ML032790354
| ML032790354 | |
| Person / Time | |
|---|---|
| Site: | Waterford  |
| Issue date: | 09/15/2003 |
| From: | Entergy Operations |
| To: | Document Control Desk, Office of Nuclear Reactor Regulation |
| References | |
| CNRO-2003-00038 M-EP-2003-004, Rev. 0 | |
| Download: ML032790354 (58) | |
Text
ENCLOSURE 2 C NRO -2003-00038 ENGINEERING REPORT M-EP-2003-004 REV. 0 FRACTURE MECHANICS ANALYSIS FOR THE ASSESSMENT OF THE POTENTIAL FOR PRIMARY WATER STRESS CORROSION CRACK (PWSCC)
GROWTH IN THE UNINSPECTED REGIONS OF THE CONTROL ELEMENT DRIVE MECHANISM (CEDM) NOZZLES AT WATERFORD STEAM ELECTRIC STATION, UNIT 3
Engineering Report No.
M-EP-2003-004 Page 1
Rev.
00 of 57
- Entergy ENTERGY NUCLEAR SOUTH Engineering Report Coversheet Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack (PWSCC) Growth in the Un-Inspected Regions of the Control Element Drive Mechanism (CEDM) Nozzles at Waterford Steam Electric Station Unit 3 Engineering Report Type:
New X
Revision Deleted D
Superceded E
Applicable Site(s)
ANO Echelon X
WF3 X
Report Origin:
xEl ENS Vendor Safety-Related:
x El Yes No Vendor Document No.
Prepared by:
9 A A
£,0-Verified/
Reviewed by:
Approved by:
g Hi))
Responrible Engineer Design VeFr/Re wer Responsible Supervisor or Responsible Central Engineering Manager (for multiple site reports only)
Comments:
Date:
E/l 1 Yes r
No Date: ct/15/065 iy-es El No Date:
El Yes D
NV Attached:
El Yes l No El Yes MNo E Yes E1 No
Engineering Report M-EP-2003-004 Rev. 00 Page 2 of 57 RECOMMENDATION FOR APPROVAL FORM 307% ^*S; A
G Comments:
Prepared by:
(rC%(Q 6
wvwkesDate: >1/I [lI Yes Responsible Engineer I] No Not Applicable Concurrence:
Concurrence:
Concurrence:
Date:
__ate:_
El Yes
[3 No Responsible Engineering Manager, ANO Not Applicable Responsible Engineering Manager, GGNS Not Applicable Attached:
El Yes E No El Yes El Yes El No D Yes El No Date:
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Yes D No Date:
El Yes
[] No Re nsible aineerin nager, RBS Concurrence:
frepj ible Engineering Manager, WF3 Date: r-i 5
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No 7,/i
Engineering Report M-EP-2003-004 Rev. 00 Page 3 of 57 Table of Contents Section Title Page Number List of Tables 3
List of Figures 4
List of Appendices 5
1.0 Introduction 6
2.0 Stress Analysis 11 3.0 Analytical Basis for Fracture Mechanics and Crack 28 Growth Models 4.0 Method of Analysis 33 5.0 Discussion and Results 38 6.0 Conclusions 55 7.0 References 56 List of Tables Table Number Title Page Number 1
Nodal Stress data for 00 Nozzle.
18 2
Nodal Stress data for the 7.80 nozzle at the downhill location.
19 3
Nodal Stress data for the 7.80 nozzle at the uphill location 20 4
Nodal Stress data for the 7.80 nozzle at the mid-plane location.
21 5
Nodal Stress data for the 29.1 0 nozzle at the downhill location.
22 6
Nodal Stress data for the 29.10 nozzle at the uphill location.
23 7
Nodal Stress data for the 29.10 nozzle at the mid-plane location.
24 8
Nodal Stress data for the 49.70 nozzle at the downhill location.
25 9
Nodal Stress data for the 49.7° nozzle at the uphill location.
26 10 Nodal Stress data for the 49.70 nozzle at the mid-plane location.
27 11 Comparison of Fracture Mechanics Models 43 12 Results for compression zone 44 13 WSES-3 Estimated As-Built Analyses Results Summary 46
Engineering Report M-EP-2003-004 Rev. 00 Page 4 of 57 List of Figures Figure Title Page Number Number 1
Details of guide-cone connection to CEDM [2]. Detail extracted from 8
Drawing 1564-4086 R1 [2].
2 Sketch of a typical inspection probe sled [3a].
9 3
Estimated as-built nozzle configuration based on evaluation of the UT and 13 design data.
4 Hoop Stress contours for the 00 nozzle.
15 5
Hoop Stress contours for the 7.80 nozzle.
15 6
Hoop Stress contours for the 29.10 nozzle.
16 7
Hoop Stress contours for the 49.7° nozzle.
16 8
Plot showing hoop stress distribution along tube axis for the 0° nozzle.
18 9
Plot showing hoop stress distribution along tube axis for the 7.80 nozzle at 19 the downhill location.
10 Plot showing hoop stress distribution along tube axis for the 7.8° nozzle at 20 the uphill location.
11 Plot showing hoop stress distribution along tube axis for the 7.80 nozzle at 21 mid-plane location.
12 Plot showing hoop stress distribution along tube axis for the 29.10 nozzle 22 at the downhill location.
13 Plot showing hoop stress distribution along tube axis for the 29.10 nozzle 23 at the uphill location.
14 Plot showing hoop stress distribution along tube axis for the 29.10 nozzle 24 at the mid-plane location.
15 Plot showing hoop stress distribution along tube axis for the 49.70 nozzle 25 at the downhill location.
16 Plot showing hoop stress distribution along tube axis for the 49.70 nozzle 26 at the uphill location..
17 Plot showing hoop stress distribution along tube axis for the 49.7° nozzle 27 at the mid-plane location.
18 SICF shown as a function of normalized crack depth for the 'a-tip" and the 29 c-tip" 19 Curve fit equations for the 'extension and bending" components in 32 Reference 8.
20 Plots showing effect of nodal data selection on the accuracy of polynomial 36 regression fit, 21 Comparison of SICF for the edge crack configurations with the membrane 41 SICF for current model.
22 Comparison of SIF for the current model and conventional model.
42 23 SIF comparison between current model and conventional model.
42
Engineering Report M-EP-2003-004 Rev.
00 Page 5 of 57 Figure Title Page Number Number 24 Crack growth and SIF for 00 nozzle ID surface crack.
48 25 Crack growth and SIF for 00 nozzle through-wall crack.
48 26 Crack growth and SIF for 7.80 nozzle ID surface crack.
49 27 Crack growth and SIF for 7.80 nozzle through-wall crack.
50 28 Crack growth and SIF for 29.10 nozzle through-wall crack.
50 29 Crack growth and SIF for 49.70 nozzle through-wall I crack.
51 30 Nozzle 49.7° at mid-plane location. (hoop stress distribution) 52 31 Nozzle 49.7° at mid-plane location ID surface crack.
53 32 Nozzle49.70 at mid-plane location with a larger ID surface crack.
54 33 Nozzle49.70at mid-plane location with an edge crack.
54 List of Appendices Appendix Content of Appendix Number of Number Attachments In Appendix A
Design, UT probe characterization, UT analysis results, and 5
evaluation for as-built configuration B
Mathcad worksheets annotated to describe the three models 3
C Mathcad worksheets for WSES-3 Analyses 33 D
Verification and Comparisons (Mathcad worksheets) 6
Engineering Report M-EP-2003-004 Rev. 00 Page 6 of 57 1.0 Introduction The US Nuclear Regulatory Commission (NRC) issued Order EA-03-009 [1],
which modified licenses, requiring inspection of all Control Element Drive Mechanism (CEDM), In-Core Instrumentation (IC), and vent penetration nozzles in the reactor vessel head. Paragraph IV.C.1.b of the Order requires the inspection to cover a region from the bottom of the nozzle to two (2.0) inches above the J-groove weld. In the Combustion Engineering (CE) design the CEDM nozzles have a guide-cone attached to the bottom of each CEDM. Figure 1 [2] provides a drawing showing the attachment detail and a sketch showing the typical CEDM arrangement in the reactor vessel head. The attachment is a threaded connection with a securing set-screw between the guide-cone and the CEDM nozzle. The CEDM nozzle is internally threaded and the guide-cone has external threads. Thus, the CEDM nozzles in the region of attachment, including the chamfered region, become inaccessible for Ultrasonic Testing (UT) to interrogate the nozzle base material. The design of the UT probes result in a region above the chamfer (0.200 inch [reference 3a &3b]) that cannot be inspected. Therefore, the region of the CEDM base metal that can be inspected begins at about 1.544 inches above the bottom of the CEDM nozzle and extends to two (2.0) inches above the J-groove weld. The unexamined length (here after called the blind zone) constitutes the threaded region, the chamfer region, and the UT dead zone (1.250 + 0.094 + 0.200). The terms used in this report are defined as follows:
Freespan = (bottom of weld - blind zone); this area below the weld is accessible for volumetric examination.
Propagation Length = (bottom of weld -top of crack tip); area available for crack growth.
Note: For an outside diameter (OD) surface crack, this length is always less than the freespan; for through-wall it is equal to the freespan; and, for an inside diameter (ID) surface crack, the criterion is the propagation length and a through-wall penetration condition.
Augmented Inspection Area: The axial and circumferential extent of the CEDM below the blind zone subject to an OD surface examination to ensure sufficient region for crack growth in one (1) cycle of operation without compromising the weld. This region may include weld material when the weld extends into the blind zone.
The nozzle as-built dimensions were determined by a detailed review of applicable Waterford Steam Electric Station Unit 3 (WSES-3) design drawings and UT data from sister plant (Plant A), since no volumetric inspection has been performed at WSES-3. These two units are of similar CE NSSS design and both are rated at 3410 mwt. The results of the comparison are provided as Attachments four (4) and five (5) in Appendix A. The results of this assessment was used to develop the finite element model which obtains the prevailing stress distribution (Residual+Operating) used in the deterministic fracture mechanics analyses. The deterministic fracture mechanics
Engineering Report M-EP-2003-004 Rev. 00 Page 7 of 57 analyses, in turn, assess the potential for primary water stress corrosion cracking (PWSCC) in the blind zone of the nozzles. The details of the stress analysis including the finite element models are discussed in Section 2. The UT data from Arkansas Nuclear One Unit 2 (ANO-2) was not used because the reactor vessel design for ANO-2 is significantly different from that of WSES-3. The reactor vessel design for Plant A is very similar to that for WSES-3 because of a common design platform.
Therefore a more accurate estimate for the as-built configuration for WSES-3 could be achieved by using the UT data from Plant A.
In order to exclude the blind zone from the inspection campaign, a relaxation of the Order is required pursuant to the requirements prescribed in Section IV.F and footnote 2 of the Order [1].
The purpose of this engineering report is to:
- 1. Determine if sufficient propagation length between the blind zone and the weld exists to facilitate one (1) cycle of axial crack growth without the crack reaching the weld, and
- 2. For nozzles not meeting 1 above, determine how much of the blind zone combined with the available freespan is required to facilitate 1 cycle of crack growth without the crack reaching the weld. This area is subject to augmented surface examination.
Figure 1 below shows the general arrangement of the CEDM nozzles with connection details. In this figure the various regions are defined. This figure provides a general overview of the CEDM penetration and the regions planned for volumetric inspection, and the regions that cannot be inspected (blind zone) by the volumetric UT method.
Engineering Report M-EP-2003-004 Rev. 00 Page 8 of 57 DETAIL "A"
WV CIL CEOM NOZZLE W
CUIOEZ CONE DETAIL CEO'-
"OZZIE
.. a b
C Figure 1:
Details of guide cone connection to CEDM[2]. A sketch of a typical CEDM connection showing regions of interest is provided.
a) CEDM nozzle tube.
b) Details of the chamfer in the machined recess of the threaded region. Provides dimensions for the threaded and chamfer regions.
c)
Details of guide-cone connection to CEDM
[2].
d)
Sketch of a typical CEDM penetration showing the region of interest.
Detail extracted from Drawing 1564-4086 RI (WSES-3) (21. The threaded region in the CEDM is 1.344 inches (Threads plus Recess plus chamfer).
I
-A cE~
GIde Cone d
The detail of the guide-cone-to-nozzle connection shows that the threaded +
chamfer region is 1.344 inches in height. The UT dead band, determined to be 0.200 inch above the top of the threaded plus chamfer region in the nozzle, is based on a typical inspection probe sled design [3b] (shown in Figure 2).
Engineering Report M-EP-2003-004 Rev. 00 Page 9 of 57 CEDM Nozzle 0.200" Dead Band Threaded Connection and Chamfer Region 0
0.a UT Inspection Probe Schematic - See Table Below For Transducer Information Position Mode Diameter Description 1
Transmit 0.25" Circumferential Scan Using TOFD 2
Receive 0.25" Circumferential Scan Using TOFD 3
Transmit 0.25" Axial Scan Using TOFD 4
Receive 0.25" Axial Scan Using TOFD 5
Transmit 0.25" Standard Zero Degree Scan Receive 6
Transmit 0.25" Standard Zero Degree Scan Receive 7
EC NA Standard Driver/Pickup Eddy Current Probe Figure 2: Sketch of a typical inspection probe sled [3a].
The UT dead band is shown with respect to the thread + chamfer region Based on the probe design and the geometry of the nozzle at the threaded connection, the explanation provided in Reference 3b shows the UT dead band to extend 0.200 inch above the chamfer region immediately above the threads.
Therefore, to account for the thread region, chamfer and the UT dead band, the blind zone height is determined to be 1.544 inch (1.250" + 0.094" + 0.2") above the bottom of the nozzle.
Engineering Report M-EP-2003-004 Rev. 00 Page 10 of 57 The analysis used to determine the impact of not examining the blind zone independently evaluates a part through-wall axial crack initiated from the ID, a part through-wall axial crack initiated from the OD, and a through-wall axial crack.
Paft Throuqh-Wall Cracks The initial crack depth obtained from Reference 4 is 0.04627 inch deep for an ID axial crack and 0.07932 inch deep for an OD axial crack. The crack length is based on the detected length of 4 mm (0.157 inch) from Reference 4. In the deterministic fracture mechanics analyses, the part through-wall crack lengths are doubled to 0.32 inch and the crack center is located at the top of the blind zone. Thus, the crack spans both the blind zone and the inspectable region.
The postulated crack sizes and depths are two times the detectable limits with one-half (0.16 inch) of the flaw length being located in the examinable area.
This provides for a conservative evaluation because:
A)
By extending the postulated crack 0.16 inch into the inspectable region, it places the crack tip closer to the weld where the hoop stresses are higher; and B)
It assumes that 0.16 inch of the inspectable region is already cracked, reducing the remaining area for crack propagation.
Throuqh-Wall Crack In addition to evaluating the part through-wall cracks, this evaluation also conservatively evaluates a through-wall axial crack. The through-wall axial crack is postulated to exist from the top of the blind zone down to a point where the hoop stress is < 10 ksi. This is a very conservative assumption, since for a crack to initiate on the surface and propagate through-wall while being totally contained within the blind zone would result in an unrealistic aspect ratio. As can be concluded from the following analysis, the length of a part through-wall crack would propagate into the inspectable region long before its depth reaches a through-wall condition. However, evaluation of the through-wall crack provides completeness to this assessment and ensures all plausible crack propagation modes are considered. Like the part through-wall crack, the hoop stresses at the top of the blind zone were used as the initial stress with adjustments to account for the increased stresses as the crack approaches the weld.
The analyses include a finite element stress analysis of the CEDM nozzles and a fracture mechanics-based crack growth analysis for PWSCC. These analyses are performed for four nozzles (the nozzles were chosen at four head angles 0°, 7.8°,
29.10, and 49.70) in the reactor vessel head to account for the varied geometry of the nozzle penetration. In this manner the analysis provides a bounding evaluation for all CEDM nozzles in the reactor vessel head. The sections that follow contain a description of the analyses, the results, and conclusions supported by the analyses.
Engineering Report M-EP-2003-004 Rev. 00 Page 11 of 57 2.0 Stress Analysis Finite element-based stress analyses for WSES-3 CEDM penetrations, using the highest tensile yield strength for each group of nozzles, were performed using the best-estimate geometries based on Plant A UT and WSES-3 design information. The UT data obtained form Plant A were reviewed to determine the locations of the top and bottom of the J-weld at two azimuthal locations, downhill (00) and the uphill (1800).
The UT data obtained from this analysis is presented in Attachment 4 to Appendix A.
This UT data was compared to the design information obtained from design drawings for WSES-3 using an Excel spreadsheet to estimate the as-built condition. The spreadsheet used in this analysis is presented in Attachment 5 to Appendix A. In the evaluation five nozzle groups were considered in order to ensure the accuracy of the evaluation. The nozzle groups considered were 00, 7.80, 29.10, 42.40, and 49.7 °.
These evaluations showed the following:
- 1) In all cases the measured length from the blind zone to the top of the weld was consistently higher than the estimated length from design drawings.
The average difference was about 0.3 inch.
- 2) The downhill side fillet welds on the peripheral CEDM nozzles (29.10, 42.40 and 49.70) have a longer leg than estimated from the design information. A fillet weld radius of 3/8 inch instead of the specified 3/16 inch provided the fillet weld leg length that matched the UT data. This evidence was also observed in another CE fabricated reactor vessel head. The fillet weld on the uphill side matched the information on the design drawing. Thus, only the downhill side fillet weld leg was extended for the model. The weld length on the uphill side matched the design information.
- 3) The larger length estimated in Item 1 above indicated that the attaching J-weld must have been longer than the design drawings specification. When the longer J-weld lengths were used, the difference between the as-measured and as-built estimate were considerably reduced. The longer J-weld length, in accordance with the design specification, would increase the radial dimension of the weld at the ID surface of the head. Thus, a larger weld size was developed for the finite element model. This larger weld size, in turn, would increase the magnitude of the residual stresses in the weld region.
The evaluation to estimate the as-built dimensions of the CEDM configuration, taking into consideration the Plant A UT data and design information, consisted of the following steps:
- 1) The blind zone elevation of 1.544 inches from the nozzle bottom was taken to exist for all CEDM nozzles.
- 2) The design lengths for freespan at both the downhill and uphill locations were established (design length from weld bottom - blind zone).
Engineering Report M-EP-2003-004 Rev. 00 Page 12 of 57
- 3) The design dimensions were compared to the measurements obtained from the Plant A UT data analysis. The differences were recorded.
- 4) The design length to the top of the J-weld was compared to the measured length from the Plant A UT data for both the downhill and uphill locations and the differences recorded.
- 5) The weld lengths from design drawings were compared to the as measured data from the Plant A UT results. This was done for both the downhill and uphill locations. The differences were recorded.
- 6) The differences were evaluated to assess the variation between the design and as-measured data. This comparison showed that the differences for the length from the blind zone to the top of the weld to be 0.3 inch larger for the Plant A UT measurement. Thus, the J-weld size was increased to accommodate the longer as-measured length. The higher hillside angle nozzles (29.10 and 49.70) showed the variation to be more on the downhill side indicating a longer fillet weld leg length. This variation was minimized when the fillet weld radius was changed to 3/8 inch instead of the design specified value of 3/16 inch. Similar findings have been observed for another reactor vessel head fabricated by CE. Therefore, the increased fillet weld radius reasonably explains the larger fillet weld leg length observed in the Plant A UT data. For these nozzles the fillet weld leg length was increased. Figure 3 presents the sketches for all four nozzle groups considered in this analysis. The original design is represented by the black lines and the estimated as-built configuration by the blue lines. The location of the blind zone top, based on the NDE consideration, is located 1.54 inches from the nozzle bottom and is shown in green. These figures clearly show that the top of the J-weld is at a higher elevation than the specified elevation. In addition these sketches show that the attaching J-weld is larger than specified. The larger weld would tend to produce higher residual stress and hence provide a bounding estimate for the residual stress field.
This geometry was used to develop the estimated as-built finite element model.
Engineering Report M-EP-2003-004 Rev. 00 Page 13 of 57 Top of UT Inspection "Dead Zone' Top of UT Inspection "Dead Zone' 00 Nozzle 7.8-Nozzle R 316 Filil (As Designoe 8.
R 316" Fillet tAs Designed)
R 3" Filidt fEst.
As Buiit)
Norinh-As-Dasi~d Gsesornoy Shows is Blkck E5,s-ted As-Biit Gwrnetry Shoes in Blue I
R 318" Fillet (Est. As Built) 0op o ULT I l, si cfio rDead zol ¢eb Iopo+UT nspxtior CeadZond 29.1° Nozzle 49.7° Nozzle Figure 3: Estimated as-built nozzle configuration based on evaluation of Plant A UT and WSES-3 design data. For all nozzle groups evaluated the J-weld height was found to be 0.3 inch longer. The downhill fillet welds on the higher angle nozzles (29.10 and 49.7°) were estimated to have a larger fillet radius. Thus the fillet weld bottom (intersection with the nozzle OD) was determined to be at a lower elevation. The modified geometry, representing the best estimate of as-built configuration, were used to develop the finite element geometric model.
The finite element modeling for obtaining the necessary stress (residual+operating) distribution for use in fracture mechanics analysis followed the 00~~~~
Engineering Report M-EP-2003-004 Rev. 00 Page 14 of 57 process and methodology described in Reference 5a. The modeling steps were as follows:
- 1)
The finite element mesh consisted of 3-dimensional solid (brick) elements.
Four elements were used to model the tube wall and similar refinement was carried to the attaching J-weld.
- 2)
The CEDM tube material was modeled with a monotonic stress strain curve.
The highest yield strength from the nozzle material bounded by the nozzle group was used. This yield strength was referenced to the room temperature yield strength of the stress-strain curve described in Reference 5a. The temperature dependent stress strain curves were obtained by indexing the temperature dependent drop of yield strength.
- 3)
The weld material was modeled as elastic-perfectly plastic for the weld simulation. This approximation is considered reasonable since most of the plastic strain in the weld metal occurs at high temperatures where metals do not work-harden significantly (Reference 5c). The temperature in the weld is always high during the welding process and once the weld begins to cool, the temperatures in the weld at which strain hardening would persist are of limited duration (Reference 5c). This was borne out by the comparison between the analysis based residual stress distribution and that obtained from experiments (Reference 5d).
- 4)
The weld is simulated by two passes based on studies presented in Reference 5a.
- 5)
After completing the weld, a simulated hydro-test load step is applied to the model. The hydro-test step followed the fabrication practice.
- 6)
The model is then subjected to a normal operating schedule of normal heat up to steady state conditions at operating pressure. The residual plus operating stresses, once steady state has been achieved, are obtained for further analysis. The nodal stresses of interest are stored in an output file.
These stresses are then transferred to an Excel spreadsheet for use in fracture mechanics analysis [5b].
The stress contours for the four nozzle groups obtained from the finite element analysis are presented in Figures 4 through 7. The stress contour color scheme are as follows:
Dark Navy blue from Minimum (Compression) to -10 ksi Royal blue from -10 to 0 ksi Light blue from 0 to 10 ksi Light green from 10 to 20 ksi Green from 20 to 30 ksi Yellow green from 30 to 40 ksi from 40 to 50 ksi Red from 50 to 100 ksi
Engineering Report M-EP-2003-004 Rev. 00 Page 15 of 57 I
I I
I I
I I
I I
I I
Full Cross-section Zoomed in right weld Figure 4: Hoop stress contours for the 00 nozzle. High tensile stresses occur in the weld and adjacent tube material. The bottom of the tube is in compression.
Full cross-section Zoomed in Downhill side Figure 5: Hoop stress contours for the 7.80 nozzle. High tensile stresses occur in the weld and adjacent tube material. The bottom of the tube is in compression.
C 09
Engineering Report M-EP-2003-004 Rev. 00 Page 16 of 57 Full cross-section Zoomed in Downhill side Figure 6: Hoop stress contours for the 29.10 nozzle. High tensile stresses occur in the weld and adjacent tube material. The bottom of the tube is in compression.
Full cross-section Zoomed in Downhill side Figure 7: Hoop stress contours for the 49.7° nozzle. High tensile stresses occur in the weld and adjacent tube material. The bottom of the tube is in compression.
Engineering Report M-EP-2003-004 Rev. 00 Page 17 of 57 The nodal stresses for the locations of interest in each of the four nozzle groups were provided by Dominion Engineering Inc. and were tabulated in Reference 5b. The nodal stresses and associated figures representing the OD and ID distributions along the tube axis are presented in tables and associated figures in the following pages. The location of the weld bottom was maintained at the node row ending with "601". The blind zone location is shown on the associated figure. The three azimuthal locations downhill (00), uphill (1800), and mid-plane (900) are shown in the figures presented in the following pages. The zone of compressive stress is also marked in the figure.
From the tables and associated figures, a full visualization of the stress distribution in the nozzle, from the nozzle bottom (located at 0.0 inch) to the top of the J-weld is obtained. These figures are also shown in the Mathcad worksheets provided in the Appendix "C" attachments. The nodal stress distribution, provided by Dominion Engineering, is used to establish the region of interest and the associated stress distribution that will be utilized in the subsequent analyses. In the low angle nozzle groups (00 and 7.80) there exists a well defined compression zone. The higher angle nozzle groups (29.10 and 49.70) tensile stresses were found to exist at the nozzle bottom. Hence there was no well defined compression zone in these nozzles. In most cases the tension stress magnitude was low (<10.0 ksi), and the distribution through the wall thickness had compressive stresses. For these nozzles the presence of a low magnitude tensile stress on one surface is not expected to cause PWSCC initiation. In one isolated case (49.70 nozzle at the mid-plane) the ID surface had a tensile stress of 19.02 ksi but the OD surface was in compression. This location was selected for further evaluation using deterministic fracture mechanics and is discussed in a later section.
In the following pages, the stress data from the Excel spreadsheet provided by Dominion Engineering (Reference 5b) and plots representing the axial distribution at the ID and OD locations are presented for each nozzle group with the specific azimuthal location that is evaluated. The location of the compression zone the blind zone and bottom of the weld are marked by colored reference lines.
Engineering Report M-EP-2003-004 Rev. 00 Page 18 of 57 1
0.000
-12.796
-11.857
-11.688
-11.588
-11.36 101 0.696
-5.757
-6.987
-8.359
-9.647
-10.654 201 1.253 12.517 6.554 0.301
-3.045
-5.052 301 1.699 28.961 26.385 19.217 11.596 2.764 401 2.057 41.814 37.112 30.325 22.635 14.562 501 2.343 46.95 39.385 33.873 34.257 41.315 701 2.754 35.285 36.135 40.478 54.515 68.35 801 901 1001 1101 1201 1301 1401 2.935 3.116 3.298 3.479 3.660 3.842 4.023 26.742 22.009 23.061 29.388 37.093 43.246 48.434 32.322 29.241 28.564 30.619 35.562 40.265 43.969 40.928 40.652 39.667 38.892 39.2 43.583 47.621 56.857 55.17 53.418 49.245 47.87 47.63 53.333 69.509 67.675 67.54 61.158 53.459 48.466 47.405 Table 1: Nodal stress for 0° nozzle. This nozzle is symmetric about the nozzle axis hence these stresses prevail over the entire circumference. The weld location is shown by the shaded row.
IDHop Stress j
O D Hoop Stress 60 X.,:i1 4 07 Comprssio Zon Topof Bind Zon.
CX
_20I Wevld B otto m
.Axial Distance From'Nozzle Botm{nh Figure 8: Plot showing hoop stress distribution along tube axis for the 0 nozzle. The top of compressive zone, the top of blind zone, and the bottom of the weld are shown.
Engineering Report M-EP-2003-004 Rev. 00 Page 19 of 57 LLIgpC~He~ht; Djp 32 5%j~5O%
5%ffiO DD,
1 0.000
-9.806
-9.211
-9.151
-9.105
-9.007 101 0.688
-5.963
-6.674
-7.601
-8.5
-9.173 201 1.240 5.968 1.891
-1.405
-3.639
-4.887 301 1.681 27.297 20.8 14.757 9.074 2.762 401 2.035 38.318 34.255 28.387 21.562 14.198 501 2.319 46.033 38.236 33.079 32.77 40.164 MM-73=0 701 2.731 35.382 36.514 40.837 54.397 68.177 801 2.916 26.506 32.532 41.33 56.353 69.718 901 3.100 21.356 29.603 40.6 53.912 66.27 1001 3.285 22.658 28.094 39.312 52.055 65.066 1101 3.470 29.358 30.505 38.363 47.564 57.082 1201 3.655 37.587 36.019 38.912 45.886 49.473 1301 3.839 43.927 40.888 43.157 46.294 45.271 1401 4.024 48.902 44.809 47.033 52.096 45.311 Table 2: Nodal stress for 7.8° nozzle at the downhill location. The weld location is shown by the shaded row.
I76TDi~op tresY]
70OHoop Sttess
-1 50X
-A
-,I'
-'<:'-Compression Zone Tof Blind Zon X,.~~ GIT
' <k'f 30 0-93 S WH Z'
Xt~~
2 3 24:
S w
r O
Av Distance F
N t
{jinch
(,;<
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- ¢l.
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-Ax; ail t mo i}
Figure 9: Plot showing hoop stress distribution along tube axis for the 7. 8°nozzle at the downhill location. The top of compressive zone, the top of blind zone, and the bottom of the weld are shown.
Engineering Report M-EP-2003-004 Rev. 00 Page 20 of 57 v~!Ulif T7
'5°ODI0j 80001 0.000
-5.726
-5.185
-5.434
-5.6
-5.492 80101 0.865
-7.337
-8.091
-9.159
-10.193
-10.923 80201 1.558 7.091 1.373
-5.197
-8.848
-10.873 80301 2.113 26.693 25.132 16.282 5.761
-3.828 80401 2.558 42.764 38.917 31.475 20.343 8.754 80501 2.914 48.936 41.129 35.127 34.232 39.321
=_~~~~~~~~~~~
80701 3.379 35.68 37.241 42.049 56.338 70.072 80801 3.559 27.845 33.635 43.013 58.939 70.865 80901 3.738 24.118 31.111 43.097 58.308 69.669 81001 3.918 26.082 31.59 42.539 56.818 71.115 81101 4.098 32.763 33.661 41.893 52.978 66.259 81201 4.277 39.969 37.991 41.726 51.369 58.443 81301 4.457 45.611 42.302 45.962 50.525 52.859 81401 4.636 49.715 45.468 49.012 54.716 54.088 Table 3: Nodal stress for 7.8° nozzle the uphill location. The weld location is shown by the shaded row.
X~~
- -< v-- - ~ --
- - - -, -,. 2. -.
, ~.' I ? i' :
~ID Hoo Stress
.. -a,,-OD Hoop Stress "6-',
L A-'
'-i'-i e
a-';i-N;4 -S 4.X~iba L-
- 0
- -,'Compression Zone WedBtto3 NozzlFrom N ozzle Boj Figure 10
- Plot showing hoop stress distribution along tube axis for the 7.80 nozzle at the uphill location. The top of compressive zone, the top of blind zone, and the bottom of the weld are shown.
Engineering Report M-EP-2003-004 Rev. 00 Page 21 of 57 H
5%
I/
D 40001 0.000
-6.545
-6.457
-6.902
-7.265
-7.484 40101 0.777
-5.985
-7.029
-8.206
-9.34
-10.214 40201 1.399 7.507 2.446
-2.972
-5.766
-7.284 40301 1.898 26.16 22.721 15.759 8.375 0.041 40401 2.297 40.097 35.774 28.929 20.399 11.338 40501 2.617 46.142 38.476 32.974 32.389 38.226 40701 3.056 32.813 34.635 39.401 53.167 67.334 40801 3.238 24.577 30.972 39.991 55.653 68.712 40901 3.420 20.31 28.175 39.858 54.123 66.017 41001 3.602 22.014 27.816 39.083 52.555 66.373 41101 3.784 28.847 30.254 38.501 48.599 60.122 41201 3.966 36.991 35.326 38.82 47.31 52.716 41301 4.149 43.391 40.133 43.159 47.049 48.17 41401 4.331 48.5 44.008 47.17 52.559 48.301 Table 4: Nodal stress for 7.80 nozzle at mid-plane location. The weld location is shown by the shaded row.
OCHoop Stress O DHoop StrU
~~~~To of
- _i Z _= e-
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- X.is
....f.~.....IX,
_ 20 I
Compresion Zon 1.0'59- ~ ~
~
~
~
~
~
~
~ ~
Wl Bottom..
0 :
Aial Distance FrmNzlBotm{nh Figure 11: Plot showing hoop stress distribution along tube axis for the 7.80 nozzle at mid-plane location. The top of compressive zone, the top of blind zone, and the bottom of the weld are shown.
Engineering Report M-EP-2003-004 Rev. 00 Page 22 of 57 E~oeig
+
=
1 0.000
-14.124
-10.614
-8.602
-6.672
-4.573 101 0.590
-9.002
-7.115
-5.966
-4.979
-3.958 201 1.062
-2.278
-2.811
-3.527
-4.069
-4.39 301 1.441 8.127 5.389 2.032
-0.491
-2.546 401 1.744 14.353 12.404 8.325 4.616
-0.624 501 1.987 25.675 22.473 16.062 14.285 21.33 701 2.338 52.639 44.805 43.227 62.866 66.642 801 2.495 48.491 45.796 49.068 69.125 71.441 901 2.652 40.376 42.428 49.872 69.009 76.543 1001 2.808 32.134 38.242 49.303 66.994 78.115 1101 2.965 24.603 34.87 46.678 60.594 69.068 1201 3.122 23.685 33.276 44.123 55.798 65.338 1301 3.278 27.332 32.426 42.486 51.565 55.205 1401 3.435 35.907 34.579 39.896 46.002 43.157 1501 3.592 46.337 40.244 40.848 42.543 34.309 1601 3.749 52.99 47.3 45.438 43.858 34.055 1701 3.905 56.481 52.662 51.652 51.197 36.851 1801 4.062 58.443 55.268 56.274 54.453 28.004 Table 5: Nodal stress for 29.10 nozzle at the downhill location. The weld location is shown by the shaded row.
ID Hoop Stress.
80
~~OD oop Stress
~~60
--- '~~~~
distonpe Frof Nczie'Blttoindh}
Zn F
e X)
Figure12: Plot showinghoopstress distribution along tubeaxisforthe 29.1nozzleatthedownhil location. The top of compressive zone, the top of blind zone, and the bottom of the weld are shown.
Engineering Report M-EP-2003-004 Rev. 00 Page 23 of 57
~owj~eigtI_25%
5 t/S:7%ZJ/
80001 0.000
-7.856
-4.209
-2.262
-0.333 1.664 80101 1.395
-7.372
-7.026
-7.468
-7.776
-7.782 80201 2.513 9.689 1.331
-9.445
-17.448
-23.769 80301 3.408 33.861 32.362 12.257
-12.427
-25.502 80401 4.125 52.72 49.983 44.295 16.295
-6.038 80501 4.700 58.423 51.453 44.992 43.352 43.691 VW RM~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.
80701 5.277 42.502 47.798 56.694 75.697 78.963 80801 5.394 40.405 46.006 60.817 78.524 74.751 80901 5.511 38.57 45.679 61.294 79.499 77.406 81001 5.628 38.794 46.357 62.694 78.409 80.796 81101 5.746 41.618 48.042 62.285 81.469 79.834 81201 5.863 45.71 49.558 61.713 77.329 86.469 81301 5.980 50.437 50.656 60.84 75.644 88.343 81401 6.097 54.187 52.444 58.721 73.531 80.04 81501 6.214 57.478 54.532 59.24 69.029 69.068 81601 6.331 59.894 56.464 60.408 68.494 66.808 81701 6.448 59.731 57.443 61.006 65.393 65.674 81801 6.565 57.557 56.634 58.076 59.573 68.266 Table 6: Nodal stress for 29.10 nozzle at the uphill location. The weld location is shown by the shaded row.
A~~~~~...
A~~~~I opStrSSS~f a-.,
e t
t em w
- (ln c h
80 Top oFB md Zon U CO ~ ~
~
~
~
xbsacerm~ozleBtoii Figure 13: Plotshowing hoop stress distribution along tube axis forthe 29.10nozzle at the uphill location. The top of blind zone and the bottom of the weld are shown. No compression zone exists because the OD surface has a 1.66 ksi tensile stress.
Engineering Report M-EP-2003-004 Rev. 00 Page 24 of 57 40001 0.000 6.948 3.273 0.645
-1.57
-4.013 40101 0.996
-2.696
-4.363
-5.71
-7.053
-8.174 40201 1.794
-0.898
-3.157
-5.009
-5.653
-5.545 40301 2.434 16.369 12.049 9.098 6.045 1.522 40401 2.946 32.337 25.967 21.347 16.296 11.16 40501 3.356 32.897 26.895 24.305 26.191 32.374 MMO Mm
<2 40701 3.822 11.456 17.713 24.721 41.335 55.712 40801 3.958 5.786 13.749 24.907 44.824 54.092 40901 4.095 1.689 11.142 24.388 45.417 55.597 41001 4.231
-0.207 10.05 24.642 44.414 58.862 41101 4.368
-1.289 9.633 25.292 43.956 53.198 41201 4.504 1.416 11.33 25.601 40.773 56.861 41301 4.641 7.489 14.883 26.733 39.707 54.264 41401 4.777 15.637 19.015 27.69 38.643 45.561 41501 4.914 24.745 23.487 29.735 38.023 38.616 41601 5.050 32.666 28.867 33.069 40.224 38.325 41701 5.187 39.699 33.623 36.829 41.921 39.312 41801 5.324 46.043 38.391 40.193 44.363 38.244 Table 7: Nodal stress for 29.10 nozzle at the mid-plane location. The weld location is shown by the shaded row.
.~~~~~~~~~~~~~
Hoop Stress]
'D Hoop Stress 50 30
~No Compression Zooe 10 10 tension 5n 10
.:..... 4.
-. --rs --'
--..._ '+;.:4 Ai Dista
'.nce From'/
eN WBottom finchi-
t"'+*1'0J5.
,,X
.t-Figure 14: Plot showing hoop stress distribution along tube axis for the 29.10 nozzle at the mid-plane location. The top of blind zone and the bottom of the weld are shown. No compression zone exists because the ID surface has a 6.95 ksi tensile stress.
Engineering Report M-EP-2003-004 Rev. 00 Page 25 of 57 1
0.000
-25.293
-15.585
-9.281
-3.55 2.324 101 0.531
-19.083
-11.521
-6.114
-1.13 3.359 201 0.956
-14.191
-8.992
-5.326
-1.956 0.535 301 1.297
-9.505
-6.849
-5.457
-4.207
-6.943 401 1.570
-6.96
-5.721
-5.585
-4.994
-5.582 501 1.788
-4.629
-4.487
-4.569 5.408 14.041 IN W_61 W
42 701 2.164 25.317 21.609 33.649 60.257 59.632 801 2.364 33.389 34.286 51.327 80.788 77.004 901 2.564 33.392 37.9 52.631 84.392 84.917 1001 2.764 31.76 39.607 54.276 79.772 85.213 1101 2.964 28.788 39.667 53.114 65.06 66.065 1201 3.164 27.224 38.236 48.192 55.742 60.127 1301 3.364 32.689 37.256 43.242 46.629 42.883 1401 3.563 44.941 39.574 39.801 41.064 31.994 1501 3.763 56.515 46.23 41.283 38.032 24.134 1601 3.963 63.562 56.367 49.774 41.645 28.074 1701 4.163 64.94 62.927 59.882 51.049 27.971 1801 4.363 63.021 63.156 63.633 52.077 16.479 Table 8: Nodal stress for 49.70 nozzle at downhill location. The weld location is shown by the shaded row.
40 Top of BlindSZone P
v-:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-
o
~~No Compresoion Zone 0a i
2'32' E
Axial Distance From Ninch)
Figure 15: Plot showing hoop stress distribution along tube axis for the 49.7° nozzle at downhill location.
The top of blind zone and the bottom of the weld are shown. No compression zone exists because the OD surface has a 2.32 ksi tensile stress.
Engineering Report M-EP-2003-004 Rev. 00 Page 26 of 57 ow~ei 80001 0.000
-19.259
-10.122
-4.181 0.963 6.112 80101 2.122
-5.733
-6.473
-6.392
-5.545
-4.564 80201 3.823 17.602 15.215
-2.897
-18.501
-27.612 80301 5.185 46.67 43.171 21.37
-23.742
-38.612 80401 6.276 59.222 56.012 41.664
-5.652
-38.455 80501 7.150 60.408 57.07 52.143 37.519 13.387 80701 8.000 64.307 66.286 72.427 77.908 61.803 80801 8.150 64.615 66.416 74.368 79.161 62.859 80901 8.299 64.71 67.265 75.078 78.64 67.335 81001 8.449 63.827 67.565 76.55 77.75 69.871 81101 8.598 64.066 68.261 76.294 82.56 71.21 81201 8.748 65.836 68.7 76.838 80.68 75.875 81301 8.897 67.546 68.706 76.691 83.462 82.658 81401 9.047 68.524 68.185 74.926 84.387 80.56 81501 9.196 69.324 68.4 73.71 80.602 73.251 81601 9.346 68.105 66.995 70.758 73.71 62.557 81701 9.495 62.104 62.794 64.776 62.766 54.693 81801 9.645 48.843 51.232 53.851 47.743 50.949 Table 9: Nodal stress for 49.7° nozzle the uphill location. The weld location is shown by the shaded row.
Si ~
~
+_..-..
. ~.,
, L
-z;
~ID~cpStress OD Hoop Stress
.:optf~lind.Zon'e.
31' 0 -..,.',. ; 0.$.le!. n 'l,
.N com~pression Zone
-6
\\
- w
- ~r
_; ?.
u e
4,...
.s...
f
-I 0~~~~~~~~~~~~
Axial Distance FrmNzlOttom {nch)'-.'~#.
Figure 16: Plot showing hoop stress distribution along tube axis for the 49.7° nozzle at the uphill location. The top of blind zone and the bottom of the weld are shown. No compression zone exists because the OD has a 6.11 ksi tensile stress.
Engineering Report M-EP-2003-004 Rev. 00 Page 27 of 57 Ej-i He ght, LL o06 40001 0.000 19.022 9.579 3.372
-2.08
-7.96 40101 1.348 4.884
-0.011
-3.322
-6.536
-9.387 40201 2.427 4.116
-0.784
-2.075
-2.213
-2.987 40301 3.292 11.593 9.74 9.093 5.504 1.989 40401 3.985 15.695 11.005 11.902 12.478 10.549 40501 4.540 0.999 3.689 8.873 18.835 26.599 40701 5.158
-28.802
-16.466 1.395 28.031 40.149 40801 5.332
-31.335
-20.973
-0.499 28.531 38.487 40901 5.505
-32.983
-22.942
-2.556 28.318 37.997 41001 5.678
-34.296
-23.308
-2.308 25.931 41.376 41101 5.852
-35.436
-22.605
-1.594 23.026 31.353 41201 6.025
-33.277
-18.547
-0.377 19.783 39.547 41301 6.198
-27.734
-13.191 2.942 18.396 35.147 41401 6.372
-18.454
-7.646 5.99 18.869 29.932 41501 6.545
-6.281
-1.898 9.271 20.258 23.726 41601 6.718 5.112 4.631 13.319 22.664 23.438 41701 6.892 15.025 11.245 16.303 22.156 22.622 41801 7.065 25.534 19.107 20.223 23.174 20.075 Table 10: Nodal stress for 49.7° nozzle at the mid-plane location. The weld location is shown by the shaded row.
10 No ComEpStression eo SWrBot n -M -XO.D. = ocompressiog a.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,
3,0 A
'0 Top of Blind Zon e
< *gH,,~~~Aia aDistance From Nozze Bo{<ttom {inch)
L ~
£ ia v;_
id
}-
lsa~n
_'*:t
~
a L-'6 zrH M3 Figure 17: Plot showing hoop stress distribution along tube axis for the 49.70 nozzle at the mid-plane location. The top of blind zone and the bottom of the weld are shown. No compression zone exists because the ID surface has a 19.02 ksi tensile stress.
Engineering Report M-EP-2003-004 Rev. 00 Page 28 of 57 The nodal stress data presented in the previous pages are the data imported into the respective Mathcad worksheet (discussed later) for further processing to obtain the pertinent stress distributions required for the fracture mechanics analysis.
The processing of the nodal stress data is described in Section 4.
3.0 Analytical Basis for Fracture Mechanics and Crack Growth Models Fracture Mechanics Models Surface Crack The mean radius-to-thickness ratio (Rm/t) for the CEDM nozzle was about 2.5.
The fracture mechanics equation used in the proposed revision to the ASME Code Section Xl is based on the solution from Reference 6. This solution is valid for an outside radius-to-thickness ("R0/t") ratio from 4.0 to 10.0. The CEDM nozzle "Rdt" ratio is lower (3.06), indicating that the CEDM nozzle is a thicker wall cylinder than those considered in Reference 6. Therefore, the fracture mechanics formulations presented in Reference 7 were chosen (the applicable "Rm/t" ratio is from 1.0 to 300.0).
The stress intensity factor (SIF) for the postulated crack under an arbitrary stress distribution was obtained from Reference 7. The model was for both an internal and external part through-wall surface crack subjected to an arbitrary stress distribution. This model is valid for a ratio of mean radius (Rmean)-tO-thickness (t) between 1.0 and 300.0. Since the ratio for the CEDM nozzle is about 2.5, this model is considered applicable.
The equation for the SIF for the deepest point of the crack is given as [7]:
3 K,=(a)o5 *[ZaoG ]
Q 1=0O Where:
K, = SIF {ksNin.)
Q = Crack shape factor, defined as Q=1+1.464*(a)165 when a/c< 1.0 and, C
Q=I+1.464*() '65 when a/c > 1.0 a
a = Crack depth (inch)
Engineering Report M-EP-2003-004 Rev. 00 Page 29 of 57
= Coefficients of the stress polynomial describing the hoop stress variation through the crack depth. Describes the power loading on the crack face.
Gi = Stress Intensity Correction Factors (SICF), which are provided in tables in Reference 7.
In Reference 7 SICF is presented for both the depth point of the crack ("a-tip")
and for the surface point of the crack ("c-tip"). Separate tables are provided for the internal (ID) and external (OD) surface cracks. In addition the values are provided in association with the Rm/t ratio, a/c ratio (crack aspect ratio), and a/t ratio (normalized crack depth). The SICF tables are large and a suitable interpolation scheme is necessary to obtain proper coefficients dependent on crack size and shape for a given cylindrical geometry. Selected SICF from the tables for internal cracks for two different Rm/t ratios and a/c ratios are presented in Figure 18 below.
,2.73,9 2
m3 6-9 m5
_3 t,-
00.
,1 00.3 0
02 0.4 0.6 0.8 A]
X a/t ratio R/t = 2 & a/c = 0.2 Rit=2&a/c=0.4 Rt= 2 & a/c = 1.0 R/t=4&a/c=0.2 R/t = 4 & a/c = 0.4 R/t=4&a/c= 1.0 0.4 L 0
0.2 04 0.6 0.8 a
~~~~~x a/t ratio R/T=2 & a/c =.2 R/t=2&a/c=.4 R/t=2&a/c= I R/t = 4 & a/c =.2 Rt = 4 & a/c =.4 R/t-4&a/c-I Figure 18: SICF shown as a function of normalized crack depth for the "a-tip" (left figure) and the "c-tip" right figure. These figures show that simple linear interpolation would not provide accurate coefficients. These figures also show that a proper Rr,/t is essential to provide a reasonably accurate estimate of the SIF.
Cos
Engineering Report M-EP-2003-004 Rev. 00 Page 30 of 57 The figure above shows two features that are significant;
- 1) The interpolation used to obtain the SICF must be carefully performed such that the value accurately represents the crack geometry. This is accommodated by selecting a suitable order for the polynomial prior to performing an interpolation to obtain the specific value. This aspect is discussed in further detail in the section describing the analysis method.
- 2) The correct Rm/t ratio is essential for obtaining a reasonably accurate estimate of the SIF. Using a higher ratio will tend to underestimate the SIF and hence under predict the crack growth.
Both these features have been considered in the development of the analysis model such that a reasonable, yet conservative, estimate of the SIF is obtained.
Through-Wall Axial Crack The analysis for a through-wall axial crack was evaluated using the formulation of Reference 8. This formulation was chosen since the underlying analysis was performed considering thick-wall cylinders that had an "Ro/t" ratio in the range of the application herein. The analysis used the outside surface (OD) as the reference surface and, hence, the same notation is used here.
It was noted in Reference 8 that the formulations based on thin shell theory do not consider the complete three-dimensional nature of the highly localized stress distribution. This would be the case for the residual stress distribution from welding.
The nonlinear three-dimensional stress distribution coupled with shell curvature must be properly addressed to account for the material behavior at the crack tip, which controls the SIF, such that the SIF is not underestimated. The information presented in Reference 8 compared the results from formulations derived using thin shell theory and those derived using thick shell formulation, these results highlighted the need to use thick shell based formulation for situations such as the current application to CEDM nozzle through-wall axial cracks.
The formulation provides the correction factors, which account for the "R0It" ratio and crack geometry (X), that are used to correct the SIF for a flat plate solution subjected to similar loadings. The correction factors were given for both "extension" and 'bending" components. The flat plate solutions for both membrane and bending loads were to be used to obtain the applied SIF. The formulations for SIF were given as [8]:
K outer = {Ae + A b }
- K P for the OD surface;
- and,
Engineering Report M-EP-2003-004 Rev. 00 Page 31 of 57 Kinner = {Ae -'Ab}* Kp for the ID surface; where:
Ae and Ab are the "extension" and "bending" components; and, Kp is the SIF for a cracked Flat Plate subject to the same boundary condition and loading as the cracked cylinder.
The flat plate SIF solutions are written as:
Kp-Afembrane = 1h
- for membrane loading, and Kp-Bending = 00b
- for bending loading.
Where:
ah and ab are the membrane and bending stresses and "I is one-half the crack length.
The reference surface used in the evaluation was the OD surface. The stresses at the ID and OD at the axial elevation of interest were decomposed into membrane and bending components as follows:
e
= Cres-OD + ares-ID for membrane loading; and 2
1b
= (7res-OD 7rev-ID for bending loading.
2 where:
ures-OD is the stress (residual+operating) on the OD surface; and, ares-ID is the stress (residual+operating) on the ID surface.
The data presented in the tables in Reference 8 for determining the Ae and Ab components were curve fit using a fifth order polynomial such that they could be calculated knowing the parameter X, which is defined as [8]:
A = [12 *(I_ V )]02 *(R l {)0.5 where v is Poisson's ratio and R is the mean radius.
Engineering Report M-EP-2003-004 Rev. 00 Page 32 of 57 The data obtained from the tables in Reference 8 were curve fit using a fifth order polynomial. The curve fitting was accomplished using Axum 7 [9]. The curve fit results for the components are presented in Figure 19 below.
Extension and Bending Constants for Throughwall Axial Flaws R/t = 3.0 1ACRIA MID RIn 1a07- -- dAre 6
4 C
0 E
2 r
(U 00 0
-2 AeM:- 1.0090 + 0.3621 *x + 0.0565*X2 _ 0.0082*X3 + 0.0004,X4 -8.3264E-006-x 5 AbM:- -0.0063 + 0.0919'x - 0.0168x 2 -0.0052*x 3 + 0.0008x 4 -2.9701E_005*x5 I
I 0
2 10 1
12 4
6 8
Parameter Lambda {dimensionless}
Figure 19: Curve fit equations for the "extension and "bending" components in Reference 8. Tables Ic and Id for membrane loading and Tables 1g and lh for bending loading of Reference 8 were used.
Crack Growth Model To evaluate the potential for crack growth due to PWSCC, the crack growth rate equation from EPRI-MRP 55 [10] was used. The crack growth rate as a function of the SIF with a correction for temperature effects is given as [11a]:
da l
I,)
dt R TTrft Where:
da/dt = crack growth rate at temperature T {m/s)
Engineering Report M-EP-2003-004 Rev. 00 Page 33 of 57 Qg = thermal activation energy for crack growth (31.0 kcal/mole)
R = universal gas constant {1. 103x 103 kcal/mole-OR)
T = absolute operating temperature at crack tip {0R)
T = absolute reference temperature for data normalization (1076.67 0R) a = crack growth amplitude (2.67x10-12)
K = crack tip SIF (Mpa4rmn Kth = threshold SIF for crack growth (MPa4m)
,f = exponent {1. 16)
The above equation represents the seventy-fifth percentile curve. Since the PWSCC crack growth of interest is in the primary water, this model would provide a reasonably conservative crack growth. The operating temperature of 604 IF was verified to be a conservative upper bound based on the information provided in References 1 Ob and 1 Oc.
4.0 Method of Analysis Mathcad Worksheet Format The analytical scheme was developed using Mathcad [11] which facilitates calculations (including recursive) in a logical manner. Appendix B provides annotated versions of the three sets of worksheets used in the current analysis. The three sets are for the ID surface crack, the OD surface crack and for the through-wall crack. In the paragraphs below the general approach used to develop the worksheet is presented.
The first part of the worksheet is common to all three sets and requires the proper identification for the analysis being performed. In this region the component and the reference location in that component are identified. Immediately below the identification entry are the geometric landmark entries. For the surface cracks three entries are required and these are:
- 1)
The location of a reference line (e.g. blind zone location) referenced to the nozzle bottom {Refpoint.
- 2)
The location of the crack with respect to the reference line (Upper crack tip at the reference line, center of crack at the reference line or lower crack tip at the reference line) {Val};
- 3)
The location of the bottom of the weld measured upwards from the nozzle bottom {ULstrs.Distl.
For the through-wall crack the location of the crack upper tip is always at the reference line, while the two other land mark entries (reference point and bottom of weld) are similar to that for the surface crack. This completes the entries on the first page of the worksheet.
Engineering Report M-EP-2003-004 Rev. 00 Page 34 of 57 The second page of each Mathcad worksheet contains the inputs for crack dimensions, tube geometry, internal pressure, years of operation, iteration limit, operating temperature, and the constants for the PWSCC crack growth parameters. It should be noted that the crack growth is performed using metric units; hence, those constants are required to be in metric units. The remainder of this sheet does not require user input. The calculation shown is simple arithmetic to determine the values necessary for the analysis.
The third page of each worksheet is designed to import the entire nodal stress data from the Excel spreadsheet provided by Dominion Engineering (described earlier). After the required data has been imported, the graph below the data table depicts the ID and OD stress distributions along the axial length of the nozzle. This graph is needed to aid in the selection of the nodal stress data to be used in the subsequent analysis. Once the data needed for the evaluation has been selected, it is pasted onto the third sheet at a variable defined as "Data". No further user input is required. The worksheets presented in Appendix C reflect this design.
Determination of Stress Field (Distributions)
The first step in the analysis is to develop the appropriate stress distribution to be used in the determination of the SIF. This is needed because the SIF formulation is based on use of a uniform stress distribution along the length of the tube. However, the stress field at the bottom portion of the nozzle, starting from the nozzle bottom, increases in magnitude as the bottom of the weld is approached. Consequently, if an assumed crack located in the vicinity of the reference line were to grow by PWSCC, it would be subjected to an increasing stress field. Thus, to use the stress distribution at the initial crack location would lead to an underestimate of the SIF since the SIF is directly proportional to the applied stress. In order to obtain a reasonably representative SIF under the prevailing stress field variation, a moving average scheme was developed. This scheme is as follows:
- 1) For the initial crack location the stress distribution at the two crack tips (lower and upper) and the crack center are averaged to produce an average stress field that is applied to the crack. It is this stress distribution that is used to ascertain whether there exists a potential for PWSCC crack growth.
This method is considered reasonable since it is similar to the superposition principle used in finite element based SICF determination.
- 2) The remaining portion of the nozzle extending from the upper crack tip to the bottom of the weld is divided into twenty (20) equal segments.
- 3) The stress distribution in the first segment, above the upper crack tip, is an arithmetic average of the first three initial crack region distribution (Lower tip, center of crack and the upper tip) plus the distribution in the first segment. Thus, when the crack enters the first segment the magnitude of the stress distribution is appropriately increased to account for the increased applied stress. Similarly, as the crack progresses upward to the weld bottom through the various segments, the applied stress distribution is
Engineering Report M-EP-2003-004 Rev. 00 Page 35 of 57 adjusted accordingly. The small extent of the length between the reference line and the bottom of the weld can be sufficiently accommodated by the twenty-segment characterization.
To accomplish this averaging scheme, the nodal stresses at the five (5) nodal locations through the tube thickness and its variation along the length of the nozzle are individually regressed with a third order polynomial. Hence, it is important to ensure that the axial distribution can be described by a third-order polynomial. The regression is performed along the nozzle axis at each of the five (5) locations individually. The result of the regression provides the spatial coefficients required to describe the stress distribution. The nodal stress data representing the region of interest, from the nozzle bottom to an elevation just above the bottom of the weld, is selected. In this manner, it is expected that proper representation of the stress distribution, pertinent to crack initiation and growth, can be accurately described.
An example of this approach is presented in Figure 20 below. In this example, the stress at the ID and the OD locations were selected from a typical set of nodal stress data. The graphs immediately below show the individual stress distribution and the result from the third-order polynomial fit. In the first set, the entire data set from the bottom of the nozzle to the top of the J-weld was used. The regression curve shows that the general trend is captured; however, the fit in localized regions are not accurate representation of the original data. Significant variation that might cause errors in the determination of the SIF could occur, which in turn could lead to an inaccurate estimate in crack growth.
The two lower plots follow the scheme utilized in the current analysis. In this process the nodal stress data from the bottom of the nozzle to an elevation just above the bottom of the J-weld is selected. In this manner the stress distribution in the region of interest is chosen for the regressed curve fitting.
This is necessary since the stresses in the weld region show significant variation (top plot) and cannot be adequately represented by a third-order polynomial. Limiting the stress distribution data to the region of interest would limit the variation and results in a more accurate fit. The plots in the lowest row, in Figure 20, show the improvement in the accuracy of fitting. The regression fit does provide an accurate representation of the stress distribution of the region. Therefore, the stress distribution used in the fracture mechanics analysis would be a reasonably accurate representation of the actual stress distribution in the region where the initial crack and subsequent crack growth are of interest.
This example and the associated plots in Figure 20 show that the regression method, as developed for the current analyses, provides an adequate representation of the stress distribution.
The analysis worksheets (Appendix C) contain a cautionary statement such that inaccurate regression is avoided. The Mathcad worksheet used to develop this example is presented in Appendix D, Attachment 1. However, it should be
Engineering Report M-EP-2003-004 Rev. 00 Page 36 of 57 noted that this attachment is not annotated but does follow the method used in the analysis worksheets.
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- 11) Selected Nodal Data
(<I) 1Selected DSata Set Figure 20: Plots showing effect of nodal data selection on the accuracy of polynomial regression fit.
The first plot represents all nodal stress data from the nozzle bottom to the top of the J-weld.
The two plots, in the middle row, are the comparison of regression fit with nodal stress data; the full data set of nodal data for the ID and OD distribution was used.
The two plots, in the lower row, use a limited data set comprising the axial length to the bottom of the weld. The regression curve shows a significantly improved fit to the data.
Engineering Report M-EP-2003-004 Rev. 00 Page 37 of 57 Once the five polynomial equations for the axial distribution are established, the through-wall stress distribution for the three locations defined by the crack and the twenty segments are established. The distributions at the twenty-three locations are subjected to a third order polynomial regression to obtain the coefficients describing the through-wall distributions. These coefficients are used within the recursive loop to assign the coefficients based on the current crack location. The five axial distributions are used for the surface cracks (ID and OD) whereas only two are required for the through-wall crack (ID and OD distributions).
Iterative Analysis to Determine SICF For the surface cracks (ID and OD) the SICF coefficients were incorporated in two data tables. The first table contains the geometry data (Rm/t, a/c and a/t) and the second table consists of the SICF data for the appropriate cylinder and crack geometry. The values for the data were obtained from Reference 7. The data contained in the two tables were regressed into function statements with an appropriate polynomial order. The data for cylinder geometries from Rm/t ranging from one (1) to four (4) were regressed with a third-order polynomial, and for those above four, a second-order polynomial was used. The selection of the polynomial order was based on matching the value in the table given, for a selected set of independent variables, with that obtained from the interpolation performed using the regressed coefficients. In this manner the accuracy of the regression-interpolation method was established. The interpolation equation was defined outside the recursive loop and function call was made inside the loop using the pertinent variables at the time of the call.
The through-wall crack SICF was obtained using the fifth-order polynomial equation presented earlier. These equations were provided inside of the recursive loop.
The recursive loop starts the calculation scheme to determine the crack growth for a specified time period under the prevailing conditions of applied stress. The first few statements are the initialization parameters. The calculation algorithm begins with the assignment of the through-wall stress coefficients based on the current crack location. Once the four coefficients (uniform, linear, quadratic and cubic) are assigned, the through-wall stress distribution is used as the basis to establish the stress distribution along the crack face in the crack depth direction. That is, the stresses through the thickness are used to determine the stress along the crack face for application in the determination of the SIF in accordance with Reference 7. Once again, five locations along the crack depth were used to define the crack face distribution. The stresses representing the crack face values were regressed with a third-order polynomial to obtain the stress coefficients that would be used in the determination. At this point, the internal pressure is added to the stress coefficient (SICF) for the uniform term. Therefore, the crack face is subjected to an additional stress representing the internal pressure.
Engineering Report M-EP-2003-004 Rev. 00 Page 38 of 57 Following the determination of the stress coefficients, the function call to obtain the four SICF coefficients is made. In this case the two function calls were necessary to account for the "a-tip" and the "c-tip". The crack shape factor ("Q") was then computed using the appropriate crack dimensions. The SIF is calculated separately for the 'a-tip" and the "c-tip" using the stress coefficients, appropriate SICFs and crack dimensions.
In the through-wall crack solution; the fifth-order polynomial equations were solved using the current crack dimensions. The SIFs were computed for both the ID and OD locations and were then averaged. This averaged SIF was used for crack growth calculation. The crack growth calculation and the remainder of the program for both the surface cracks (ID and OD) and through-wall crack are identical.
The calculated SIFs were converted to metric unit for the computation of crack growth. The crack growth rate, based on the prevailing SIF was computed in metric units. Once this was done, a conditional branch statement was used to calculate the crack growth within the prescribed time increment. The crack growth was computed in English units by converting the calculated crack growth rate in meters-per-second to inches-per-hour. Thus, the crack growth extent was obtained in inches for the specified time period. Since the operating time was selected to be four years and the number of iterations chosen at one thousand five hundred (1500), the time increment for each crack growth block was about twenty-four (24) hours. After the calculations were performed, all necessary information (crack growth, SIFs etc.) was assigned to an output variable such that it is stored in an array. The last step of the recursive loop consisted of updating the essential parameters (namely, the index, crack length, time increment etc.).
Graphical displays of the results using both Mathcad and Axum plots complete the work sheet. The Mathcad plots are used to determine whether or not the crack reached the bottom of the weld in one operating fuel cycle and the Axum plots were generated for incorporation into this report.
The three attachments in Appendix B are sufficiently annotated to provide summary details for each major step in the program.
5.0 Discussion and Results Discussion The goal of the inspection program designed for the reactor vessel head penetrations is to ensure that the postulated crack in the vicinity of the blind zone does not reach the weld during the upcoming operating cycle following the refueling outage when the inspections are performed. Safety analyses performed by the MRP have demonstrated that axial cracks in the nozzle tube material do not pose a challenge to the structural integrity of the nozzle. Axial cracks, if allowed to exist undetected for sufficient periods of time can produce a primary boundary leak that can cause
Engineering Report M-EP-2003-004 Rev. 00 Page 39 of 57 damage to the reactor vessel head (carbon steel) and create a conducive environment for initiating and propagating OD circumferential cracks. These conditions challenge the pressure boundary; hence, critical importance is paid to proper periodic inspection and to the disposition of cracks that may be discovered. Therefore, proper analyses are essential to ascertain the nature of axial crack growth such that appropriate determination can be accomplished.
The analyses performed in this report were designed to capture the behavior of postulated cracks that might exist in the blind zone for the CEDM nozzle. The growth region for the postulated cracks was to the bottom of the weld along the tube OD.
The design review of the reactor vessel head construction, the detailed residual stress analyses, the selection of representative nozzle locations, selection of representative fracture mechanics models, and the application of a suitable crack growth law have provided the bases for arriving at a comprehensive and prudent decision.
The axial crack geometry is selected for evaluation because this crack has the potential for propagation into the pressure boundary weld (the J-groove weld); and since the circumferentially oriented cracks will not propagate towards the pressure boundary weld, this crack type is not evaluated. The hoop stress distribution at the downhill location (00), at the Mid-Plane location (900 rotated from the downhill), and at the uphill (1800) location were chosen for evaluation. The axial distribution of the hoop stress magnitude for both the ID and OD surfaces shows that at an axial location below the evaluated elevation, the stresses drop off significantly and become compressive except for the specific group of nozzles identified earlier. In nozzles where a compression zone exists or where localized low tensile stress exists at the nozzle bottom, the potential for PWSCC crack growth would be significantly low to non-existent in these locations. For the isolated location (49.70 nozzle at mid-plane) where the tensile stress on the ID surface was 19.02 ksi, an additional fracture mechanics analysis was performed. The analysis and the results are presented in the following section.
The fracture mechanics evaluation considered the crack face to be subjected to the operating reactor coolant system (RCS) pressure. This is accomplished by arithmetically adding the RCS pressure to the uniform stress coefficient in the surface crack analysis and to the membrane stress for the through-wall crack analysis. In this manner, the stress imposed on the crack is accurately and conservatively modeled.
In order to ensure that the moving average technique did not create numerical errors, a Mathcad worksheet was created by using the stress averaging portion of the regular analysis worksheet. In this worksheet, the data table, which is used to import data from an Excel spreadsheet, was entirely populated with a linear through-wall stress distribution. The axial distribution of the stresses along the axis was kept constant. In this manner, the moving average method should provide results that have the same distribution at all locations along the tube axis. This implies the through-wall distribution is invariant along the length of the tube. The example and
Engineering Report M-EP-2003-004 Rev. 00 Page 40 of 57 the associated worksheets are provided in Appendix D, Attachment 2. The results of the experiment show that the stress distribution across the wall remained unchanged along the axis of the tube. Therefore the moving stress averaging method is validated.
The through-wall axial crack could have been considered as a single edge crack in a plate. For this model to work properly, it is essential that the plate geometry be described accurately. The CEDM nozzle is welded to the head; hence the nozzle OD surface is clamped at the bottom of the weld. Therefore, the plate height would be equal to the length of the nozzle from the bottom of the nozzle to the bottom of the J-weld. When this plate height is assumed and the length of the through-wall axial crack is taken to be the length (height) of the blind zone, then the ratio of crack length to the plate height (assumed) violates the pre-requisite for the SICF of 0.6. It is possible to assume the plate height to be equal to the nozzle height or some lower elevation (e.g. length equal to top of the J-weld). These assumptions tend to keep the crack-to-plate height ratio within the limit; however, the resulting SICF is lower than the membrane SICF from the model used in this analysis. A Mathcad worksheet showing the comparison is presented in Appendix D, Attachment 3. The results presented in this attachment demonstrate that the SICF for the model used in the current analysis is higher than the SICF produced by an edge crack model with longer plate lengths. In addition, the bottom zone of the CEDM nozzle is in compression, as shown in Figures 8-12, which further argues against postulating an edge crack for evaluating a through-wall crack. Therefore, for the two reasons cited herein the model developed for through-wall crack is considered valid and provides an accurate (but conservative) estimate of the SIF. The SICF comparison is presented in Figure 21 below.
Engineering Report M-EP-2003-004 Rev. 00 Page 41 of 57 20 20 19 18 17 16 15 I 544 Top of TW axial @
w Blind Zone o F bs 8 F bsl.
F ' bs2
'O A M Jo
'4 13 1 2 10 9
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,1,792, Flaw length {inchj Edge Crack Panel Height upto Bottom of fillet weld Edge Crack Panel Height upto Top of J-weld Edge Crack Panel Height equal Full Nozzle Length {
20 inches)
Entergy Model Membrane Figure 21: Comparison of SICF for the edge crack configurations with the membrane SICF for current model. The current model results in a higher SICF value for the application considered.
The models used in the analysis presented here were compared with the conventional approach used by the industry. The OD surface crack evaluated shows that the model used provides a higher SIF and, in addition, has the capability of separately evaluating the SIF at the two crack locations (the "a-tip" and the "c-tip").
The SIF comparison for a sample case from Appendix D, Attachment 4 is shown in Figure 22.
co
Engineering Report M-EP-2003-004 Rev. 00 Page 42 of 57 3.2 -
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- 4 Figure 22
- Comparison of SIF for the current model and conventional model.
The conventional approach for the through-wall axial crack is the Center Cracked Panel (CCP) with an SICF of one (SICF = 1.0). This conventional model is compared to the current model used within this analysis. The Mathcad worksheet for this comparison is presented in Appendix D, Attachment 5. The results presented in this attachment clearly demonstrate that the SIF obtained by the current model is significantly higher than that from the conventional approach. Therefore, the estimated crack growth would be higher for the current model than that estimated using the conventional approach. This would lead to an underestimate of the crack growth, by the conventional model, leading to a non-conservative propagation length estimate. Figure 23 shows a comparison between the conventional and current models. Though the SIF for both models are below the threshold SIF of 8.19 ksi4in., it is clear from this figure that the conventional model SIF is lower.
7.9 7 7 Currnnt M odel(E rt n"Iy C o n otio n a I m od l (10 I
ostry )
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5-7.3 7.1 t7.1 Operating Time (years)
Figure 23: SIF comparison between current model and conventional model.
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Engineering Report M-EP-2003-004 Rev. 00 Page 43 of 57 A comparison of the fracture mechanics models for the current analyses and the conventional method are summarized in Table 11. The comparison shows that the models used in the current analyses would provide a higher estimate for the SIF.
The net result would be a higher crack growth rate and hence a larger crack propagation length for one (1) cycle of operation. These improvements in analysis methods are believed to more accurately predict crack behavior in the CEDM configuration and may be conservative compared to the conventional approach.
Table 11 Comparison of Fracture Mechanics Models l..
Flaw Type
[ I? -
Feature'_j '.: t<;Co nventional Approach`:.--
Entergy Approach I aW Tv. l'
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-hs Surface Flaws Stress Distribution Fixed a Initial flaw Variable Distribution along Length (ID & OD)
Location of Tube & Flaw face Pressurized Part Throughwall Cylinder Fixed 'R/t' ratio of 4.0 Variable 'R/t" ratio from 1 to 300 PartThrughall Geometry Flaw Geometry Fixed Aspect Ratio; "a/c" = 0.33 Variable Aspect Ratio; 'a/c" from 0.2 to 1.0 Flaw Growth Only Growth in Depth direction Growth both in the Depth and Evaluated Length directions evaluated Independently Throughwall Stress Uniform Tension @ Initial flaw Variable along Length; Both Axial Flaws Location Membrane and Bending components considered; Flaw face Pressurized Model Center Cracked Panel without Thick Cylinder with correction for Correction Factors Flaw/Tube geometry Results Analysis for the As-Built Condition The first set of analyses was performed using the as-built dimensions for the welds which were estimated from the review of the Plant A UT data. In addition, these analyses were performed by setting the blind zone elevation at 1.544 inches above the nozzle bottom. These analyses were performed at three azimuthal locations on the nozzle (downhill, mid-plane, and uphill). At each location, three crack geometries (ID surface, OD surface, and through-wall) were evaluated. The extent of the compression zone in each nozzle group at the three locations was obtained from the stress distributions presented in Figures 8-17. From these figures, the compression zone at the three azimuthal locations is presented in Table 12, below. In these regions of compression, no PWSCC-assisted crack growth is possible; therefore, these zones can be excluded from consideration for inspection. For those nozzle groups with tensile stress below 10 ksi the possibility for PWSCC crack initiation is
Engineering Report M-EP-2003-004 Rev. 00 Page 44 of 57 extremely low. The region showing a high hoop tensile stress, (49.70 nozzle at mid-plane), was selected for additional fracture mechanics analysis.
Table 12: Results for Compression Zone Nozzle Group Azimuthal Location Height of Compression Zone t-.;
- <4 (inch)
- Cowmmen
.- 'Head Angle.B..
(Measured from Nozzl 0
All (3600) 0.89 Downhill 0.97 7.8 Uphill 1.26 Mid-Plane 1.059 Downhill 1.148 29.1 Uphill 0
OD Tension {1.66 ksi}
Mid-Plane 0
ID Tension {6.95 ksi}
Downhill 0
OD Tension {2.32 ksi}
49.7 Uphill 0
OD Tension {6.11 ksi)
Mid-Plane 0
ID Tension {19.02 ksi}
All nozzles at the three principal locations (downhill, uphill and mid-plane) showed a measurable freespan length to exist. For these nozzles the three configurations; ID and OD surface and through-wall axial cracks were evaluated.
Thirty (30) analyses cases were performed. The worksheets representing these evaluations are presented in Appendix C, Attachments 1 - 30. The results from this set of analyses are summarized in Table 13. Table 13 provides the 'Propagation Dimension" which represents the available freespan for the limiting nozzle within the specific nozzle group. For the surface Crack Type, the length dimension excludes the 0.16 inches that was assumed for the portion of the crack that extends into the freespan.
Table 13 also provides "Growth/Cycle" dimensions. This is the calculated crack growth for one cycle of operation and is used to evaluate the available propagation dimension of each individual nozzle (as determined from the UT data). This is done by comparing the available nozzle propagation dimension to the "Growth/Cycle" dimension. Where the available propagation dimension is larger, adequate margin for flaw growth is available without compromising the weld. When comparing the OD surface crack, 0.16 inch is subtracted from the available propagation dimension to account for the portion of the assumed crack that extends into the freespan.
The analysis results indicate that the OD surface or the through-wall axial crack configurations are not susceptible to crack growth by PWSCC. The analyses show
Engineering Report M-EP-2003-004 Rev. 00 Page 45 of 57 that the prevailing stresses at the crack location produce a SIF which is below the threshold value. Hence, the potential for crack growth due to PWSCC does not exist.
None of the postulated ID part through-wall cracks came close to reaching the bottom of the weld or penetrating through the wall to meet the weld. Only in two of the cases evaluated (00 nozzle and 7.80 nozzle at the downhill location) did the analysis indicate potential for PWSCC crack growth. In both cases the estimated growth for one cycle of operation was well within the acceptable limits. Hence, there is no evidence to support that an ID initiated part through-wall crack would provide a leak path or reach the weld within one operating cycle.
In all thirty (30) cases evaluated for cracks postulated at the blind zone, the results demonstrate that a postulated flaw in the blind zone region will not compromise the weld in one cycle of operation. The analysis further demonstrates that a larger margin exists (longer than one fuel cycle) at all the plausible locations evaluated.
One nozzle location (49.70 nozzle at mid-plane) showed tensile stress of 19.02 ksi to exist on the ID surface at the nozzle bottom (Figure 17 and Table 10). The nozzle at this location was analyzed to ascertain the behavior of a postulated crack in this region. The analysis performed and the results obtained are discussed in the following subsection (Additional Analysis) for the 49.70 nozzle.
Engineering Report M-EP-2003-004 Rev. 00 Page 46 of 57 Table 13: WSES-3 Estimated As-Built Analyses Results Summary Fracture Mechanics Resultsv.
'-Propagation
',:Growth I Cycle.
ttchen Vessel~
~~~~~~~~~~.4U061 Head)56 D det)4~di 0 Degreeil OD 0.842 05 TW 1.002 0
6 7.8 Degree ID 1.49610.661D 0 L/0D ^7 Uphill OD 1.496 08 1W 1.656 0
9 ID
~~1.169U10.661 D 0 UO0D *10 Mid-Plane OD 1.169 011 1W 1.329 0
12 ID
~~0.477U0.661 0 UJ0D ^13 Downhill OD 0.477 14 TW 0.637 015 ID
~~3.456U10.661 D 0 U0D ^16 29.1 Degree Uphill OD 3.456 0
17 7W
~~3.616 0
18 ID
~~1.981U10.661D 0 L/0D ^19 Mid-Plane OD 1.981 20 1W 2.141 0
21 ID 0.26UL0.661D 0 /U0 D
22 Downhill OD 0.26 0
23 TW 0.42 0
24 49.7 Degree ID 6.14710.661D 0 / D ^25 Uphill OD 6.147 0
26 TW 6.307 0
27 ID 3.281LJ0.661D 0 UO D 28 Mid-Plane OD 3.281 0
29 1W 3.441 0
30 C For IDSurfaceCracks te dimenIonD o oh nLnt 0()I.61 and Oept (01repovdd I...
For ID Surface Cracks the dimensions for both in Length (L) and Depth (D) are provided.
Engineering Report M-EP-2003-004 Rev. 00 Page 47 of 57 The graphical presentation of results for those nozzle groups which showed insufficient propagation length are discussed below, by nozzle group. In the graph for length growth, a vertical red line represents one fuel cycle and a horizontal blue line represents available propagation length. When the curve is below the intersection point of these two lines, the analysis indicates that the postulated crack will not reach the bottom of the weld in one operating cycle: In addition graphs for the through-wall cracks for all nozzle groups at the downhill location, which has the smallest available propagation length, are provided. Since the through-wall cracks are the limiting configuration, the absence of crack growth demonstrates that there exists sufficient margin to preclude PWSCC growth from compromising the weld 0° Nozzle In this nozzle the ID surface crack showed potential for PWSCC assisted crack growth. The crack growth and the corresponding SIF are presented in Figure 24.
The plots show that the crack growth is very small and significantly lower than the limiting condition that would compromise the weld. The graph for the through-wall crack, Figure 25, shows that a through-wall crack postulated at the blind zone shows no crack growth. The SIF for this crack is below the threshold value required for crack growth.
Engineering Report M-EP-2003-004 Rev. 00 Page 48 of 57 0.6 -
i A
g04-002 -
0,0 -
,02 0.0 0
1 2
Oper.ting Tie. f(years) 3 4
0 1
2 Ope..ng Tim.e {years) 3 4
{Depth Growth)
Figure 24: Nozzle at 00ID Surface Crack Crack growth in both the depth and length are shown. In both cases the crack growth is well below the intersection of the red and blue lines indicating sufficient margin. The SIF plot shows the SIF at both the depth (a-tip) and surface (c-tip) points.
Note the surface point SIF is higher than the depth point SIF indicating that the crack growth would be more pronounced along the surface
{Length Growth) it Ii8
- j14 0312
{SIF)
+
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a j 4
-(3D Saia~ce SIF
- ~~~~~~ID Surface SIFl
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~~~~-
Average SIF l I l
I 0
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opeatng Time (y.e-1}
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0 1
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Figure 25: Nozzle at 00 through-wall crack. No crack growth is observed. The SIF plot shows that the average SIF is below the threshold value of 8. 19 ksiin.
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Engineering Report M-EP-2003-004 Rev. 00 Page 49 of 57 7.80 Nozzle Group In this nozzle the ID surface crack showed potential for PWSCC assisted crack growth. The crack growth and the corresponding SIF are presented in Figure 26.
The plots show that the crack growth is very small and significantly lower than the limiting condition that would compromise the weld. The graph for the through-wall crack, Figure 27, shows that a through-wall crack postulated at the blind zone shows no crack growth. The SIF for this crack is below the threshold value required for crack growth.
06 04 Z
°02.
00-0 1
2 3
4 OperairUT.m snag
{Depth Direction)
Figure 26: Nozzle at 7.8° ID Surface Crack.
Crack growth in both the depth and length are shown. In both cases the crack growth is well below the intersection of the red and blue lines indicating sufficient margin. The SIF plot shows the SI at both the depth (a-tip) and surface (c-tip) points. Note the surface point SIF is higher than the depth point SIF indicating that the crack growth would be more pronounced along the surface 1
V I
0 8
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0 0 -
0 1
2 3
4 Opre-bM Tim {yeam}
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Operating Time t
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Engineering Report M-EP-2003-004 Rev. 00 Page 50 of 57 l
1.0 -
08 -
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00 -
00 j 6
-2 I
ID A~Sg.o SIF 0
1 2
Op-b~Tn i-~ (y.... )
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0 1
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(Crack Growth)
{SIF)
Figure 27: Nozzle at 7.8° through-wall crack. No crack growth is observed. The SIF plot shows that the average SIF is below the threshold value of 8.19 ksibin.
29.10 Nozzle Group The results for this nozzle group showed no potential for crack growth at all locations and the three crack configurations evaluated. The results for the through-wall crack at the downhill location are presented in Figure 28 below.
0.6-0.4 2
0.2-eo-4 G6
.6 JI 0
1 2
CpwabMT-~ {fin 3
4 2~
cO P mu igrn (y-1) 3 4
{Crack Growth)
(SIF)
Figure 28: Nozzle at 29.10 through-wall crack. No crack growth is observed. The SIF plot shows that the average SIF is below the threshold value of 8.19 ksi-'in.
Engineering Report M-EP-2003-004 Rev. 00 Page 51 of 57 49.70 Nozzle Group The results for this nozzle group showed no potential for crack growth at all locations and the three crack configurations evaluated. The results for the through-wall crack at the downhill location are presented in Figure 29 below.
0s Sm'se SIF~
0.3 2
0.1 e
v~~~~~~~~~~~~~o
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-41 0
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3 4
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4 0pm.bn9 Tim Ty-)
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{Crack Growth)
{SIF}
Figure 29: : Nozzle at 49.70 through-wall crack. No crack growth is observed. The SIF plot shows that the average SIF is below the threshold value of 8.19 ksi-1in.
Additional Analysis In nozzle group at 49.70 it was determined that the ID stress at the nozzle bottom was about 19.02 ksi. The stress distribution in the region immediately above the nozzle bottom up to the weld bottom was reviewed. Figure 30 presents the stress distribution in this region for the ID surface, the mid-wall, and the OD surface.
These distributions were obtained from the regression analyses presented in of Appendix D. The stress distribution shows that the hoop stress on the ID surface is rapidly decaying to zero and that the distributions at the mid-wall and OD surface show compressive stresses in the immediate vicinity. Therefore it is unlikely that a through-wall edge crack can be supported by the prevailing stress distribution. However, the close proximity of the nozzle bottom necessitates a fracture mechanics analysis using an edge crack formulation in addition to the ID surface crack evaluation. Therefore, three crack configurations were evaluated for this location. Two crack sizes for the ID surface crack geometry and one edge crack geometry were used. The analysis results for these cases are presented in Attachments 31 through 33 of Appendix C, a graphical display of the results are presented and discussed in the following pages.
Engineering Report M-EP-2003-004 Rev. 00 Page 52 of 57 I
MUSD-ark MUMs Or-ithl i
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I l lUlAiUJSion Figure 30: Nozzle 49.70 at mid-plane location.
Hoop stress distribution near nozzle bottom at the ID surface, mid-wall, and OD surface. The vertical red line is set at 0. 75 inch from the nozzle bottom.
Though the ID surface at the nozzle bottom has a tensile stress of 19.02 ksi, the stress decays rapidly to zero within a short distance. Whereas the stresses at the mid-wall and OD surface are compressive in this region.
/
I I I 10 2
3 Dullk Nat Ad-0thj Two ID surface cracks were postulated close to the nozzle bottom. The first crack, with similar dimensions to those considered here was located close (crack center 0.5 inch above nozzle bottom) to the nozzle bottom. The fracture mechanics evaluation (Mathcad worksheet) is presented in Attachment 31 of Appendix C. The graphical results from this analysis are presented in Figure 31. These results show that the postulated crack will not grow by PWSCC. The second crack configuration, a larger ID surface crack which had a depth of 0.33 inch (50% TW) and 0.75 inch long (based on the axial distribution of the hoop stress) was evaluated. The fracture mechanics evaluation (Mathcad worksheet) is presented in Attachment 32 of Appendix C. The results are graphically shown in Figure 32. Once again these results show that there is no potential for crack growth.
Since the location of the postulated crack was so close to the free end of the nozzle and the fracture mechanics models were for cracks removed from the edge, an edge crack model was evaluated to ensure that the results from the ID surface analysis could be supported. The edge crack model was the same model used in the comparison study presented in Attachment 3 of Appendix D. The Mathcad formulation and the analysis are presented in Attachment 33 of Appendix C. The results from this analysis are presented in Figure 33. The initial flaw length was 0.75 inch (based on the stress distribution) and the plate height was set at 4.985 inches (bottom of weld). In this configuration the limiting flaw size, to maintain the validity of
Engineering Report M-EP-2003-004 Rev. 00 Page 53 of 57 SICF (i.e. Crack Length/Plate Height < 0.6), was 2.99 inches. The results show that the postulated crack does not reach the weld in forty (40) years of operation. Though the stress distribution does not favor a through-wall edge crack configuration, this crack configuration would provide the limiting case if the limit of the crack length to plate height ratio remained below 0.6. In the analysis presented in Attachment 33 of Appendix C, the crack length of 2.99 inch (that is; 0.6 x 4.985) is reached in about thirty nine (39) years. This limit is well below the bottom of weld elevation. The results from this analysis are extremely conservative because the initial through-wall crack is not likely to form. However, this analysis does show that the localized region at the bottom of the nozzle would not be cause for concern. Therefore not inspecting this region will not (negatively) impact the level of quality or safety.
Depth Growth Length Growth 0.05 is 0 05 e 004 003 0.3 0.1 (i
0 -03 0r 1
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Figure 31: Nozzle 49.70 at mid-plane location ID surface crack The crack dimensions are similar to that used for the as-built analysis at the blind zone location. The crack was placed close to the nozzle bottom. The fracture mechanics results demonstrate that this ID surface crack will not grow by a PWSCC mechanism.
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Opwaq Time 1years) 3 4
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Engineering Report M-EP-2003-004 Rev. 00 Page 54 of 57 0.5 1 Depth Direction Length Direction 04 c
e 0.3 02 j03-
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the5 I0.03I ti o 01-a 0
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Figure 32: Nozzle 49.70 at mid-plane location with a larger ID surface crack. The crack dimensions are larger than that used for the as-built analysis at the blind zone location. The crack depth was 0.33 inch and the length was 0. 75 inch. The crack was placed close to the nozzle bottom. The fracture mechanics results demonstrate that this ID surface crack will not grow by a PWSCC mechanism.
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30 40 Figure 33: Nozzle 49.7 at mid-plane location with an edge crack. The estimated crack growth does not cause the initial postulated crack to reach weld bottom in forty (40) years. The SIF at the validity limit is 175 ksNin., which is significantly higher than the asymptotic maximum for crack growth. Hence the crack
Engineering Report M-EP-2003-004 Rev. 00 Page 55 of 57 growth rate would be about 0.5 inch per year after thirty five (35) years (knee in the curve).
6.0 Conclusions The evaluation performed and presented in the preceding sections support the following conclusions:
- 1) The detailed deterministic analyses incorporating the as-built dimensions for the weld and nozzle length were used to accurately define the inspection zones for the CEDM nozzle groups. The use of a sister plant's UT data provided a reasonable estimate for the as-built configuration. UT examination at WSES-3 obtained during the Fall 2003 refueling outage will be used to confirm the as-built estimate.
- 2) The developed models, incorporating a method to account for applied stress distribution variation along the nozzle length, have been shown to be a reasonably realistic but conservative representation of the expected phenomenon. The models are generalized and have the potential to be used at other locations of the nozzles.
- 3) The fracture mechanics models were shown to be representative of the expected crack and nozzle configurations. A review of the current model results and that from the conventional approach showed that the current model produced higher SIF than the conventional model. Therefore, the current model provides a more accurate and conservative estimate of crack growth.
- 4) The analyses demonstrate that the UT inspection above the normal blind zone will provide an adequate assurance that the weld will not be compromised in one operating cycle.
- 5) The plan for the work presented herein, defined additional evaluations that needed to be performed for the determination of an augmented inspection region. However, the deterministic fracture mechanics analyses demonstrated that no additional analyses were required.
- 6) The additional analysis performed for one location in one nozzle group (49.70 nozzle at the mid-plane location) where the ID surface stress was high shows that the postulated cracks at this location will not compromise the weld for nearly forty (40) years of operation.
- 7) The regions below the lowest inspection elevation, at other locations, experience lower stresses or have a compression zone. Hence, at elevations below the lowest inspection elevation, a significantly lower potential for crack growth by PWSCC exists. Thus, at these lower locations PWSCC, crack growth is not expected.
- 8) The ID surface cracks either did not show any potential for crack growth, or the crack growth was well within acceptable limits. Hence, ID surface cracks in a region below the weld are not expected to compromise the weld.
Engineering Report M-EP-2003-004 Rev. 00 Page 56 of 57
- 9) The deterministic fracture mechanics analysis demonstrates that the proposed changes to the inspection requirements specified in the NRC Order will still provide an acceptable level of safety and quality commensurate with the NRC Order.
References
- 1) NRC Order; Issued by letter EA-03-009 addressed to "Holders of Licenses for Operating Pressurized Water Reactors"; dated February 11, 2003.
- 2) Drawing Number 1564-4086 R1 WSES-3 Design Engineering Drawing files.
- 3) a: E-mail from R. V. Swain (Entergy) to J. G. Weicks (Entergy); Dated 5/15/2003.
b: E-mail from R. V. Swain to J. G. Weicks; Dated 5/12/2003.
Wesdyne Qualification": Transmitted by e-mail from B. Rassler (EPRI) to K. C.
Panther (Entergy); Dated 3/27/2003.
- 5) a: "PWSCC of Alloy 600 Materials in PWR Primary System Penetrations";
EPRI TR-103696; Electric Power Research Institute, Palo Alto, CA; July 1994.
b: DEI E-Mail containing the Nodal Stress Data for WSES-3 CEDM Analysis; J. Broussard (DEI) to J. S. Brihmadesam (Entergy); E-4162-00-8, Dated 9/2/2003.
c: "BWR Vessel and Internals Project - Evaluation of crack growth in BWR Stainless Steel RPV Internals (BWRVIP-14)"; EPRI TR-105873; Electric Power Research Institute, Palo Alto, CA; March 1996.
d: "BWR Vessel and Internals Project - Evaluation of crack growth in BWR Nickel Base Austenitic Alloys in RPV Internals (BWRVIP-59)"; EPRI TR-108710; Electric Power Research Institute, Palo Alto, CA; December 1998.
- 6) "Stress Intensity Factor Influence Coefficients for Internal and External Surface Cracks in Cylindrical Vessels"; I. S. Raju and J. C. Newman, Jr.; ASME PVP Volume 58 "Aspects of Fracture Mechanics in Pressure Vessels and Piping";
1982.
- 7) "Stress Intensity Factors for Part-Through Surface Cracks in Hollow Cylinders":
S. R. Mettu etal; NASA TM-I 11707; Prepared by Lockheed Engineering &
Science Services; Houston, Texas; July 1992.
Engineering Report M-EP-2003-004 Rev. 00 Page 57 of 57
- 8)
"New Stress Intensity factor and Crack Opening Area Solutions for Through Wall Cracks in Pipes and cylinders": Christine C. France, etal.; ASME PVP Volume 350 "Fatigue and Fracture"; 1997.
- 9) Axum 7; Data Analysis Products Division, Mathsoft Inc., Seattle, WA; February 1999.
- 10) a: "Materials reliability Program (MRP) Crack Growth Rates for Evaluating Primary Water Stress Corrosion cracking (PWSCC) of Thick Wall Alloy 600 Material": MRP-55 Revision 1; Electric Power Research Institute; May 2002.
b: "Engineering Report to Support 1.5 percent Power Uprate @ Waterford 3 Steam Electric Station"; ER-WS-ST-0001 Rev. 3; September 2001.
c: "Waterford 3 Extended Power Uprate Report"; (Draft); August 2003.
- 11) Mathcad - 11; Data Analysis Products Division; Mathsoft Inc.; Seattle WA; November 2002.
- 12) "Stress Intensity Factors Handbook Volume 1"; Y. Murakami, Editor-in-Chief; Pergamon Press; 1986; Section 1.3.