4.000 0.400 0.800 389 4.000 0.400 1.000 40 4.000 1.000 0.000 41 4.000 1.000 0.200 42 4.000 1.000 0.500 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 51 10.000 0.400 0.200 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000
.63 300.000 0.400 0.000
,.6 300.000 0.400 0.200 67 300.000 0.400 0.500 68 300.000 0.400 0.800 69 300.000 0.400 1.000 70 300.000 1.000 0.000
'7,-O 300.000 1.000 0.200 72 300.000 1.000 0.500 73 300.000 1.000 0.800 74 300.000 1.000 1.000 Developed by.
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 11 of 30 Engineering Report M-EP-2003-002-01 Sambi :=
0 1
2 3
4 5
6 7
-o 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 10 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009
.2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4
4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5
1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6
1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023
- 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8
2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9
2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114
.10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023
- 21.
1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27#
1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068
-29, 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 t31 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
'33 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
@35 1
0.655 0.518 0.44 0.754 0.118 0.036 0.017 36:
1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073
.39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1
.4 0.986 0.711 0589 0.513 1.127 0.189 0.068 0034 Developed by:
J. S. Brihmadesam Veifed by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 12 of 30 Engineering Report M-EP-2003-002-01 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04
- 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064
'44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 46 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07
.54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059
.-59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07
'65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 w69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 W := Jsb()
X := Jsb( )
Y := Jsb(2) aU := Sambi(o)
CU := Sambi(4) aL := Sambi(1)
CL := Sambi(5) aQ := Sambi(2)
Q := Sambi(6) aC := Sambi(3) cc := Sambi(7)
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 13 of 30 Engineering Report M-EP-2003-002-01 n :=
3 if Rt < 4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W,X,Y)
VaU:= aU RaU := regress(Mau VaU n) faU(W,X,Y) :=
fau (4,4,.8) = 1.741
/IW)_
aU,MaU, VaU X
C a Y)_
Check Calculation Linear Term MaL := augment(W, X, Y) faL(WX,Y) := interp R faL(4,.4,.8) = 0.919 VaL := aL RaL := regress(MaL, VaL n)
Wa]
X I
,Y)_
Check Calculation Quadratic Term Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 14 of 30 Engineering Report M-EP-2003-002-01 MaQ:= augment(W,X,Y)
VaQ := aQ RaQ := regress(MaQ, VaQ, n) faQ(W.X,Y) := inte faQ(4,.4,.8) = 0.656 aWQ eMaQ VaQ, X I
,Y)_
Check Calculation Cubic Term MaC := augment(W, X, Y)
VaC := aC RaC := regress(MaC, VaC, n)
W)-
fac (W. X, Y) := interp RaC MaC, VaC X I faCWXY faC(4,.4,8) = 0.524 Developed by:
J. S. BrIhmadesam Check Calculation Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 15 of 30 Engineering Report M-EP-2003-002-01 U6 Tip coetticients Uniform Term MCu := augment(W,X,Y)
VCU : Cu RCu := regress(MCu, VcU, n)
Wf fcU(WUX, Y) :=interp RCU nMcU SvCU X I "I Y )_
fCu(4,.4,.8) = 1.371 Check Calculation Linear Term McL := augment(W,X,Y)
VcL := CL RCL := regress(McL, VcL, n)
_c Y :e{R LVcW)]
feL (W, X, Y) := interp RcL, McL, VcL X
fcL(2,.4,.8) = 0.319 Check Calculation Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 16 of 30 Engineering Report M-EP-2003-002-01 Quadratic Term MCQ := augment(W,X,Y)
VcQ Q
RcQ : regress(MCQ, VCQ, n) fcQ (W, X,Y) y)]
fCQ(4,.4,.8) = 0.126 Check Calculation Cubic Term Mc := augment(W,X,Y)
VCC : Cc ReC := regress(McC, VcCC n)
_c(WX,)neCrW)-
fc (W. X, Y) := interp RCC, MCC, VC X
fcC(4,4,.8) = 0.068 Check Calculation A-
-Cl----
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix B; Attachment 2 Engineering Report Page 17 of 30 M-EP-2003-002-01
%.*aicuiaons; ecursive caicuations Io esumLmae iaw growmn.
Recursive Loop for Calculation of PWSCC Crack Growth Entergy Model CGRsambi j<-o aO < aO Co - CO NCBo<
Cblk while j <Iim o0 ODRG1 ifcj<co ODRG2 ifco < j co + Ifncstrs.avg ODRG3 ifC0+ Incstrs.avg <
co + 2dIncStrs.avg ODRG4 if co + 2Incstrs.avg < cj < co+ 3Incstrs.avg ODRG 5 if Co + 3Incstrs.avg < ci< Co+ 44Incstrs.avg ODRG63if Co + 4ncstrs.avg < ci< Co + 5Incstrs.avg ODRG7 ifCo + 5Incstrs.avg < cj < Co + 6Inctrs.avg ODRG83if co0+ 6ncstrs.avg < ci< CO + 7IncStrs avg ODRG 9 if co + 7Ifncstrs.avg < cj < CO + 8Ilncstrs.avg 3
ODRG 10 if co+ 8IncStrs.avg < ci <o+ 9lncstrs.avg ODRG 13 ifc+9ncStrs.avg< ci<CO+ oIncstrs.avg ODRG12 if co+ l0IncStrs.avg < j < co0+ Incstrs.avg ODRG 13 if CO +iIncStrs avg <j<
C+ l2fIncStrs.avg 3
ODRG14 if co+l2tncstrsavg <<co+ 3IncStrs.avg INT)
F, J
r -
3 T--
1 -
I S
T.
Developed by:V J. S. Brfhmadesam Verifled by:-
B. C. Gra3y
Entergy Operations Inc Central Engineering Programs "LJ 1 53 ODRG1 6 3 ODRG1 7 3 ODRG1 8 ODRG1 9 O D R G2 0 ODRG20 ODRGI4 ODRG24 4
ODRG3 4 ODRG4 4 ODRG5 4 ODRG6 4 ODRG 7 4 ODRG 8 4 ODRG 9 0DRG1 0 4 ODRG14 ODRG12 4 ODRG13 4 ODRG 14 4 ODRG15 4 ODRG16 4 Appendix B; Attachment 2 Page 18 of 30 11 c llilCStrs.avg cj if co+ 14InCstrs.avg < cj if co+ 15lncStrs.avg < Cj if co + 16InCStrs.avg < Cj if co+ 17InCStrS.avg < cj otherwise Engineering Report M-EP-2003-002-01 ot 14'lluIStrs.avg
< co + 15 InCstrs.avg
< C + 16InCstrs.avg
< Co + l7InCstrs.avg
<co + 18InCstrs.avg if j < Co if co < cj < co + ICStrs.avg if co + Incstrs.avg < cj < C + 2InCStrs.avg if Co + 2Incstrs. avg < Cj < co+ 3-lncStrs.avg if co + 3Incstrs.avg < cj < Co + 4fCStrs.avg if co + 4IneStrsavg < ci < co + 5-IncStrs.avg if co + 5Incstrsavg < cj < co + 6IncStrs.avg if co + 6Incstrs.avg < cj < Co + 7IfCStrs.avg if c + 7-IncStrsavg < c 0
< c + 8IncStrs.avg if co + 8IncStrs.avg < cj < co + 9ncStrs.avg if C + 9fIncstrsavg < cj < co + l°IncStrs.avg if c + ioIncstrs.avg < cj < co +
InCStrs.avg if co +
IncStrs avg <
j < Co+
12IncStrs.avg if co+ 12IncStrs.avg < cj < co + 13IncStrs.avg if co + 13-IncStrs.avg < cj < co + 14InCStrs.avg if co+ 14.IncStrs.avg < cj < Co + 15 InCStrs.avg Developed by:
J. S. Brihmadesam Verified by:
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Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Prograns Page 19 of 30 M-EP-2003-002-01 ODRG17 if Co+
5iflnCStrs.avg < Cj < C+ 16flncStrs.avg ODRG 18 4 if Co+l6CInCStrs.avg < cj < Co+ l7flncstrs.avg ODRG19 if Co+ 17*IfnCStrs.avg < Cj < C+ l8-InCStrs.avg 4
ODRG2 0 otherwise 4
62<
ODRG if cj < co ODRG2 if co < cj < Co + InCStrs.avg ODRG4 if co + ncStrsavg < c < o+ 1 ncStrs.avg 5
ODRG5 if CO + InCStrsavg < Cj < Co + 3flnCStrs.avg 5
ODRG65 if co+,IncStrsavg < c < o+ 4l ncStrsavg 5
ODRG7 if C+ 4flnCStrs.avg < Cj < Co+ 4* IncStrs.avg 5
ODRGg if Co+
InCstrs.avg <
< co + 6lncStrs.avg 5
ODRG8 if Co+
flnCtrs.avg < cj < Co+ InCStrsavg 5
ODRG95 if C + iflnCStrs.avg
< Cj < c +
ilnCStrsavg ODRGI4 if CO+
,Incstrs.avg < cj < co+ IfncStrsavg 5
ODRG1 3 if co+
-IncStrs.avg < cj < Co+ 1lncStrs.avg 5
ODRG1 4 if cO+ 1IncStrs.avg < cj < Co+ lIncstrs.avg 5
ODRG1 5 if
+13-IncStrs avg <j C
0 c+
1-IflcStrs.avg 5
ODRG17 if Co+ 12IncStrs.avg < cj < co+ 16 Incstrs.avg ODRG1 o f c + 16 Incor.--
C C + 1I Incctrav Developed by.
J. S. Brihmadesam Verified by.-
B. C. Gray
Entergy Operations Inc Central Engineering Programs 03 E Appendix B; Attachment 2 Page 20 of 30 1 5
-3L-S.av g
-J -
us.avg ODRG1 95 if Co + l7-ncStrs avg < cj co + 18.lncStrs.avg ODRG2 0 otherwise 5
ODRG6 if cj co ODRG2 if Co < Cj co + InCStrs.avg 6
ODRG 3 if co + InCStrsavg < Cj S Co + 2 InCStrsavg 6
ODRG4 if co + 2IlnCStrs avg < cj
- Co + 3 1ncstrs avg 6
ODRG56 if co + 3 InCStrs avg < cj
- co + 4 ncstrs avg O DRG66 if Co + 4iflCstrsavg < Cj
- CO + sIflCstrs avg 6
ODRG7 if CO + 5nCstrs.avg < Cj
- co + 6CStrs.avg 6
ODRG8 if co + 6 InCStrs.avg < Cj
- C + 7lncstrs avg 6
ODRG9 if C+ 7eStrs~avg c ! C 8lncStrs.avg 6
Engineering Report M-EP-2003-002-01 O DRG10 if C0 + 8-Ilestrsavg < Cj S Co + 9IflCstrs.avg ODRGI 16 if Co + 9 InCstrs.avg < Cj Co + 10 Incstrs avg ODRGI2 6 if co+ - IncStrs.avg < C
- Co + IIncstrsavg ODRG13 if co+ Il-IncStrs.avg < Cj
- co+
2 Incstrs.avg ODRG14 if co + l2 ifCstrs6avg < Cj
- CO + l3ifCstrs avg ODRG136 if Co+
3 InCStrs.avg < Cj
- Co+ 14 InCStrs.avg ODRG16 if co + 142InCStrs.avg < cj
- Co + 13Incstrs.avg 6
ODRG176 if co+ 15 IncStrs avg < Cj S Co + 164IncStrs.avg ODRG18 6 if co+ 146 IncStrs.avg < Cj K Co + I15Incstrs.avg ODRG19 if CO+ 17 lnCStrs.avg < Cj
- C + IT InCStrs.avg Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 21 of 30 Engineering Report M-EP-2003-002-01 lODRG2 0 otherwise t0*- G0 42 <--(o+
43 0
G+
4<-
O+
0.2YaI (2-.25.aj 2
(0.25.aj) t
)
t ta) t
)
(o~s-aj) (0 5 aj2 0 s aj )3 GI t
) +(2 -
t
) + (3 t
t
)
0111
(
'0.75-aj+
075aj) 00.75.aj 3
____2 2
0F3i t )
t L. 7S ai)
)oaj 02 (-)
+
X0 -
0.0 xi -
0.25 X2 0.5 X3 <- 0.75 x4 <--1o X<- stack(x 0,xlpx2,x 3,x 4 )
ST <- stack(to S4 2
3 4)
RG <- regress(X, ST, 3) 000 *- RG 3 + Plnt C70 RG4 020
- RG5 030* RG6 ARj *-
Cj aj ATj <- a t
G u.--fURAjAj Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Appendix B; Attachment 2 Engineering Report Central Engineering Programs Page 22 of 30 M-EP-2003-002-01 Gal faL(Rt,AR-,ATi)
J~~~~~~~
Gaqj < faQ (Rt, ARj, ATj)
G
< fac(Rt,ARj,ATj)
GCl fcL(RtARiATi)
J Gcq <- fcQ (Rt, ARj, ATj)
GCC fC(Rt,ARj,ATj) 1.464{A1.6 Qj <-
I + 1464 ej if Cj aj
.65 1 + 1.464-Kia otherwise K K 00 Gauj +
I
+/-
- 0. Gal. + 02OGaqj + c730Gac j)
Kc i<(
Qj)
(6Oo Gcu+/-i + 1o Gcl + 20Gcqj + 30Gccj)
Ka <-Kaj*1.099 i
i KYj ÷- KC -. 099 K(X <-
9.o if K
< 90 lKoc otherwise K*
-l 9.o if K
< 9.0 K K, otherwise J
Da*CO(K
- 90) 1 D agj <
Da& Finhr cblk if Ko< 80.0 Developed by:
Verified by:
J. S. Brihmadesam B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix B; Attachment 2 Page 23 of 30 14 10- '0 CFinhrCblk otherwise DC i <- C (Kyj _ 9.0)116 DCgj *-
DC CFinhr Cblk if K
< 80.0 4*1 0- 1 CFinhr Cblk otherwise output(j, 0) <- j output(j, ) <- aj OUtpUt(j, 2) <- Cj - Co output(j, 3),
Dag.
output(j, 4 ), Dcgj output(j, 5) & Ka.
output(j 6) <- Kc.J NCBj OUtpUt(j, 7) <F 365 24 output(j, 8) (- Gau.
output(j, 9 )
Gal output(j, 10) *- Gaqj output(j, 1) <- Gaci outPut(j, 12) <- Gcuj OUtpUt(j, 13) <- Gc OUtpUt(j, 14) 4-Gcqj output(j, 15) *- Gccj j*-j+I aj - aj1, + Dagj c; -C;
+
r Engineering Report M-EP-2003-002-01 Developed by.
J. S. BrIhmadesam Verified by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 24 of 30 Engineering Report M-EP-2003-002-01
-J-Cj-l aj <-
t if aj t
aj otherwise NCBj - NCBj-j + Cblk output k := o.. im Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 25 of 30 Engineering Report M-EP-2003-002-01 ProPLength = 0.242 Flaw Growth in Depth Direction 0
-c so 0
0.6 0.4 0.2 I I
I I
I I
I I
0 0 0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
Entergy-CEP Model 4
0.8 0.6 2.03 1.6
.2 0.4 0.2 [
0 0 0.5 I
1.5 2
2.5 3
Operating Time {years}
3.5 4
Entergy-CEP Model Developed by:
J. S. BrihMadesam Verified by.
B. C. Gray
Entergy Operations Inc Centra I Engineering Programs Appendix B; Attachment 2 Page 26 of 30 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 0
0 c
5 V)
U)
L._
Cnl 80 60
_~~~~~~~~~~~~~~~~~.
..................... I............................................................... -.
40 20 o L l l l
l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0 0.5 1
1.5 2
2.
Operating Time {years}
Depth Point Entergy-CEP Model Surface Point Entergy-CEP model
.5 3
3.5 4
Developed by:
J. S. Brihmadesam Verified by:-
B. C. Gray
Entergy Operations Inc Central Engineering Programs 1.2 c
0.8 0.6 0 0.4 0.2 Appendix B; Attachment 2 Page 27of 30 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw o -
o 1.5 2
2.5 3
3.5 4
Operating time years}
Ia" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip-- Linear
' c" - Tip -- Quadratic Ic" - Tip -- Cubic Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray C
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 28 of 30 Engineering Report M-EP-2003-002-01 CGRsambi (k,
8) 1.158 1.158 1.158 1.158 1.158 1.158 1.158 1.157 1.157 1.157 1.157 1.157 1.157 1.156 1.156 1.156 CGRsambi(k 6 16.383 17.9 17.905 17.91 17.915 17.919 17.924 17.929 17.934 17.939 17.943 17.948 17.953 17.958 17.962 17.967 CGRsambi (k, )
14 15.225 15.229 15.233 15.237 15.241 15.245 15.249 15.253 15.257 15.261 15.265 15.269 15.273 15.277 15.281 Developed by:
J. S. BrIhmadesam Verified by; B. C. Gray
Entergy Operations Inc Central Engineering Programs Appendix B; Attachment 2 Page 29 of 30 Engineering Report M-EP-2003-002-01 c 0.3 o 0.2 D 0.1 0.0 0
2 Operating Time {years}
4 Developed by, J. S. Brihmadesam Ver/fled by.
B. C. Gray
Entergy Operations Inc Central Engineering Programs 40
[
e
, 30 c
j 20 Appendix B; Attachment 2 Page 30 of 30 Engineering Report M-EP-2003-002-01 Surface Point {"c"-tip Deptt Point ("a"- tip) r in 0
1 2
3 4
Operating Time years)
Developed by:
J. S. Brhmadesam Verified by:
B. C. Gray cr7
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page I of 11 Through-Wall Axial Crack Model 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 R.,f,.lt 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 Environrnents; 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. I The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
Through Wall Axial Flaw The same first part as the previous attachments. (see Attachment 1 of this Appendix)
The first Input is to locate the Reference Line (eg. top of the Blind Zone).
The throughwall flaw "Upper Tip" is located at the Reference Line.
Enter the elevation of the Reference Line (eg. Blind Zone) above the nozzle bottom in inches.
13Z:= 1.544 Location of Blind Zone above nozzle bottom (inch)
The Second Input is the Upper Limit for the evaluation, which is the bottom of the fillet weld keg.
This is shown on the Excel spread sheet as weld bottom, Enter this dimension (measured from nozzle bottom) below.
[JLS,r-)ist := 1,786 Upper axial Extent for Stress Distribution to be used in the analysis (Axial distance above nozzle bottom)
Only two inputs one defining the location of the reference line {BZ} and the other the bottom of the weld ULstrsDist} are needed. The flaw description is not needed for this crack type, because the flaw upper tip is placed at the reference line (i.e.
at the top of the blind zone)
Input Data :-
L := 794 od:= 4.05 id := 2.728 I 111t
- = 2.235 Ycars:= 4 li := 1500 T := 604 v = 0.307 Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 2 of 1 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 oc:=2.6710 12 Q, = 3 1.0 I rf := 617 Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F The input data is similar to that in Attachment 1, except that the crack (flaw) length is based on stress distribution consideration. The flaw length determination is made by locating the lower tip of the flaw at a location where the average stress ([ID + OD]/2} is about 10 ksi. In this manner the lower tip is at a location where no PWSCC growth towards the bottom of the nozzle is possible.
[
Qs lI Co :
1.103-lo' 3 T+159 67 T+ 159.67)] "0C Iiniopr := Yars 365 24 Rod 2
Tirn~p1 Cblk:=
lhill id Ri:=2 t := Ro - Ri R 2 CFi,,I,,.:= 1.417 10 5 Pnltblk:= l-i:= L2 Determination of constants. Note the conversion for crack growth rate {da/dt}
from metric (m/sec) to English units (inch/hr) is obtained by the factor defined as C Finhr.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 3 of II Stress Distribution in the tube. The outside surface is the reference surface for all analysis in accordance with the refere Stress Input Data Import the Required data from applicable Excel spread Sheet. The column designations are as folio Cloumn O' = Axial distance from Minimum to Maximum recorded on the data sheet (inches)
Column "1" = ID Stress data at each Elevation ksi)
Column "5' = OD Stress data at each Elevation (ksi)
DataA\\
=
0 1
2 3
4 5
0 0
-27.4
-24 36
-22.21
-20.41
-18.98 1
0.48 0.63
-1.49
-3.6
-4.44
-5.27 2
0.87 17.66 16.42 14.61 12.41 9.38 3
1.18 29.8 26.05 22.72 18.95 14.2 4:
1.43 33.62 27.79 24.8 24.32 26.99 5
1.63 32.36 28.47 27.59 34.28 45.1 6
1.79 27.39 28.92 31.39 43.88 63.72 7
1.92 21.5 25.56 33.55 48.09 66.36 8
2.05 16.94 23.79 34.06 49.47 67.67 9
2.18 14.83 22.26 34.78 4905 63.38 AIIAxI := DataAll A1I1D):= Data 1 I)
AIIOD Data.l
.5 The nodal stress information is fully imported from the appropriate Excel spread sheet provided by Dominion Engineering. However, only the ID and OD distributions are required for this analysis. The stress input for this calculation uses the applied stress as defined by Membrane and bending components.
These components are dependent on the stresses at the ID and OD surface.
The model used uses the OD surface as the reference surface and the same method is followed in the calculation for this model.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 4 of II 114I 5i1 II (15 I
I 5 A\\ial D~istanlce aom Bttomli linichl
- 11) Is)itribution
)ID distrimutiuln The ID and OD distribution are plotted. The blind zone is located. The upper flaw tip is at the blind zone location and the lower flaw tip is located close to the region where the average stress (membrane) is about 10 ksi.
Observing the stress distribution select the region in the table above labeled Data, 4, 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).
--27 404 -24.356 -22.209 -20407
-18.97S8 (483 16033
-1 486
)aj:=
0,87 1.18 1 428 1 627 1 786 17 665 29 798 33.623 32.364 27.3)4 16 422 26,049 27792 28 469 28 918
-3 599)
-4.44
-5.268 14601 12415 9376 22.723 18.95 142(01 24.8 24,321 26,989 27.591 34284 45 1(4 31 388 43,882 63,718 )
Axl.= D)ata° I)
I)ata OD:= Data ROD := regress(AxlIOD.3!
Ru):= regre\\s(AxillD3)
The Data matrix is obtained in a similar manner as described in Attachment 1 of this appendix. The regression is only performed on the ID and OD distributions as these are the only distributions required for the computation.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 5 of II FL(-,,,,-:= B
- I Flaw Center above Nozzle Bottom IlCStrs.avg :=
IJL-Stis
- BZ 20 Location of the crack center and the segment height are defined. Once again twenty (20) segments are utilized.
Hoop Stress Profile in the axial direction of the tube for ID and OD locations N:= 20 Number of locations for stress profiles Loco 1'
i := I.N+ 3 Iocri:=
if li<4 l
rsCs.aN ag other se Loci := LoC;_6 + Incr.
$ID.
RID3 R11}4 LocI+ RID (Lo 2
RID 6( oci)
SODi:= IZOD3 + R0D,4 Ioci + RZOD5 (Loci) + Ro1)6(I °ci)
In a similar manner to Attachment 1 of this appendix, the ID and OD stress profiles along the nozzle length are determined.
j:= I.. N Sid, I=
SIlj + SDj+l + SIDj+2 ifjI 3
i sod.:=
SOD + SODj+ + SOD.+2 3
if j=I Sodj (j + ) + SOD j j-i j+2 otherwise j+/- 2 Sidj, (j + 1) + SDj+2 j+2 othervise Sod +
Id l c5 =
I
+ l fl Sod - Sid, 0b.
J2 The moving average stress, the membrane (m) containing the internal pressure (PI5t) and the bending component (b) are computed.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 6 of ll ID Stress Membrane Stress Bending Stress OD Stress 0
0 23.795 27.339 29.561 31.121 32.304 33.253 34.044 34.727 35.33 35.875 36.374 36.839 37.276 37.69 38.086 1)=
0 0
-3.536
-1.932
-0.851
-0.028 0.649 1.238 1.771 2.266 2.735 3.186 3.626 4.058 4.485 4 91 5.333 Sod 0
0 0
1 18.023
.2 23.172
- 3 26.475 4
28.858 5
30.719 6
32.256 7
33.58 8
34.757 9
35.83 10 36.826 1
37.766 12 38.662 13 39.526 14 40.365 1 541.185 Sj( =
0 0
25.096 27.036 28.176 28.914 29.42 29.779 30.039 30.226 30.361 30.453 30.513 30.546 30.555 30.545 30.518 Tabular display of the various stress components are printed to ensure that the regression and the moving average methods are functioning properly.
ProPi
- I-ent
= tJILSir.Djsi - (F1.(Cntr + I)
I'ropI,,,jIi = 0 242 Allowable Propagation Length {PropLength}is defined as the difference between the bottom of weld elevation and the blind zone (upper flaw tip location) elevation. Since the Flaw Center {FLcntr} is located at half flaw length below the blind zone the second term within the parenthesis is the location of the blind zone.
Trwcpwc i <- O 10 "'
NCB0
- Cbk Jr hile i
- li,,
Start and initialization of the recursive loop. The crack dimension used in the analysis is the half crack length defined as {I}. Therefore the initial crack size is set to the initial crack half length {Io}.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 7 of l Uni-apphi (Yi m if I -
- 2 if lo I c 0 + IllStrs.avg Gtl3 f 0 +IItrS.a
< j C 0 +.
lllcStrs.avp (Till if I + _ IncSirs.avg I <
+ 3 ICsltrs.avg 4
0
-fcwao i -
0-(Till if 1 + 3-1cstr sav, < I
+ 4 ncStrs.ajg
-S 0
fC tisav
-i (ill 6if 10 + 41ncSirs avg Ic 10 + 5 InCSa~s.avg if I0 + 5-IncStrs.a%,g < l C lo + 6 nc Strs.avg (Tll if Io+ 64-llcStrs.ag < V <I + 7 lfnCStrs.avrg aII if I + 7 IflCStrsav < Xi < I + 81flcSts.aNsg ey111 1 if I0 + 8 IlcStrs.avrg <
I0
+ 9 IlILcStrs.aClg GII 11 if] 0I 9 IlcSirs.avg < I* c0 + 0 lncSts.a%,g Assignment of the applied stress component. This example shows the membrane component {cm} for eleven segments. In the model all twenty (20) segments are considered and similar assignment is made for the bending component {Gb}. The assignments are based on the current flaw location and the boundaries for the segment. This assignment is similar to the assignments described in Attachment 1 of this appendix.
xi -
12 (1 - v2)]I05
-0 (Rit Definition of the Crack parameter with respect to cylinder geometry (mean radius and thickness). This parameter accommodates the effect of cylinder geometry on the SIF.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 8 of 11 Ae) 10090 + 0.3621 -i + 00565.(?4 -
0+
0.0004 (
- 8316 6 5
Al5fl, - -0.0063 + 0.0919 i - 00168-.(?)2 - 0.oos (i) 3 + O.OOS.(hi)1 - 2.9701 10 -(i)
Aeb. < 0.0029 + 0.0707-Hi - 0.0197-(X;
+ 0.0034-(x;-
0.0003(i)
+ 8.805 10 (x1 Y Abb1
--0.9961 -
.3806-?Xi + 01 239(x)
I
- 0(1 i.(j)3 + 0.0017 ()
- 4.9939.10 0
Determination of the SICF for the two component stress loadings based on current crack half length and cylinder geometry (using the non dimensional flaw length X.
Kpil_4 ClinLappId. (7TIi)
Kph. 4 b.appld- (Z.
I i)
Calculation of SIF for an equivalent flat plate geometry for the two applied stress conditions (membrane and bending).
K~llllll-ll(I~i AeC1l + Ab,,, ) -l' Kni~enibjrn) D <- (ei
\\ U) i K11jlenibmrllDj <- (Aell-Aj)j-K<l,,lji KbeiidOD v (Aeb j + Ajl)
K 1 KbendlD (Ael Alb) Kp Calculation of the SIF at the ID and OD for the two component stresses. Note the SICF factors are used as multipliers to the equivalent plate solutions determined above in calculating the SIF for the cylinder geometry.
KAppOD
- KmelmniOD. +/- KbendOD KAppID
-- KmembrnllD + KbenlID.
The applied SIF at the ID and OD are determined by the sum of the sub-component SIF for the two conditions (membrane and bending).
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 9 of ll KAI)pOD. + KAtpp1D KApp4 2
Kca; - KXpp i-1.099 KCA 9.0 jf K
<9.0 Kl,.othenvise The applied SIF used for determining the crack growth is taken as the arithmetic average of the ID and OD SIF. The second statement converts the SIF from English units to metric units. The third statement ensures that the threshold criterion is appropriately satisfied. This conditional statement is used to prevent obtaining an imaginary value for the crack growth rate {da/dt} by a negative value for the (SIF-SIFThreshold) term. Therefore this conditional statement ensures that the difference is zero (0) when the applied SIF is below the threshold value.
Dlen. 4-CO (l'U - 9 0)I16 Dlengrii. v L* ejjCFinjhrj1-Cblk if K c
}
80.0
- 10 4-10 (Cl inhr bl)k othemrise Calculation of crack growth rate {da/dt} and the crack growth within a time block.
The crack growth rate is calculated in metric units (m/sec) and the crack growth in English units by use of the conversion factor {CFinhr}
output 4-NCBi output.
4 i,
)
365-24 oiutniit. -
Output statements to store variables required for loop operation and those for evaluation of time dependent crack growth. This part is similar to the same step described in Attachment 1 of this appendix.
Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page lOoflH i+
I Ij X i-
+ IellhlI NCL3i - NCI3_1 + Cbik Loop increment and redefinition of parameters for the next recursive loop calculation.
rPLenglt= 0.242 Flaw L.en-th s. Time t Try Spsec; 3
/
~~~~~~~~~~~~~~~~~~~~
Is~l
_____Ax 212 0
0 0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
Operating Time '>ears' Entergv Mseodel Typical Mathcad graphics used to compute the impact of crack growth. Note the allowable propagation length information in the top left corner. In this example the crack growth in one cycle exceeds the allowable propagation length, therefore the postulated flaw would reach the bottom of the weld within one operating cycle (1.5 years).
I WUP" pSC c(m }
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 I V W C P cc 0. 7) =
35 69 39 253 39.279 39.305 39.331 39.357 39.382 39408 39.434 39.46 39.486 39,512 39.538 39 564 39 59 39.617 Engineering Report M-EP-2003-002-01 Appendix B; Attachment 3 Page 11 of 11 35.246 40.52 40.549 40.579 40.608 40.638 40.667 40.697 40.726 40.756 40.785 40.815 40.844 40.874 40.904 40 933 Typical tabular output to ensure proper functioning of the model.
300-.
A s C SIa F sIF p
i200 P~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1 2 0 0-Ia 10 0
0 1
2 3
4 o pea s tit Ti.*
a's I Typical Axum plot for use in the report. This is similar to Attachment 1 of this appendix.
C1q
Engineering Report M-EP-2003-002-01 Appendix C Appendix C Mathcad worksheet for CEDM Deterministic Fracture Mechanics Analyses This Appendix has 48 Attachments. Attachment 32 is Intentionally Blank
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 1 Page 1 of II Engineering Report M-EP-2003-002-01 Primary Water Stress Corrosion Crack Growth Analysis ID flaw; Developed by Central Engineering Porgrams, Entergy Operations Inc.
Developed by: J. S. Brihmadesam Verified by: B. C. Gray Refrences:
- 1) "Stress Intensity factors for Part-through Surface cracks"; NASA TM-1 1707; July 1992.
- 2) Crack Growth of Alloy 600 Base Metal in PWR Environments; EPRI MRP Report MRP 55 Rev. 1, 2002 Arkansas Nuclear One Unit 2 Component: Reactor Vessel CEDM -"0" Degree Nozzle, All Azimuths, 1.544" above Nozzle Bottom Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to-Thickness Ratio:- "Rm/t" -- between 1.0 and 300.0 Note: Used the Metric form of the equation from EPRI MRP 55-Rev. 1.
The correction is applied in the determination of the crack extension to obtain the value in inch/hr.
ID Surface Flaw The first Required input is a location for a point on the tube elevation to define the point of interest (e.g.
The top of the Blind Zone, or bottom of fillet weld etc.). This reference point is necessar to evaluate the stress distribution on the flaw both for the initial flaw and for a growing flaw.
This is defined as the reference point. Enter a number (inch) that represnets the reference point elevation measured upward from the nozzle end.
RefPoint = 1.544 To place the flaw with repsect to the reference point, the flaw tips and center can be located as follows:
- 1) The Upper "C-tip" located at the reference point (Enter 1)
- 2) The Center of the flaw at the reference point (Enter 2)
- 3) The lower "-
tip" located at the reference point (Enter 3).
Val :=2 The Input Below is the Upper Limit for the evaluation, which is the bottom of the fillet weld eg. This is shown on the Excel spread sheet as weld bottom. Enter this dimension (measured from nozzle bottom) below.
ULStrs.Dist := 1.796 Upper axial Extent for Stress Distribution to be used in the Analysis (Axial distance above nozzle bottom).
Developed by; J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 1 Page 2 of 11 Engineering Report M-EP-2003-002-01 Input Data :-
L := 0.32 ao := 0.661 0.07 od := 4.05 id := 2.728 PInt := 2.235 Years := 4 him := 1500 T := 604 UOc := 2.67 10- 12 Qg := 31.0 Tref := 617 Initial Flaw Length (Twice detectable length)
Initial Flaw Depth (Minimum Detecteble Depth was 5% TW)
Tube OD Tube ID Design Operating Pressure (internal)
Number of Operating Years Iteration limit for Crack Growth loop Estimate of Operating Temperature Constant in MRP PWSCC Model for 1-600 Wrought @ 617 deg. F Thermal activation Energy for Crack Growth {MRP)
Reference Temperature for normalizing Data deg. F od R := 2 Rid : id Rid:
2 t:= Ro - Rid Rm := Rid +
Timopr := Years365s24 CFinhr := 1.417*105 Timopr Cblk:
11im Iim Prntblk =
50 L
Co := 2 Rm Rt
-Qg -(
I I I i
1 103 lo-3T+459.67 Tref+ 459.67)
CO = C=1
%1.
oc Temperature Correction for Coefficient Alpha 75 th percentile MRP-55 Revision 1 Developed by:
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 3 of 11 Engineering Report M-EP-2003-002-01 Stress Input Data Input all available Nodal stress data in the table below. The column designations are as follows:
Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)
Column "1" = ID Stress data at each Elevation (ksi)
Cloumn "2" = Quarter Thickness Stress data at each Elevation (ksi)
Cloumn "3" = Mid Thickness Stress data at each Elevation (ksi)
Column "4" = Three quarter Thickness Stress data at each Elevation (ksi)
Column "5" = OD Stress data at each Elevation (ksi)
AllData :=
0 1
2 3
4 5
0 0
-25.09
-27.55
-27.79
-25.62
-23.76 1
0.49
-0.56
-0.54
-2.11
-4.85
-6.16 2
0.87 21.52 18.64 17.12 14.84 10.09 3
1.19 32.75 28.49 24.14 19.64 14.45 4
1.44 35.67 29.6 26.17 25.59 28.42 5
1.64 34.24 29.57 28.29 35.41 45.38 6
1.8 29.45 29.81 31.39 43.34 61.71 7
1.93 23.67 26.5 33.26 47.61 64.65
- 8 2.07 18.93 24.56 33.97 49.07 65.88 9
2.2 16.54 22.85 34.79 49.52 62.8 AXLen:= AllData()
IDAL := AllData(l)
ODAIl := AllData)
Stress Distribution 100 50 1 I
I I
I I
1344 1.96 --------------------------
I I
l l 1-I I
0
-50 0 0.5 I
1.5 2
2.5 3
Axial Elevation above Bottom [inch]
ID Distribution OD Distribution Developed by:
J. S. Brihmadesam Verified by; B. C. Gray
Entergy Operations Inc.
Central Engineering Prograns Appendix "C"; Attachment 1 Page 4 of 11 Engineering Report M-EP-2003-002-01 Observing the stress distribution select the region in the table above labeled DataAl, that represents the region of interest. This needs to be done especially for distributions that have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Higlight the region in the above table representing the region to be selected (click on the first cell for selection and drag the mouse whilst holding the left mosue button down. Once this is done click the right mouse button and select "Copy Selection"; this will copy the selected area on to the clipboard. Then click on the "Matrix" below (to the right of the dtat statement) to highlight the entire matrix and delete it from the edit menu.
When the Mathcad input symbol appears, use the paste function in the tool bar to paste the selection.
Data :=
0 0.485 0.874 1.186 1.436 1.635 1.796 1.932 2.068
-25.088
-0.563 21.515 32.751 35.667 34.244 29.45 23.674 18.928
-27.546
-0.539 18.635 28.494 29.598 29.574 29.814 26.502 24.564
-27.787
-2.111 17.122 24.136 26.166 28.286 31.385 33.261 33.968
-25.624
-4.851 14.843 19.645 25.589 35.408 43.337 47.609 49.071
-23.763 )
-6.157 10.089 14.45 28.417 45.379 61.713 64.65 65.876 )
AxI := Data(°)
(3)
MD:
Data" K')
ID :=Data TQ := Data)
QT := Data(2)
OD := Data(5)
RID := regress(Axl, ID, 3)
RQT := regress(Axl, QT, 3)
ROD := regress(Axl,OD, 3)
RMD := regress(Axl, MD, 3)
RTO := regress(Axl,TQ,3)
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 1 Page 5 of 11 Engineering Report M-EP-2003-002-01 FLCntr =
Refpoint - CO if Val =
RefPoint if Val = 2 RefPoint + O otherwise Flaw center Location above Nozzle Bottom ULStrs.Dist - UTip UTip := FLCntr + CO InlcStrs-avg 20 No User Input is required beyond this Point J9. Sat Aug 09 10:59:39 AM 2003 Developed by.
J. S. Brihmadesam Verified by' B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 1 Page 6 of 11 Engineering Report M-EP-2003-002-01 ProPLength = 0.092 Flaw Growth in Depth Direction 0.6 0
0.4 0.(D 0.2 0
02 0
c0 IE
-a i° 0
0.5 1
1.5 2
2.5 3
3.5 Operating Time {years}
4 0.092
-I ;)
0.5 I
1.5 2
2.5 3
3.5 4
Operating Time {years}
Developed by.
J. S. Brilmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 7 of 11 Engineering Report M-EP-2003-002-01 Stress Intensity Factors 100 U
r.
t U,
0 C(3 U.
(A 80 -
60 _
40 _
=
20 0 0 0.5 l
1.5 2
2.5 3
3.5 4
Operating Time {years}
Depth Point Surface Point Developed by:
J. S. Brihmadesam Verified by.
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment 1 Page 8 of 11 Engineering Report M-EP-2003-002-01 Influence Coefficients - Flaw 1.1 0.9 CA a:0 r)C E
c c
0
.Q U
U U
0.8 0.7 0.6 0.5 0.4
-~~~~~ _
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 la" - Tip -- Linear la" - Tip -- Quadratic "a" - Tip -- Cubic "c" - Tip -- Uniform "c' - Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Developed by.
J. S. Brihmadesam Verified by.-
B. C. Gray C2-2
Entergy Operations Inc.
Central Engineering Programs CGRsambi (k, 8) 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 1.103 Appendix "C"; Attachment 1 Page 9 of 11 Engineering Report M-EP-2003-002-01 CGRsambi(k 6) 16.561 16.414 16.42 16.426 16.433 16.439 16.445 16.451 16.457 16.463 16.469 16.475 16.482 16.488 16.494 16.5 CGRsambi(k 5) 13.786 13.676 13.682 13.688 13.695 13.701 13.708 13.714 13.721 13.727 13.733 13.74 13.746 13.753 13.759 13.765 Developed by.
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs Appendix "C"; Attachment I Page 10 of 11 Engineering Report M-EP-2003-002-01 I
ID H ooD Stress I
I OD H oop Stress l
Top f Blind Zone AS W BId B otlo m
/,
7 0
00-0.5
- 1.
1 i..
i5 2 0 2.5 3.0
--. I--
.o - nn 1-n.n}
0.16 0.14 20.12
. 0.10 -
0
° 0.08 0.06 -
0.04 0
1 2
3 4
Operating Time {years}
Developed by:
J. S. Brihmadesam Verified by:
B. C. Gray
Entergy Operations Inc.
Central Engineering Programs 0-1 0
I ri 0 1 c
I I
- o. oo -
Appendix "C"; Attachment I Page 11 of 11 Engineering Report M-EP-2003-002-01 0
1 2
3 4
O perating Time (years) 22 -
°6 20 8-12I it 1 6
, i 14 -
12 -
S IF D epth P oint S I F S u rra c e P o in t
:
L_
t f
(
0 tS t0:
f:,:
0
0 0 an :
f
/-
0' S ::E 0:; f
-\\f X
7 I
II 3
4 O p eraitin g T ime (ye a rs Developed by:
J. S. Br/hmadesam Verified by:
B. C Gray C-