CNRO-2003-00035, Arkansas, Unit 2 - Response to Request for Additional Information Pertaining to Relaxation Request to NRC Order EA-03-009 for In-Core Instrumentation Nozzles: Difference between revisions

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{{#Wiki_filter:;                                        .                                      Entergy
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                                                                                  .      Operations, Inc.
1340 Echelon Parkway Tel 601 368 5758 Michael A. Krupa Director Nuclear Safety &Licensing CNRO-2003-00035 September 3, 2003 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001
 
==SUBJECT:==
Entergy Operations, Inc.
Response to Request for Additional Information Pertaining to Relaxation Request to NRC Order EA-03-009 for In-Core Instrumentation Nozzles Arkansas Nuclear One, Unit 2 Docket No. 50-368 License No. NPF-29
 
==REFERENCE:==
: 1. NRC Order EA-03-009, "Issuance of Order Establishing Interim Inspection Requirements for Reactor Pressure Vessel Heads at Pressurized Water Reactors," dated February 11, 2003
: 2. Entergy Operations, Inc. Letter CNRO-2003-00033 to the NRC, Relaxation Request to NRC Order EA 03-009," dated August 27, 2003 Pursuant to Section IV.F of NRC Order EA-03-009, (Reference #1), Entergy Operations, Inc.
(Entergy) requests relaxation from Section IV.C(1)(b) of the Order for Arkansas Nuclear One, Unit 2 (ANO-2). Specifically, Section IV.C(1)(b) of the Order requires either an ultrasonic test (UT) or a wetted surface examination using eddy current testing (ECT) or dye penetrant testing (PT) be performed on the total population of reactor pressure vessel (RPV) head penetration nozzles. Compliance with Section IV.C(1)(b) does not allow the use of a combination of inspection techniques; therefore, Entergy Is requesting that a combination of techniques and supplementary analysis be allowed for determining the condition of the In-Core Instrumentation (ICI) nozzles at ANO-2. Enclosure 1 of this letter contains the relaxation request for ANO-2. Enclosure 2 contains a copy of the fracture mechanics analysis report (Engineering Report M-EP-2003-003, Rev. 0) that supports this request.
Engineering Report M-EP-2003-003, Rev. 0 utilizes information pertaining to material properties and analytical methods provided by Dominion Engineering, Inc. via Dominion letter L-4162-00-1, wMaterial Properties and Modeling Methods Used in ANO Unit 2 Welding Residual Stress Analysis." Entergy provided this letter to the NRC staff via Reference #2.
This letter contains new commitments as identified in Enclosure 3.
                                                                                                        \401
 
CNRO-2003-00035 Page 2 of 2 Should you have any questions, please contact Guy Davant at (601) 368-5756.
Sincerely, M. A. Krupa Director, Nuclear Safety & Licensing MAKIGHD/bal
 
==Enclosure:==
: 1. Relaxation Request #3 for Arkansas Nuclear One, Unit 2
: 2. Engineering Report M-EP-2003-003, Rev. 1
: 3. Licensee-identified Commitments cc:    Mr. C. G. Anderson (ANO)
Mr. W. A. Eaton (ECH)
Mr. G. A. Williams (ECH)
Mr. T. W. Alexion, NRR Project Manager (ANO-2)
Mr. R. L. Bywater, NRC Senior Resident Inspector (ANO)
Mr. T. P. Gwynn, NRC Region IV Regional Administrator
 
ENCLOSUREI CNRO-2003-00035 ARKANSAS NUCLEAR ONE, UNIT 2 RELAXATION REQUEST #3
 
ENTERGY OPERATIONS, INC.
ARKANSAS NUCLEAR ONE, UNIT 2 RELAXATION REQUEST #3 TO NRC ORDER EA-03-009 ASME COMPONENTS AFFECTED Arkansas Nuclear One, Unit 2 (ANO-2) has ninety (90) ASME Class 1 reactor pressure vessel (RPV) head penetration nozzles comprised of eighty-one (81) Control Element Drive Mechanism (CEDM) nozzles, eight (8) In-Core Instrument (ICI) nozzles, and one (1) vent line nozzle. This request pertains to the ICI nozzles only. The locations of RPV head penetrations are provided in Figure 1.
I1. REQUIREMENTS The NRC issued Order EA-03-009 (the Order) that modified the current licenses at nuclear facilities utilizing pressurized water reactors (PWRs), which includes ANO-2.
The NRC Order establishes inspection requirements for RPV head penetration nozzles.
In accordance with Section IV.A of NRC Order EA-03-009, the ANO-2 susceptibility category is Ohigh" based on a calculated value of 12.4 effective degradation years (EDY) at the beginning of the upcoming fall refueling outage.
Section IV.C of the Order states in part:
nAII Licensees shall perform inspections of the RPV head using the following techniques and frequencies:
(1) For those plants in the High category, RPV head and head penetration nozzle inspections shall be performed using the following techniques every refueling outage.
(a) Bare metal visual examination of 100% of the RPV head surface (including 3600 around each RPV head penetration nozzle), AND (b) Either:
(i) Ultrasonic testing of each RPV head penetration nozzle (i.e., nozzle base material) from two (2) inches above the J-groove weld to the bottom of the nozzle and an assessment to determine if leakage has occurred into the interference fit zone, OR (ii) Eddy current testing or dye penetrant testing of the wetted surface of each J-groove weld and RPV head penetration nozzle base material to at least two (2) inches above the J-groove weld."
Entergy is performing a bare metal visual examination of the ICI nozzles in accordance with Section IV.C(1)(a) of the Order.
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Ill. REASON FOR REdUEST Section IV.F of the Order states:
    "Licensees proposing to deviate from the requirements of this Order shall seek relaxation of this Order pursuant to the procedure specified below. The Director, Office of Nuclear Reactor Regulation, may, in writing, relax or rescind any of the above conditions upon demonstration by the Licensee of good cause. A request for relaxation regarding inspection of specific nozzles shall also address the following criteria:
(1) The proposed alternative(s) for inspection of specific nozzles will provide an acceptable level of quality and safety, or (2) Compliance with this Order for specific nozzles would result in hardship or unusual difficulty without a compensating increase in the level of quality and safety.
    "Requests for relaxation associated with specific penetration nozzles will be evaluated by the NRC staff using its procedure for evaluating proposed alternatives to the ASME Code in accordance with 10 CFR 50.55a(a)(3)."
Pursuant to Section IV.F(1) of the Order, Entergy Operations, Inc. (Entergy) requests relaxation from the requirements of Section IV.C(1)(b). Entergy plans to inspect RPV head ICI penetration nozzles at ANO-2 using the ultrasonic testing (UT) method in accordance with Section IV.C(1)(b)(i) of the Order to the maximum extent possible.
However, limitations due to nozzle configuration cause reduced UT inspection coverage of each nozzle. These are discussed below.
A. Counterbore Blind Zone ICI nozzles are manufactured with a counterbore as shown in Figure 2. Due to lift-off of the UT transducers at the counterbore, a UT blind zone exists at the upper hillside location (1800 azimuth) of each ICI nozzle. Measuring approximately 0.88 inches in axial length, the bottom of the blind zone is located 1.080 inches above the top of the J-groove weld. Centered at the upper hillside location of each nozzle, the counterbore blind zone has a circumferential extent of 820. See Figure 6 for additional details.
It should also be noted that the blind zone associated with the counter bore does not exist at any other azimuthal locations along the circumference of the ICI nozzle.
Due to the RPV head angle at the ICI locations, the counterbore is significantly closer to the J-groove weld on the upper hillside of the nozzle than on the lower hillside. Specifically, the distance from the top of the J-groove weld to the bottom of the counterbore blind zone on the lower hillside of the ICI nozzle is 9.96 inches as shown in Figures 6 and 7. At the 900 and 2700 azimuthal locations, the counter bore is approximately 4.64 inches above the top of the J-groove weld. See Figure 8 for additional details.
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B. Blind Zone at 1`o2zle Bottom A blind zone exists along the bottom of each ICI nozzle and varies from approximately 0.2 inch to 0.5 inch. This blind zone occurs due to loss of couplant as the transducers traverse across the bottom end of the nozzle. This problem is further compounded by the configuration of the ICI nozzle bottom which is cut to match the contour of the RPV head. See Figures 3, 4, and 5 for additional information.
IV. PROPOSED ALTERNATIVE AND BASIS FOR USE Paragraph IV.C(1)(b)(i) of the Order requires that the UT inspection of each RPV head penetration nozzle encompass 'from two (2) inches above the J-groove weld to the bottom of the nozzle." Due to the reasons stated above, Entergy requests relaxation from this requirement for ANO-2 ICI nozzles and proposes a three-step alternative, which involves the use of analysis, UT examination, and surface examination techniques, as described below.
A. Proposed Alternative
: 1. Analysis An analysis has been performed to ensure that an unidentified surface crack in the counterbore blind zone will extend along the length, into an inspectable region, at least one operating cycle prior to growing through the thickness. The analysis, based on design information and actual UT data obtained during the previous refueling outage, is discussed in further detail in Section IV.B.1 below and is fully documented in Engineering Report M-EP-2003-003, Rev. 0 (Enclosure 2). Based on this analysis, no examination of the counterbore region is required.
: 2. UT Examination The ID of each ICI nozzle (i.e., nozzle base material) shall be ultrasonically examined in accordance with Section IV.C(1 )(b)(i) except as follows:
a) For the area of the counterbore blind zone that falls within two (2) inches above the J-groove weld on the upper hillside; and b) For the area of the nozzle end blind zone.
In addition to the UT examination, an assessment to determine if leakage has occurred into the interference fit zone will be performed, as currently specified in Section IV.C(1 )(b)(i) of the Order.
: 3. Augmented Inspection Plan Because meaningful UT data cannot be collected at the bottom of the ICI nozzle, Entergy will augment the UT inspection with a surface examination of the nozzle ID, OD, and J-groove weld area that falls within the blind zone at the nozzle end. As previously mentioned, the nozzle end blind zone varies in length from 0.2 inch to 0.5 inch Page 3 of 19
 
depending bri probe location (see Figures 3, 4 and 5). This augmented inspection plan will be performed on a sample of the ICI nozzle population. The examination methods and sampling plan are described below.
a) Examination Method The augmented inspections will be performed using the manual PT examination method as the primary technique.              Because the PT examination method cannot distinguish acceptable fabrication discontinuities from primary water stress corrosion cracking (PWSCC), PT indications are conservatively assumed to be PWSCC. Under these conditions, PT indications will be investigated by either.
(i)  Supplemental inspection using the ECT examination method; or (ii)  Grinding followed by additional PT examinations.
b) Sampling Plan Entergy will select two (2) of the eight ICI nozzles for augmented inspection. The size of the sampling population may increase based on the following criteria:
(i)  If PWSCC is identified in any ICI nozzle during the performance of the UT inspections, that nozzle will be included in the augmented inspection scope.
(ii)  If PWSCC is confirmed in an ICI nozzle during the performance of the augmented inspections, the remaining ICI nozzles will be added to the augmented inspection scope.
Entergy will provide in the 60-day report for ANO-2, as required by the Order, specific inspection information including the type, extent, and results of inspections and results of inspections performed on the ICI nozzles.
B. Basis for Use
: 1. Analysis The extent of the proposed alternative is established by an engineering evaluation comprised of a finite element stress analysis and fracture mechanics model of the ICI nozzle counterbore blind zone. The purpose of this engineering evaluation is to ensure that an unidentified surface crack in the counterbore blind zone will extend along the length, into an inspectable region, at least one operating cycle prior to growing through the thickness.
Only an ID fracture mechanic analysis is required for this justification. This Is due to the fact that the OD surface of the nozzle is not in a reactor coolant environment which promotes PWSCC. The UT exam discussed in Section IV.A.1 confirms there is no OD crack on the nozzle creating a leak path, and the triple point examination confirms there is no leak path though the weld.
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Additionally the leak assessment examination above the weld confirms there is no leak through the weld butter. Hence, PWSCC can only be initiated on the ID surface of the counterbore blind zone. Both circumferential and axial cracks were evaluated; however, detailed fracture mechanics of the circumferential crack was not required because the ID and % thickness axial stress is predominately compressive in the 820 arc being evaluated.
The finite element-based stress analysis and the fracture mechanics evaluation are described below. For additional details pertaining to the engineering evaluation and its conclusions, see Engineering Report M-EP-2003-003, Rev. 0 (Enclosure 2).
a)  Stress Analysis A finite element-based stress analysis representing the eight (8)ANO-2 ICI nozzle penetrations was performed by Dominion Engineering, Inc. (DEI) using best estimates of as-built geometries based on previous UT and available design information, and the material yield strength of the eight nozzles from the same heat number. General dimensions for reactor head and ICI nozzles were obtained from Westinghouse/Combustion Engineering (CE) design drawings and documents. To accommodate a potentially longer downhill side fillet weld as shown in the UT data, the fillet weld dimension in the model was increased from 3/16 inch to 7/16 inch.
The counterbore was not explicitly modeled; rather, the elements were angled and tapered to transition from the 4.750-inch ID below the counterbore to the 4.625-inch ID above the counterbore. The actual counterbore is 0.25 inch high with a 1-to-4 (depth-to-length) taper; this transition precludes the need to evaluate stress concentrations such as required per ASME Section 11I, Subsection NB-3680 for transitions with less than a 1-to-3 transition.
Consideration of a Circumferential Crack in the Counterbore Blind Zone Entergy considered a circumferential crack located on the ID surface, spanning the full 820 circumferential extent of the blind zone (see Figure 6).
A circumferential crack, if propagated through-wall, could potentially lead to ejection of the associated nozzle. For this circumferential crack growth to occur, both the PWSCC environment and a conducive tensile axial stress field must exist. The DEl axial stress finite element analysis data were reviewed for locations at the upper hillside and those angles spanning 450 on either side of the 1800 azimuth (1350 and 157.50) that would encompass the circumferential extent of the counterbore blind zone.
From previous fracture mechanics evaluations for the CEDM nozzles, it was shown that no crack growth will occur for an applied hoop stress of 10 ksi; that is, the resulting applied stress intensity factor is below the threshold value of 8.19 ksi 4G needed for crack growth.
The stresses at the ID and at the 25% through-wall location, covering a 900 circumferential span around the ICI nozzle, are predominantly compressive. Hence, the initiation of a circumferential crack in the Page 5 of 19
 
counterbore blind zone is precluded and presents no safety significance by not inspecting this region.
b) Fracture Mechanics Evaluation Safety analyses performed by the EPRI Materials Reliability Program (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 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.
Several crack sizes were evaluated in the counterbore blind zone on the upper hillside. Crack aspect ratios typical of ASME Section Xl (6-to-1 and 10-to-1 length-to-depth) and another aspect ratio emphasizing deep flaws (4-to-1) were evaluated to maximize through-wall growth while accommodating growth along the length of the ICI nozzle. These evaluations also considered a case in which the half-length of the crack was less than the remaining length needed to grow to the end of the blind zone. Summaries of crack depths and lengths used to evaluate the counterbore blind zone are presented in the table below.
Crack                              Desr iption                        Crack::,  Crack.
i::Case IDi:.-::i;;:.                                                    Depth.. Length
: 5; t .:;:f :. i. l!:';i V(inch)    (Inch)
I        Aspect ratio of 6-to-1 with depth initially 25% through-    0.1        .06 wall 2        Aspect ratio of 10-to-1 with an initial length of 0.4 inch  0.04        0.4 3        Aspect ratio of 4-to1 with depth Initially 25% through-      0.1        0.4 wall 4        Aspect ratio of 6-to-I with the crack spanning the length  0.147      0.88 of the blind zone In the PWSCC crack growth evaluation, the acceptability of the crack is determined by its extension outside the counterbore blind zone to a detectable length in greater than one operating cycle prior to growing through-wall. The minimum detectable crack was assumed to be 0.04 inch (2 mm) based on EPRI demonstrations. For conservatism, the detectability threshold was set at 0.16 inch. That is, a crack contained within the Page 6 of 19
 
counterbore blind zone must propagate along the length of the nozzle a distance measured from the tip of the crack to the edge of the blind zone plus an axial distance of 0.16 inch to ensure proper detection. The results of the crack growth evaluations are presented in the table below.
iCrack      Propagation Length            Time to Reach            Time to Grow Case ID            (~inch)            Prpgton'Length              Through-Wall (years)                  (years) 1                  0.3                    10.94                    13.74 2                  0.4                      >40                      >40 3                  0.4                    20.98                    23.34 4                0.16                      3.83                      6.99 A review of the stress output shows the through thickness and axial distribution of hoop stresses on the lower hillside (00 azimuth) of the nozzle to be higher than that of the upper hillside for the same relative distance above the J-groove weld. That is, for the length of the nozzle 1.08 inches above the top of the weld on the lower hillside, plus a region 0.88 inch beyond that (equivalent to the span of the counterbore blind zone on the upper hillside), the stress distribution was generally higher. However, the counterbore blind zone on the lower hillside is 9.96 inches above the top of the J-groove weld and is, therefore, not subject to the requirements of the Order. Because of the higher stress field, it is reasonable to presume that under equivalent conditions, a crack could initiate in this equivalent lower hillside area more readily than on the upper hillside. However, this region is inspectable via UT; thus, the most susceptible location based on stresses is addressed by the current inspection coverage.
c) Conclusions The engineering evaluation supports the following conclusions:
(i)    The upper hillside (1800 azimuth) of the ICI nozzle above the top of the J-groove weld possesses the highest hoop stresses in the vicinity of the counterbore for which a UT blind zone exists.
(ii)  The conservatisms used in the analysis (pressure applied to crack faces and high crack length-to-depth aspect ratio) provide assurance that an undetected crack in the counterbore blind zone on the upper hillside will not grow through-wall prior to extending out of the blind zone into an inspectable region in less than one operating cycle.
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(iii) The area above the J-groove weld on the lower hillside of the ICI nozzle is in a higher stress field than the area on the upper hillside.
Because of this, the lower hillside area is more susceptible to crack initiation than the upper hillside. However, this area is inspected by UT.
(iv) The ID surface crack on the upper hillside either did not show any potential for crack growth, or the growth in the axial direction reached a detectable area of the nozzle in at least one operating cycle prior to the crack growing through-wall. Hence, an ID surface crack in a region above the J-groove weld on the upper hillside is not significant in that it does not affect nozzle integrity.
(v)    No potential exists for an ID circumferential crack to be located in the counterbore blind zone due to the predominant compressive axial stress field spanning 450 on either side of the upper hillside of the ICI nozzle.
This analysis incorporates a crack-growth formula different from that described in Footnote 1 of the Order, as provided in EPRI Report MRP-55.
Entergy is aware that the NRC staff has not yet completed a final assessment regarding the acceptability of the EPRI report. If the NRC staff finds that the crack-growth formula in MRP-55 is unacceptable, Entergy shall revise its analysis that justifies relaxation of the Order within 30 days after the NRC informs Entergy of an NRC-approved crack-growth formula.
If Entergy's revised analysis shows that the crack growth acceptance criteria are exceeded prior to the end of Operating Cycle 17 (following the upcoming refueling outage), Entergy will, within 72 hours, submit to the NRC written justification for continued operation. If the revised analysis shows that the crack growth acceptance criteria are exceeded during the subsequent operating cycle, Entergy shall, within 30 days, submit the revised analysis for NRC review. If the revised analysis shows that the crack growth acceptance criteria are not exceeded during either Operating Cycle 17 or the subsequent operating cycle, Entergy shall, within 30 days, submit a letter to the NRC confirming that its analysis has been revised.
Any future crack-growth analyses performed for Operating Cycle 17 and future cycles for RPV head penetrations will be based on an NRC-acceptable crack growth rate formula.
: 2. UT Examination The UT inspection probe to be used to inspect the ANO-2 ICI nozzles consists of seven (7) individual transducers. The configuration of the probe has been optimized for maximum coverage. UT inspection of ICI nozzles will be performed using a combination of time-of-flight diffraction (TOFD) and standard 00 pulse-echo techniques. The TOFD approach utilizes two pairs of 0.250-inch diameter, 550 refracted-longitudinal wave transducers aimed at each other.
One of the transducers transmits sound Into the inspection volume while the other receives the reflected and diffracted signals as they interact with the material. There will be one TOFD pair scanning in the axial direction of the penetration nozzle tube and one TOFD pair scanning in the circumferential Page 8 of 19
 
direction of the tube. The TOFD technique is primarily used to detect and characterize planar-type defects within the full volume of the tube.
The standard 0° pulse-echo ultrasonic approach utilizes one 0.250-inch diameter straight beam transducer. The 0° technique is used to:
* Plot the penetration nozzle OD location and J-groove weld location,
* Locate and size any laminar-type defects that may be encountered, and Monitor the back-wall signal response to detect leakage that may occur in the interference regions of the RPV head penetration.
The UT inspection procedures and techniques to be utilized at ANO-2 have been satisfactorily demonstrated under the EPRI Materials Reliability Program (MRP) Inspection Demonstration Program.
: 3. Auwmented Inspection Plan Augmenting UT examination of the nozzle base material with surface examination ensures the ICI nozzle is adequately examined to determine its condition. The augmented inspection plan will only be used for those portions of the nozzles that could not be inspected by UT or excluded by analysis. The bases for the examination method and sampling plan are described below.
a) Examination Method The augmented inspections will be performed using the PT examination method as the primary technique. Entergy believes the use of PT to augment UT is acceptable for ensuring that the required areas not excluded by analysis are inspected. The Order recognizes and allows the use of PT as acceptable for evaluating the condition of nozzle surfaces.
Augmenting the UT examination of the nozzle base material with PT ensures the nozzle is adequately examined to determine its condition.
As discussed in Section IV.A.3.a), above, Entergy may use ECT to investigate indications identified by PT. ECT is also an acceptable technique for evaluating such indications. As with PT, the Order recognizes and allows the use of ECT as acceptable for evaluating the condition of nozzles and associated J-groove welds.
b) Sampling Plan Entergy believes that to require examination of every ICI nozzle rather than inspecting in accordance with the sampling plan would impose hardships without a compensating increase in the level of quality and safety. The basis for this position is summarized below-(i)  Low Probability of PWSCC The likelihood of finding a PWSCC crack in an ANO-2 ICI nozzle is low based on available industry data. Specifically:
Page 9 of 19
 
(1) Each ICI nozzle at ANO-2 was manufactured by Huntington Alloy using heat number NX2696 of SB-166, N06600. For this particular heat of material, there is no known industry history of PWSCC.
(2) High yield strength materials are more susceptible to PWSCC.
The lowest yield strength for nozzle material known to have cracked is 37 ksi. The yield strength of the ANO-2 ICI nozzles is 31.5 ksi, which is significantly lower.
(3) While the industry has identified PWSCC in control element drive mechanism (CEDM) nozzles, there is no industry history of PWSCC in ICI nozzles.
(ii)  High Personnel Dose As stated above, augmented inspections will be performed using the PT examination method. Entergy estimates personnel performing PT on all eight ICI nozzles would receive a radiation dose ranging between 2.4 and 4.5 man-REM.
The preferred method of investigating rounded PT indications in weld metal is supplemental inspection using the ECT examination method.
The ECT equipment that would be used to perform these supplemental inspections is being developed and has not been field proven. However, based on similar Inspections, Entergy estimates performing supplemental ECT on all eight ICI nozzles will involve a radiation exposure of approximately I man-REM. The dose estimate for performing PT with supplemental ECT on all eight nozzles would be approximately 3.4 to 5.5 man-REM.
Entergy has not estimated the radiation dose associated with grinding activities to investigate rounded indications. However, we expect the dose to be higher than that estimated for performing PT with supplemental ECT because of extended personnel stay-time under the RPV head involved with grinding activities.
(iii) Adverse Impact to Nozzle Base Material As discussed above, the PT examination method cannot distinguish acceptable rounded indications from the surface extension of a PWSCC crack on a weld. Therefore, PT indications may be explored by grinding if the ECT process is not available. Because grinding of the weld metal and/or nozzle base material causes localized work-hardening, ground areas of the nozzle and weld will experience an increased susceptibility to PWSCC.
In summary, there is no industry history of PWSCC in ICI nozzles.
Furthermore, UT inspections of nozzle regions with the higher stresses, which are believed to be more susceptible to PWSCC, are being inspected volumetrically. UT inspection of the more susceptible regions combined with the surface examinations of the nozzle end blind zone, no industry Page 10 of 19
 
experience of PWSCC, and the low susceptible ICI material properties provides assurance that the proposed sample plan will provide an acceptable level of quality and safety.
V. CONCLUSION Section IV.F of NRC Order EA-03-009 states:
uLicensees proposing to deviate from the requirements of this Order shall seek relaxation of this Order pursuant to the procedure specified below. The Director, Office of Nuclear Reactor Regulation, may, in writing, relax or rescind any of the above conditions upon demonstration by the Licensee of good cause. A request for relaxation regarding inspection of specific nozzles shall also address the following criteria:
(1) The proposed altemative(s) for inspection of specific nozzles will provide an acceptable level of quality and safety, or (2) Compliance with this Order for specific nozzles would result in hardship or unusual difficulty without a compensating increase in the level of quality and safety."
Section IV.C(1)(b) of the Order establishes a minimum set of RPV head penetration nozzle inspection requirements to identify the presence of cracks in penetration nozzles that could lead to leakage of reactor coolant and wastage of RPV head material.
Entergy believes the proposed altemative, described in Section IV, provides an acceptable level of quality and safety by utilizing inspections and supplemental analysis to determine the condition of the ANO-2 ICI nozzles. The technical basis for the supplemental analysis of the proposed alternative is documented in Engineering Report M-EP-2003-003, Rev. 0, which is contained in Enclosure 2 of this letter. Therefore, Entergy requests that the proposed alternative be authorized pursuant to Section IV.F of the Order.
Page 11 of 19
 
900 1          9    9  j      j        9  Q) va          (D CJ@                S G a
      \a 3S                            8/^lea@
        \VentV          )i          i  9 00 FIGURE 1 PENETRATION LOCATIONS IN THE ANO-2 RPV HEAD Page 12 of 19
 
ICl Nozzle Z/~
terbore RPV Head J-Groove Weld FIGURE 2 ICI NOZZLE CONFIGURATION Page 13 of 19
 
The blind zone for the arc-shooting transducers begins at 0.200" above the radius at the IDof the nozzle.
VIEW:
Looking radially outward from the ID of the tube.
The distance betvveen the UT centerline and theetop of the ID tip radius, at the C0° lower hillside point of the nozzlel would be 0.200'. This woul Idbe the UT blind zone at that Doint.
FIGURE 3 UT INSPECTION PROBE END OF NOZZLE - LOWER HILLSIDE POSITION Page 14 of 19
 
The blind zone for the circ-shooting transducers begins at 0.200' above the radius at the ID of the nozzle, at this point.
VIEW:
Looking radially outward from the ID of the tube, at the high hillside point
                                                    \ The distance byetween the UT centerline Eand the top of the ID tip radiu s, at the 1800 upper hillside rpoint of the nozzle would ble 0.200". This would be the UIT blind zone at that point.
FIGURE 4 UT INSPECTION PROBE END OF NOZZLE- UPPER HILLSIDE POSITION Page 15 of 19
 
VIEW:
Looking radially outward from the ID of the tube, at the 900 or 2700 side hillside point The distance between the UT centerline and the nearest ID tip radius, at the
                                              -iiiIIjA
        /~~    ~~~~~OOno    -- A      7nO I
flu-
                            =Wsu-ulu      o        111 0llbU:
points of the nozzle would be 0.480'. This would be the UT blind zone at that point FIGURE 5 UT INSPECTION PROBE END OF NOZZLE - SIDE VIEW @ 900 and 2700 Page 16 of 19
 
The distance between the point of UT probe lift off from the nozzle wall and the point at which the probe can ride smoothly above the counterbore can be as long as 0.880.
0 I:
The distance between where the UT transducers lift off from the nozzle wall and the 0
top of the J-groove weld can be as short as 1.080' at the upper hillside.
I The counterbore limits the ability to ultrasonically scan 2 inches above the J-weld for a circumferential distance of as much as 820 on the ICI nozzles.
FIGURE 6 COUNTERBORE - UPPER HILLSIDE POSITION Page 17 of 19
 
The distance between the point of UT probe lift off from the nozzle wall and the point at which the probe can ride smoothly above the counterbore can be as long as 0.8801.
The distance between the point of UT transducer lift-off from the nozzle wall and the top of the J-groove weld can be as short as 9.960W at the lower r
hillside. Thus, the counterbore does not interfere with the UT probe In this location.
                                /    -L FIGURE 7 COUNTERBORE - LOWER HILLSIDE POSITION Page 18 of 19
 
                                        -7 The distance between the point of UT probe I  .
lift-off and the point at which the probe can ride smoothly above the      I counterbore can be as long as 0.880".
j 3
The distance between UT probe lift-off and the top of the J-groove weld can be as short as 4.640" at the 900 and 2700 positions. Thus, the counterbore does not interfere with the UT probe In these locations.
FIGURE 8 COUNTERBORE @ 90° AND 2700 POSITIONS Page 19 of 19
 
ENCLOSURE 2 CNRO-2003-00035 ENGINEERING REPORT M-EP-2003-003, 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 IN-CORE INSTRUMENTATION (ICI) NOZZLES AT ARKANSAS NUCLEAR ONE UNIT 2
 
Engineering Report No.          M-EP-2003-003        Rev. 00 Page    1      of 35
  ~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 In-Core Instrumentation (ICI) Nozzles at Arkansas Nuclear One Unit 2 Engineering Report Type:
New      0      Revision      0      Deleted    El      Superceded    El Applicable Site(s)
ANO    0R    Echelon      0        GGNS  El        RBS    E        WF3 Report Origin:      0      ENS          Safety-Related:    0    Yes El    Vendor                            El    No Vendor Document No.
Comments:    Attached:
Prepared by:                                                                                  D  Yes Dae1 1 Date:  -Ls31~/O2 El Yes Responsible Eng eer                                  0  No          l No Verified/
Reviewed by:                                                Date: 11VVI ._      13 Yes      E Yes E No        g No Approved by:                                                Date:  z/4*i.        El Yes      E Yes Responsible Supervisor or                                  Ego          [  No Responsible Central Engineering Manager (for multiple site reports only)
 
Enginecring Report M-EP-2003-003 Rev. 00 Page 2 of 35 RECOMMENDATION FOR APPROVAL FORM Comments:    Attached:
                      , C"                            Date:  OL/31/3    E Yes        El Yes nudby
              ?/3/43    --  Responsible  Enoeer                        El No        E No Concurrence:                                          Date:  .42/I      2*Yes r            El Yes Responsil        fgint'ng Manager, ANO                    Ea No Not Applicable Concurrence:                                          Date:              El Yes      El Yes Responsible Engineering Manager, GGNS                      El No        El No Not Applicable Concurrence:                                          Date:  _E            Yes      a  Yes Responsible Engineering Manager, RBS                      El No        a  No Not Applicable Concurrence: -
Date:            a_ Yes      El Yes Responsible Engineering Manager, WF3                        D No        a  No
 
Engineering Report M-EP-2003-003 Rev. 00 Page 3 of 35 Table of Contents Section Title                                                                Page Number Table of Conents                                                            3 List of Attachments                                                        4 List of Tables                                                              4 List of Figures                                                            5 1.0      PURPOSE                                                                    6 2.0      GIVEN CONDITIONS AND KNOWN VALUES                                          8 2.1          ICI Nozzle Material, Operating Conditions, and Geometry              8 2.2          Dimensions of the Welds and Counterbore Areas                        9 2.3          Orientation and Dimensions of UT Blind Zone on the ICI              10 Nozzles 3.0      METHOD OF ANALYSIS                                                        11 3.1          Finite Element Stress Analysis of ANO-2 ICI Nozzles                Ii 3.2          ID Surface Flaw Fracture Mechanics Model                            15 3.3          PWSCC Growth Model                                                  17 3.4          Iterative Mathcad Model for Stress Curve-Fitting and Flaw          18 Growth Evaluation 3.5          Consideration of a Circumferential Flaw in the Un-Inspectable      23 Region 4.0      DISCUSSION AND RESULTS                                                    25 4.1          Discussion                                                          25 4.2          Results of the ID Surface Flaw Evaluation                          26
 
==5.0      CONCLUSION==
S                                                                33
 
==6.0      REFERENCES==
34
 
Engineering Report M-EP-2003-003 Rev. 00 Page 4 of 35 List of Attachments Attachment                        Content of Attachment                            Number of Number                                                                              Pages 1      Design Input Record from ANO-2 for the ICI Nozzles                          4 2      NDE Limitations for ICI Nozzles                                            2 3      Dominion Engineering Inc. Nodal Stress and Coordinate Data                  18 (Including Transmittal E-mails) 4      Mathcad Worksheet for Flaw Case 1: 25% Through-wall Flaw                  42 with an Initial Aspect Ratio of 6-to-I (Length-to-Depth) Centered in the Blind zone 5      Mathcad Worksheet for Flaw Case 2: 0.4 Inch Long with an                  42 Initial Aspect Ratio of 1O-to-I (Length-to-Depth) Centered in the Blind zone 6      Mathcad Worksheet for Flaw Case 3: 25% Through-wall Flaw                  42 with a Initial Aspect Ratio of 4-to- I (Length-to-Depth) Centered in the Blind zone 7      Mathcad Worksheet for Flaw Case 4: A Flaw Spanning the Entire              42 0.88-Inch Length of the Blind zone with an Initial 6-to- I Aspect Ratio (Length-to-Depth)
Total Pages of Attachments: 192 List of Tables
--Table Number                                  Title                            Page Number I            Dimensions from Tangent Line Datum Plane to specified              9 locations on the ICI Nozzle 2            Summary of flaw depths and lengths used to evaluate                26 the blind zone on the uphill side above the top of the weld (Blind zone begins a distance 1.08 inches above the top of the weld and extends 0.88 inch) 3            Results of PWSCC flaw growth evaluations in the                    27 length and depth directions
 
Engineering Report M-EP-2003-003 Rev. 00 Page 5 of 35 List of Figures Figure                                    Title                                  Page Number                                                                          Number I  ANO-2 ICI Geometry from the Bottom of the Nozzle                            8 2  Measured ICI Nozzle Locations from Tangent Line Datum                        9 3  Counterbore at the Uphill Side (1800) Position                                0 4  Hoop stress contours for the ICI nozzle. High tensile stresses occur        13 in the weld and adjacent tube material 5  Hoop stress contours in the upper portion (closer to the intersection        13 with the reactor head) of the ICI nozzle 6  Close-up of the uphill side (1800 azimuth) hoop stress in the vicinity      14 of the J-groove weld and counterbore region 7  SICF shown as a function of normalized crack depth for the "a-tip"          16 (left figure) and the "c-tip" (right figure) 8  ID Axial Stress Distribution Spanning 450 on Either Side (900 Total)        23 of Uphill 9  25% Through-Wall Position Axial Stress Distribution Spanning 450            24 on Either Side (900 Total) of Uphill 10  Flaw Case I-Depth Growth (top) and Length Growth (bottom)                  28 versus number of operating years 11  Flaw Case 2-Depth Growth (top) and Length Growth (bottom)                  29 versus number of operating years 12  Flaw Case 3-Depth Growth (top) and Length Growth (bottom)                  30 versus number of operating years 13  Flaw Case 4-Depth Growth (top) and Length Growth (bottom)                  31 versus number of operating years
 
Engineering Report M-EP-2003-003 Rev. 00 Page 6 of 35 1.0  PURPOSE The US Nuclear Regulatory Commission (NRC) issued Order EA-03-009 [Ref. 1], which modified licenses, requiring inspection of all Control Element Drive Mechanism (CEDM), In-Core Instrumentation (ICI), and vent penetration nozzles in the reactor vessel head. Paragraph IV.C. l.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.
The Combustion Engineering (CE) design for the ICI nozzles consists of a 5.563-inch outside diameter (OD) nozzle, inserted into the reactor vessel head at a 56.2833° angle with the horizontal, with the portion of the nozzle extending below the inside surface of the vessel cut to the same angle. The inside diameter (ID) of the ICI nozzle is counter-bored from a diameter of 4.625 inches to 4.750 inches at a height of 1.377 inches above the top of the J-groove weld on the uphill side (180°azimuth), and approximately 10.092 inches from top of the J-groove weld on the downhill side (0° azimuth), based on design drawings. (These dimensions are taken from Attachment I and shown in Figures I and 2.) This counterbore region of the nozzle above the J-groove weld represents a challenge to interrogate the nozzle with Ultrasonic Testing (UT). Figures I and 2 show the typical layout and geometry of the ICI nozzle, while Figure 3 schematically depicts the un-inspectable regions with UT due to the configuration of the counterbore. This un-inspectable region, measuring 0.88 inch in axial length and extending circumferentially around the ID for 820, above the top of the J-weld on the uphill side (as shown in Figure 3), is defined as the UT Blind zone (hereafter referred to as the blind zone). Due to the offset distance between the low hill side (00 azimuth) and high hillside (180°) of the nozzle at the attachment J-groove weld, the blind zone is closer to weld at the high hillside than it is on the low hillside. On the high (or uphill) side, the distance from the top of the J-groove weld to the bottom of the blind zone is 1.08 inches (Figure 3),
whereas the same measurement on the downhill and mid-plane locations are 9.96 inches and 4.06 inches, respectively, a distance outside the requirements of the Order. Thus, only a small arc length of the nozzle (820, from Attachment 2 and Figure 3) above the top of the weld on the uphill side cannot be examined with UT The unexamined region of the ICI nozzles in the counterbore region above the J-weld provides a location for surface flaws to exist with the potential to grow through the thickness of the nozzle prior to extending beyond the limits of the blind zone, into a detectable region. This is especially a concern on the uphill side of the nozzle, where the blind zone is only 1.08 inches from the top of the weld and in an area subject to the accompanying high stress field of the J-weld. An ID surface flaw could exist in this 0.88 inch-long blind zone.
In order to exclude the blind zone areas above the weld in the counterbore region 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 [Ref. I].
 
Engineering Report M-EP-2003-003 Rev. 00 Page 7of 35 The purpose of this engineering report is to ensure that an unidentified surface flaw in the blind zone will extend along the length, into an inspectable region, at least one operating cycle prior to growing through the thickness. Only an ID fracture mechanic analysis is required for this justification. This is due to the fact that the OD surface of the nozzle is not in a reactor coolant environment which promotes PWSCC. The UT exam confirms there is no OD flaw on the nozzle creating a leak path, and the triple point examination confirms there is no leak path though the weld. Additionally the leak assessment examination above the weld confirms there is no leak through the butter. Hence, PWSCC can only be initiated on the ID surface of the blind zone. ID surface axial and circumferential flaws will be considered in the analysis.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 8 of 35 2.0 GIVEN CONDITIONS AND KNOWN VALUES 2.1 ICI Nozzle Material, Operating Conditions, and Geometry:
Pipe Material: SB-167, Gr. 70 [Ref. 2a]
Pipe Outside Diameter:
Do = 5.563 in. +0.000/-0.001 in. [Ref. 2a]
Pipe Inside Diameter, above counterbore:
Di, = 4.625 in. +/- 0.01 in. [Ref. 2b]
Pipe Inside Diameter, below counterbore:
Di2 = 4.750 in. +/- 0.01 in. [Ref. 2b]
Operating Pressure = 2235 psi [Ref. 3]
Operating Temperature = 604'F. Reference 4 gives a value of 594.80 F, but 604'F will conservatively be used.
Figure 1: ANO-2 ICI Geometry from the Bottom of the Nozzle (from Ref. 2a) w X~    ~~                              /aII LzTZ    POW        f
                %41SM!W - iQS
 
Engineering Report M-EP-2003-003 Rev. 00 Page 9 of 35 2.2 Dimensions of the Welds and Counterbore Areas:
The elevations and heights of the ICI nozzles and weld positions were obtained from design drawings and transmitted in a Design Input Record from ANO (shown Attachment 1). The figure and table below provide a summary of these inputs:
Figure 2: Measured ICI Nozzle Locations from Tangent Line Datum Top of counter bore                            J Bottom of counter bore                      W Top of J-weld at 180 deqrees C -            Claddlinci at 180 Nozzle bottom at OD at 180 Nozzle bottom at IDat 180
_                                      NoZ bot at ID at 0 4 F~~~~~~~~I-
                              . o .      OK      ~~~~~Noz bot OD at 0e3 I
                                                          -Caadding at 0 deg e-~
Top J-weld at 0 deg -3 Tangent line dadum plane -
Table 1: Dimensions from Tangent Line Datum Plane to specified locations on the ICI Nozzle Dimension from the tangent line datum plane to:                      ANO-2      W-3 (inches)  (inches)
Top of counter bore transition                                      48.625    55.094 Bottom of counter bore transition                                    48.375    54.844 Top of J-weld at the 180 degree (high hill side)azimuth location    46.998    53.440 Intersection of the projected cladding surface and the nozzle OD    46.211    52.655 at the 180 degree (high hill side) azimuth location Bottom (sharp comer) of the nozzle at the OD surface at the 180      44.211    50.618 degree (high hill side) azimuth location Bottom (sharp comer) of the nozzle at the ID surface at the 180      43.602    50.031 degree (high hill side) azimuth location Top of J-weld at the 0 degree (low hill side)azimuth location      38.283    45.008 Intersection of the projected cladding surface and the nozzle OD    37.875    44.589 at the 0 degree (low hill side) azimuth location Bottom (sharp comer) of the nozzle at the ID surface at the 0        36A84      43.180 degree (low hill side) azimuth location Bottom (sharp corner) of the nozzle at the OD surface at the 0      35.875    42.594 degree (low hill side) azimuth location
 
Engineering Report M-EP-2003-003 Rev. 00 Page lO of 35 2.3  Orientation and Dimensions of UT Blind Zone on the ICI Nozzles Figure 3: Counterbore at the Uphill Side (1800) Position-the UT Blind zone starting point is 1.080 inches above the top of weld. The Axial length of the UT Blind zone is 0.880 inch. The arc length of limitation for 2" scanning above the weld is 820 [shown in Attachment 2J The distance between the point at which the sled starts to lift off and the point at which it can ride smoothly above the counterbore can be as long as 0.880 in.
The distance between where the UT transducers lift-off and can no longer communicate and the top of the j-weld can be as short as 1.080 in. at the high hillside of the ICI nozzles.
                                                        .~.......
Counterborz                      fth[
l The counterbore limits the ability to ultrasonically scan 2.0 inches above the J-weld for a circumferential distance of as much as 820on the ICI nozzles.
 
Engineering Report M-EP-2003-003 Rev. 00 Page II of 35 3.0 METHOD OF ANALYSIS The analysis used to determine the impact of not examining the blind zone of the ICI nozzle above the top of the weld in the counterbore region on the uphill side consists of a detailed finite element stress analysis combined with an ID surface flaw fracture mechanics model. The fracture mechanics model evaluates an ID-initiated part through-wall axial crack in a cylinder, located in the 0.88-inch blind zone region above the top of the weld on the uphill side of the ICI nozzle. Additional consideration of an ID circumferential surface flaw is provided in Section 3.5 The following sections provide details of the finite element stress analysis and the accompanying fracture mechanics evaluation.
3.1  Finite Element Stress Analysis of ANO-2 ICI Nozzles A finite element-based stress analysis representing the eight (8) ANO-2 ICI penetrations was performed by Dominion Engineering Inc. (DEI) using best estimates of as-built geometries based on previous UT and available design information, and the material yield strength of the eight nozzles from the same heat number. General dimensions for reactor head and ICI nozzles were obtained from Westinghouse/CE design drawings and documents. To accommodate a potentially longer downhill side fillet weld as shown in the UT data, the fillet weld dimension in the model was increased from 3/16 inch to 7/16 inch. The counterbore was not explicitly modeled due to computational resource restraints and modeling simplifications; rather, the elements were angled and tapered to transition from the 4.750-inch ID below the counterbore to the 4.625-inch ID above the counterbore.
The actual counterbore is 0.25 inch high with a 1-to-4 (depth-to-length) taper; this transition precludes the need to evaluate stress concentrations such as required per ASME Section 111, subsection NB-3680 [Ref. 5] for transitions with less than a 1-to-3 transition.
The finite element analysis (FEA) modeling steps using the above geometry data and assumptions to obtain the necessary stress (residual+operating) distribution in the ICI nozzle followed the process and methodology described in Reference 6a.
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. As referenced above, one row of angled elements represented the transition from the 4.750-inch ID below the counterbore to the 4.625-inch ID above the counterbore.
2.) The ICI nozzle material, possessing the same yield strength for all nozzles, resulting from a single heat of material, was modeled with a monotonic stress-strain curve. The yield strength of the nozzles was referenced to the room temperature yield strength of the stress strain curve described in Reference 6a.
Temperature-dependent stress-strain curves needed to model the nonlinear
 
Engineering Report M-EP-2003-003 Rev. 00 Page 12 of 35 welding process were obtained by indexing the temperature-dependent drop of the 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 [Ref. 6b]. 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 [Ref. 6b]. This was borne out by the comparison between the analysis-based residual stress distribution and that obtained from experiments
[Ref. 6c].
4.) The weld is simulated by two passes based on studies presented in Reference 6a.
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.
The stress contours for the ICI nozzle obtained from the finite element analysis are presented in Figures 4 through 6. The hoop stress contour color scheme is as follows:
Dark Navy blue-+ from Minimum (Compression) to -10 ksi Royal blue -+ from -10 to 0 ksi Light blue -e from 0 to 10 ksi Light green -+ from 10 to 20 ksi Green -4 from 20 to 30 ksi Yellow green -e from 30 to 40 ksi
            -  from 40 to 50 ksi Red - from 50 to 100 ksi
 
Engineering Report M-EP-2003-003 Rev. 00 Page 13 of 35 Figure 4: Hoop stress contours for the ICI nozzle. High tensile stresses occur in the weld and adjacent tube material.
Figure 5: Hoop stress contours in the upper portion (closer to the intersection with the reactor head) of the ICI nozzle
 
Engineering Report M-EP-2003-003 Rev. 00 Page 14of 35 Figure 6: Close-up of the uphill side (180° azimuth) hoop stress in the vicinity of the J-groove weld and counterbore region Row of transition elements simulating the counterbore Red Lines indicate the span of the 0.88-inch Blind zone The nodal stresses for locations of interest were provided by DEI and were tabulated in Reference 6d. (This data is also shown in Attachment 3.) The location of the weld bottom at each azimuth was maintained at the node row ending with "601", while the top of the weld at each azimuth was the node row ending with
" 1301". The blind zone is shown on Figure 6 as an overlay to the stress contours.
From the stress data in Attachment 3, the uphill side (the 80000 series nodes from the stress data) hoop stresses are the second highest in the ICI nozzle above the weld; the downhill side above the weld has higher hoop stresses, and these will be addressed in Section 4.2. Additionally, axial stresses used to evaluate circumferentially flaws were tabulated in Reference 6e and contained in Attachment
: 3. These stresses and the potential of circumferential flaws in the blind zone will be discussed in more detail in Section 3.5.
The nodal stress data from the DEI analyses are imported into the respective Mathcad worksheet (discussed later) for further processing to obtain the pertinent stress distributions required for the fracture mechanics analysis described in Section 3.2. Additional processing of the nodal stress data is described in Section 3.4.2.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 15 of 35 3.2 ID Surface Flaw Fracture Mechanics Model The model used to evaluate an ID surface flaw contained in the 0.88-inch Blind zone above the top of the weld is described in detail in Reference 7, and was originally presented in a NASA Publication, Reference 8. This model evaluates an axial, part through-wall flaw on the ID surface of a cylinder, subject to an arbitrary stress distribution (up to a cubic polynomial fit). This model is valid for a ratio of mean radius (Rmean)-to-thickness (t) between 1.0 and 300. Since the ICI nozzle has Rm/t equal to 6.4, this model is considered applicable.
The fracture mechanics model [Ref. 8] gives the equation for the stress intensity factor (SIF) for both deepest point of the crack and the tip of the flaw along the surface, as follows:
K    =(      a)
* C    yiGD        for the SIF at the deepest point of the flaw K, = (    C) * (afG        )    for the SIF at the tip of the flaw on the surface where:
K1 is the applied Stress Intensity Factor, or SIF { ksi,%/-Y }
Q = Crack shape factor; defined as 1.65 Q =1+1.464.      a      when a/c < 1.0 and, Q = 1+1.464 - (          when a/c > 1.0 a = Crack depth {inch}
c = Crack half flaw length {inch}
    <i = Coefficients of the stress polynomial describing the hoop stress variation through the crack depth. Describes the power loading on the crack face.
Ga i =  Stress Intensity Correction Factors (SICF) for the deepest point, which are provided in tables in Reference 8.
Ge = Stress Intensity Correction Factors (SICF) for the surface tip, which are provided in tables in Reference 8.
In Reference 3, SICFs are 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
 
Engineering Report M-EP-2003-003 Rev. 00 Page 16of 35 internal (ID) and external (OD) surface cracks. In addition, the values are provided in association with the Rm/t ratio, a/c ratio (flaw 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 SICFs from the tables for internal cracks for two different Rm/t ratios and a/c ratios are presented in Figure 7 below.
Figure 7: 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 Rm/t is essential to provide a reasonably accurate estimate of the SIF "c-Tip" uniform Coefficients
  ,2.73.9                                                      j781~
2
. Ml Xm 0I-
. m3 C) W3 0-E m5                                                        6 "5 E    .6                                                    2w"6
;5-
    ,1 003
                                                                ,0.577 a0~                      x a/tratio                                A                      ~~~~~x
            -  Rt =2&a/c =0.2
            -  RI=2&a/c =0.4                                          -  R/T =2& a/c =.2        atrao
            -  R/it =2&a/c= 1.0                                      -  R/t-2&a/c- i
            -  R/t4&a/c =0.2                                          -  Rit =4& a/c =I.
            -  R/t=4&a/c=0.4
            -  R/t=4& a/c= 1.0                                        - . Rit=4  a/=I 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 curve-fitting polynomial prior to performing an interpolation to obtain the specific value. This aspect is discussed in further detail below;
 
Engineering Report M-EP-2003-003 Rev. 00 Page 17 of 35 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. This SIF is the critical input to determine the rate of PWSCC growth in the ICI nozzle. The growth model is discussed in Section 3.3.
3.3 PWSCC Growth Model To evaluate the potential for crack growth due to PWSCC, the crack growth rate equation from EPRI Report MRP-55 [Ref. 9] was used. The crack growth rate as a function of the SIF with a correction for temperature effects is given as [Ref. 9]:
da      FQg
                          = exp  -  -    -        a-(
dt    t      R  (T T f--K-,
Where:
da/dt = crack growth rate at temperature T {meters/second}
Qg = thermal activation energy for crack growth (31.0 kcal/mole}
R= universal gas constant {1.103x10-3 kcalmole-0 R}
T = absolute operating temperature at crack tip (OR}
T = absolute reference temperature for data normalization ( 1076.67 OR}
a = crack growth amplitude of 2.67x 10-12 K = crack tip SIF {MPa.! )
Kth = threshold SIF for crack growth {MPa4 }
J = exponent of 1.16 The above equation represents the seventy-fifth (75th) percentile curve. Since the PWSCC crack growth of interest is in the primary water, this model would provide a reasonably conservative crack growth.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 18of 35 3.4 Iterative Mathcad Model for Stress Curve-Fitting and Flaw Growth Evaluation 3.4.1  Mathcad Worksheet Format The analytical scheme was developed using Mathcad [Ref. 10] which facilitates calculations (including recursive) in a logical manner. Reference 7, Appendix B, provides an annotated version of the ID surface crack worksheet used in the current analysis. In the paragraphs below the general approach used to develop the worksheet is presented. The three (3) parts of the Mathcad worksheet requiring user input is discussed in detail.
The first part of the Mathcad worksheet contains a section of imported FEA stress and elevation data for the ID, OD, and other locations through the thickness of the ICI nozzle. This section highlights the significant difference between the methodology used in Reference 7 for the CEDM nozzle evaluations and the current fracture mechanics evaluation for the counterbore region in the ICI nozzles: the "reversal" of the elevations obtained from the nodal stress and location data from DEI's FEA models.
For the CEDM nozzles, the reference point and "0"-elevation point is the bottom of the nozzle, since the bottom is level. For the ICI models, DEI indexed their data from the lowest part of the nozzle for each azimuth. For example, the ID corner on the uphill side represents the zero 0-elevation; due to the nozzle cut angle, the OD corner is at a higher elevation. DEI provided data for locations and stresses from the bottom to the top of the nozzle (as shown in Attachment 3). The CEDM evaluations and iterative loops considered a surface flaw in the nozzle below the weld growing axially upwards in the length direction. However, for a flaw in the counterbore region above the top of the weld in the ICI nozzles, due to the stress field being much higher axially down toward the weld, the flaw growth would be in the opposite direction. In order to avoid changes to the loop structure used for the CEDM analyses [Ref. 7] and definitions, the elevations referenced from the bottom of the ICI nozzle were modified to reference from the top of the nozzle as given in the FEA output data.
The second part of the worksheet 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 an ID surface crack, three entries are required and these are:
1.) The location of a reference line (for example, the Blind zone location) referenced to the top of the ICI nozzle from the FEA data (not the true top of the ICI nozzle from Reference 2a {Refprojt}.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 19 of 35 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 distance to the top of the weld, measured downward from the nozzle bottom {ElevstDi.,t}.
The third part of each Mathcad worksheet contains the inputs for crack dimensions, tube geometry, internal pressure, years of operation, iteration limit, operating temperature, constants for the PWSCC crack growth parameters, and the flaw geometry. 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 remaining parts of the Mathcad worksheet involving the regression of the stress data and the iterative analysis for flaw growth are discussed in Sections 3.4.2 and 3.4.3, respectively.
3.4.2 Regression Analysis of Axial and Through-Wall Stress Distributions A regression analysis on the FEA stress data is required to obtain the appropriate stress distribution to be used in the determination of the SIF.
Regression (that is, curve-fitting) of the stresses 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 in the nozzle above the weld, starting at the top of the nozzle where it intersects the reactor head, increases in magnitude as the top of the weld is approached. Consequently, if an assumed crack located in the vicinity of the reference line (in the blind zone) 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 lower crack tip to the top of the weld is divided into twenty (20) equal segments.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 20 of 35 3.) The stress distribution in the first segment, below the lower crack tip, is an arithmetic average of the first three initial crack region distributions (the 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 downward, out of the blind zone and toward the top of the weld through the various segments, the applied stress distribution is adjusted accordingly. The small extent of the length between the reference line and the top 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 nozzle thickness and the variation along the length of are individually regressed with a polynomial curve-fit. For the nodal stresses along the length of the nozzle, a fourth-order polynomial was used to fit the stresses in the region of interest (that is, the length of nozzle above the top of the flaw for some reasonable distance and the length below the bottom of the flaw, toward the top of the weld. The distance chosen for the axial curve-fit was evaluated for each set of stresses through the thickness to provide for precision in the area of interest and to avoid either under predicting or highly overshooting the stresses with the resulting polynomial.
Reference 7 provides details on the importance of selecting a limited region for regression. Significant variation in stresses might produce errors in the determination of the SIF, which in turn could lead to an inaccurate estimate in crack growth. 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 top of the nozzle (elevation "0") to an elevation just below the top 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. For the through-thickness stress distribution, a third-order polynomial was used to fit the stresses at each axial elevation. The results of the regression are contained in the Mathcad worksheets in Attachments 4 through 7. From these curves, it is evident that in the regions of interest, the fourth-order regression of the stresses along the length of the ICI nozzle provides an adequate representation of the stress distribution.
In the through-thickness regression, the nozzle thickness was assumed to be equal to the minimum section thickness to simplify application to the fracture mechanics iterative loop; that is, the nozzle below the counterbore with a minimum thickness (factoring in tolerances) of [(5.563-0.001)-
(4.750+0.010)1/2 = 0.401 inch was used. To simplify the computations for the fracture mechanics loop, it was assumed that that thickness of the entire
 
Engineering Report M-EP-2003-003 Rev. 00 Page 21 of 35 nozzle above the weld was 0.401 inch. This is conservative, since the thickness above the counterbore (0.4635 inch), which is 13.5% thicker than the thinner section, has slightly lower stresses (owing to it being further removed from the highly stressed weld region) and a greater thickness through which a similarly sized flaw can propagate. Thus, the five (5) nodal stresses for the thicker section were assumed to be the equivalent nodal stresses for a thinner section in that region. As discussed previously, the l-to-4 taper on the counterbore is sufficient to not incur any stress concentrations in the model; furthermore, the residual stress effects in this region are muted, and the applied stresses from the operating pressure govern above the counterbore around the full circumference, as shown in Figure 5.
Following the determination of the five polynomial equations for the axial distribution of stresses, 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 ID surface crack.
3.4.3 Iterative Analysis to Determine Stress Intensity Correction Factors (SICFs)
For the ID surface crack, the SICF coefficients were incorporated in two data tables. The first table contains the geometry data (Rmft, 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 8 and were subsequently used in Reference 7 for the CEDM nozzle flaw evaluation. The data contained in the two tables were regressed into function statements with an appropriate polynomial order. The data for cylindrical geometries with Rm/t ratios ranging from one (I) 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 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
 
Engineering Report M-EP-2003-003 Rev. 00 Page 22 of 35 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 8.
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 SICF coefficient for the uniform term. Therefore, the crack face is subjected to an additional stress representing the internal pressure.
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. The calculated SlFs were converted to metric units 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 forty (40) years and the number of iterations chosen at eight thousand (8000), the time increment for each crack growth block was approximately forty-four (44) hours. After the calculations were performed, all necessary information (crack growth, SlFs 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.). This loop was annotated in Appendix B of Reference 7 to show the various steps.
Graphical displays of the results for flaw size in the depth direction, flaw growth in the length direction, the total flaw half length, and the SIFs for the number of operating years complete the work sheet. The Mathcad plots are used to determine whether or not the crack in the blind zone will grow through the thickness prior to extending beyond the blind zone and into an inspectable region. Tabular results of this analysis are shown in Table 3 of Section 4.0.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 23 of 35 3.5 Consideration of a Circumferential Flaw in the Un-Inspectable Region With the location of the blind zone above the top of the weld, the safety concerns of a circumferential flaw are significant. A circumferential flaw located on the ID surface, spanning the full 820 circumferential extent of the blind zone (from Figure 3), has the potential to grow through thickness and around the length of the ICI nozzle, thus creating an ejection mechanism leading to a loss of coolant accident.
For this circumferential flaw growth to occur, both the PWSCC environment and a conducive tensile axial stress field must exist. The DEl axial stress FEA data in Attachment 3 were reviewed for locations at the uphill side and those angles spanning 450 on either side of the 1800 azimuth (1350 and 157.5&deg;) that would encompass the circumferential extent of the blind zone.
From previous fracture mechanics evaluations for the CEDM nozzles (Reference 7), it was shown that no flaw growth will occur for an applied hoop stress of 10 ksi; that is, the resulting applied stress intensity factor is below the threshold value of 8.19 ksi -,fin needed for flaw growth. With this premise applied to the axial stress distributions for growth of a circumferential flaw, Figures 8 and 9, below, show the axial stress distribution for the 1350 to 2250 azimuths.
Figure 8: ID Axial Stress Distribution Spanning 450 on Either Side (90&deg; Total) of Uphill ID Surface Stre as Distribution
        ^n/
          -3
                                  /____    Bottom Edge of Blind Zone
                                  /____    Middle of Blind Zone
          -5                              Ton edoe of Blind Zone 120        140      160            180              200    220 Azimuth Angle {degrees}
 
Engineering Report M-EP-2003-003 Rev. 00 Page 24 of 35 Figure 9: 25% Through-Wall Position Axial Stress Distribution Spanning 450 on Either Side (900 Total) of Uphill
      -1 (0
(0 (l
    ) -2
      -3
      -4
      -5 120      140        160          180        200        220 Azimuth Angle {degrees)
From Figures 8 and 9, the stresses at the ID and at the 25% through-wall locations, covering a 90&deg; circumferential span around the ICI nozzle, are predominantly compressive. Hence, the initiation of a circumferential flaw in the blind zone above the top of the weld on the uphill side (1800 azimuth) is precluded, thus presenting no safety significance by not inspecting this region.
Cos
 
Engineering Report M-EP-2003-003 Rev. 00 Page 25 of 35 4.0 DISCUSSION AND RESULTS 4.1 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 or propagate through-wall 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 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 ID part through-wall flaws that might exist in the blind zone region of the ICI nozzle, above the top of the weld, in the vicinity of the counterbore, on the uphill side. These would tend to grow along the tube ID, into the high stress field at the top of the weld, and through the thickness above the top of the weld.
The design review of the reactor vessel head construction, the detailed residual stress analyses, selection of representative fracture mechanics models, and the application of a suitable crack growth law has 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 the ICI nozzle). At all locations above the weld, the ID and the interior are in tension.
The OD of the nozzle experiences slight compression in the counterbore transition region and low tension just below this region before ramping to a high tensile stress field at the top of the weld; this is due to the complex, three-dimensional ovalization of the ICI nozzle resulting from the welding process.
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 ID surface crack. In this manner, the stress imposed on the crack is accurately and conservatively modeled. The moving average technique was previously verified in Appendix D of Reference 7 to be an accurate yet conservative depiction of stress application to the crack face. In this evaluation, 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.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 26 of 35 This implies the through-wall distribution is invariant along the length of the tube.
The results of the analysis showed that the stress distribution across the wall remained unchanged along the axis of the tube. Therefore, the moving stress averaging method is validated for the ID surface crack model.
4.2 Results of the ID Surface Flaw Evaluation Several flaw sizes were evaluated in the blind zone region above the weld on the uphill side. Flaw aspect ratios typical of ASME Section XI (6-to-I and 10-to-I on length-to-depth) and another emphasizing deep flaws (4-to- I aspect ratio) were evaluated that sought to maximize growth through-wall while accommodating growth along the length of the ICI nozzle. These evaluations also considered a case where the half length ("c") of the flaw was less than the remaining length needed to grow to the end of the blind zone. Additionally, for those low aspect ratios (4-to-i and 6-to-1), a conservative depth of 25% of the wall thickness (0.100 inch) was assumed. With this depth, a flaw need only propagate 0.3 inch through the thickness to reach through-wall, whereas the flaw along the length must extend 0.4 inch (measured from the tip of the flaw on the ID surface to the edge of the blind zone, plus an additional 0.16 inch in order to become detectable). Table 2 below shows the assumed flaw sizes based on these aspect ratios.
Table 2: Summary of flaw depths and lengths used to evaluate the blind zone on the uphill side above the top of the weld (Blind zone begins a distance 1.08 inches above the top of the weld and extends 0.88 inch)
Flaw Case    Description                            Flaw Depth        Flaw length ID                                                  (in.)              (in.)
I      Aspect ratio of 6-to-I with depth initially 25% through-wall                  0.1                0.6 2      Aspect ratio of 10-to- I with an            0.04                0.4 initial length of 0.4 inch                    .
3      Aspect ratio of 4-to-I with depth            0.1                0.4 initially 25% through-wall 4      Flaw spanning the length of the Blind zone with 6-to-I aspect              0.147              0.88 ratio In the PWSCC flaw growth evaluation, the acceptability of the flaw is determined by its extension outside of the blind zone region, to a detectable length, prior to growing through the thickness, with at least one fuel cycle (1.5 years) between the length and depth growths reaching these values. From Reference I1, the minimum detectable length of a flaw was 2 mm (0.08 inch), with all flaws in the EPRI demonstration between 2 mm and 4 mm (0.16 inch) being detected. Thus, the detectability threshold in the Mathcad worksheets in Attachments 4 through 7 was set to 0.16 inch(or 4 mm). That is, a flaw contained within the 0.88-inch Blind zone must
 
Engineering Report M-EP-2003-003 Rev. 00 Page 27 of 35 propagate along the length of the nozzle a distance measured from the tip of the flaw to the edge of the blind zone (mathematically, this is BZlength/2 - co, where BZ length is the blind zone length and co is the initial half flaw length), plus an additional axial distance of 0.16 to ensure proper detection. This length is defined as the Propagation Length, Prop_Length, in the Mathcad worksheets shown in Attachments 4 through 7. At the same time, the growth through the thickness is limited to reaching through-wall from the initial depth, ao. Table 3 below provides the results of the flaw growth evaluation for each of the four (4) flaw cases given in Table 2. The detailed Mathcad worksheets are contained in Attachments 4 through 7.
Table 3: Results of PWSCC flaw growth evaluations in the length and depth directions.
Flaw Case        PropLength (in.)      Time to reach        Time to go ID          (BZ-lengthI2 - co+      Prop Length        Through-wall 0.16 in.)              (years)              (in.)
1                  0.3                  10.94              13.74 2                  0.4                  > 40              > 40 3                  0.4                  20.98              23.34 4                0.16                  3.83              6.99 These results suggest that a sufficiently deep flaw in the 0.88-inch blind zone above the top of the weld on the uphill side (1800 azimuth) would grow to a detectable length at least one fuel cycle (1.5 years) prior to growing through-wall. Graphical details of the depth and length flaw growth are shown in Figures 10 through 13.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 28 of 35 Figure 10: Flaw Case 1-Depth Growth (top) and Length Growth (bottom) versus number of operating years. For Flaw Case 1, the growth through-wall occurs in 13.74 years. The length growth into an inspectable region occurs in 10.94 years.
Flaw Growth in Depth Direction II          I          I        I          I    .III 0.61 13-74 0.51 0.4017 z      0.4 S..
0.3 1 2
0.21 0.1 "U
0        2      4      6          8      10        12    14  16      IS        20 Operating Time (years) 1.
14.94
_h EL 0                                                                                              0.3 I-
$s9 31      0
____I          I_________                  ___        I
_1 0        2        4      6          8        10          12    14  16      18          20 Operating Time tyears)
 
Engineering Report M-EP-2003-003 Rev. 00 Page 29 of 35 Figure 11: Flaw Case 2-Depth Growth (top) and Length Growth (bottom) versus number of operating years. For Flaw Case 2, no growth in either the depth or length direction occurs within 40 years.
Flaw Growth in Depth Direction I            I            I              I        I      I        I 0.6 0.401 8    0-4    ------------------------------------
I-i 0.2 _
39 0            5            10            15            20        25    30        35        40 Operating Time (years)
II                          I            I            I        I      I_
2, s
C 0.4 0
U.~
        'I            I            III                        I                I        I 0          s            10            15          20        25      30      35        40 Operating Time {years)
 
Engineering Report M-EP-2003-003 Rev. 00 Page 30 of 35 Figure 12: Flaw Case 3-Depth Growth (top) and Length Growth (bottom) versus number of operating years. For Flaw Case 3, the growth through-wall occurs in 23.34 years. The length growth into an inspectable region occurs in 20.98 years.
Flaw Growth in Depth Direction s'
  .4 0.
s~
I SI:
Operating Time (years)
Th L.I
      -l 0          5            10            15          20          25          30 Operating Time {years)
 
Engineering Report M-EP-2003-003 Rev. 00 Page 31 of 35 Figure 13: Flaw Case 4-Depth Growth (top) and Length Growth (bottom) versus number of operating years. For Flaw Case 4, the growth through-wall occurs in 6.99 years. The length growth into an inspectable region occurs in 3.83 years.
Flaw Growth in Depth Direction I          I        ~~~~II 0.6                                                              6,99 0.4 0-4 __________________________-
0.3 0.2 0.1              l                    l                      l                              I 0          2                    4                      6          8        to        12        14 Operating Time (years) 2              1 3:83 I._C C:------            ;------------------------------------____
l              2                    4I                      I          I          0        I          I 0                              46_                                          10        12        14S Operating Time (years)
 
Engineering Report M-EP-2003-003 Rev. 00 Page 32 of 35 A review of DEI's FEA stress output shows the through thickness and axial distribution of hoop stresses on the downhill side (00 azimuth) of the nozzle to be higher than that for the uphill side for the same relative distance above the weld.
That is, for the length of the nozzle 1.08 inches above the top of the weld on the downhill side, plus a region 0.88 inch beyond that (equivalent to the span of the blind zone on the uphill side), the stress distribution was similar in through-wall behavior but generally higher in magnitude. The counterbore region on the downhill side, however, is 9.96 inches above the top of the weld and not subject to the requirements of the Order. Because of the higher stress field, it is reasonable to presume that under equivalent conditions, a flaw could initiate in this equivalent downhill side area more readily than on the uphill side. However, this region is inspected via UT; thus, the most susceptible location based on stresses is addressed by the current inspection coverage.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 33 of 35
 
==5.0 CONCLUSION==
S The evaluation performed and presented in the preceding sections support the following conclusions:
I) The uphill side (1800 azimuth) of the ICI nozzle above the top of the weld possesses the highest (hoop) stresses in the vicinity of the counterbore for which a UT blind zone exists.
: 2) The developed fracture mechanics model, incorporating a method to account for applied stress distribution variation along the ICI nozzle length, has been shown to be a reasonably realistic yet conservative representation of the expected crack growth and morphology.
: 3) The conservatisms used in the analysis (pressure applied to crack faces and high flaw length-to-depth aspect ratio) provide assurance that an undetected crack in the 0.88-inch Blind zone region above the top of the weld on the uphill side (1800 azimuth) will extend out of the blind zone and into an inspectable region at least one operating cycle prior to growth through the thickness.
: 4) Though the downhill side (00 azimuth) of the ICI nozzle at an equivalent distance above the top of the weld is in a higher stress field and more susceptible to crack initiation, it is inspected by UT.
: 5) The ID surface crack on the uphill side either did not show any potential for crack growth, or the crack growth in the axial direction reached a detectable area at least one operating cycle prior to the crack growing through-wall. Hence, an ID surface crack in a region above the weld on the uphill side is not significant.
: 6) No potential exists for an ID circumferential crack to be located in the 820 circumferential extent of the blind zone due to the predominant compressive axial stress field spanning 450 on either side of the uphill side (1800 azimuth) of the ICI nozzle.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 34 of 35
 
==6.0 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)    a.) ANO Drawing No. M-2001 -C2-24 (DRN 03-1315), "Closure Head Instrument Nozzle Details b.) ANO Drawing No. M-2001-C2-107-3, "Closure Head Nozzle Requirements"
: 3) ANO Calculation No. 86-E-0036-39 "Analytical Report for Arkansas Nuclear One -
Unit 2 Reactor Vessel"; prepared by Combustion Engineering, Inc.; dated August 1974.
: 4) ANO Calculation No. 02-E-0003-0 1, Rev. 0, "Time at Temperature Assessment for ANO-2 RV Head Nozzles Revised for Power Uprate"; dated 2/28/02.
: 5) ASME Boiler and Pressure Vessel Code, Section III NB, 1992 Edition.
: 6)    a) "PWSCC of Alloy 600 Materials in PWR Primary System Penetrations"; EPRI TR- 103696; Electric Power Research Institute, Palo Alto, CA; July 1994.
b) "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.
c) "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.
d) Dominion Engineering Inc. e-mails E4162-00-4, E4162-00-5, and E-4162-00-6 containing the nodal stress and coordinate data for ANO-2 ICI Analysis; J.
Broussard and S. Ahnert (DE[) to B. Gray (Entergy); dated August 25 & 26, 2003.
e) Dominion Engineering Inc. e-mail E4162-00-9 containing axial stress and elevation data for all node locations above the top of the weld; J. Broussard (DEI) to B. Gray (Entergy); dated September 3, 2003.
: 7) Entergy Nuclear South/Central Engineering Programs Engineering Report No. M-EP-2003-002, Rev. 01, "Fracture Mechanics Analysis for the Assessment of the Potential for Primary Water Stress Corrosion Crack (PWSCC) Growth in the Un-Insepcted Regions of the Control Element Drive Mechanism (CEDM) Nozzles at Arkansas Nuclear One Unit 2"; dated August 26, 2003. [Previously sent to the NRC Under Relaxation Request transmittal CNRO-2003-00033, dated August 25, 2003.]
: 8) "Stress Intensity Factors for Part-Through Surface Cracks in Hollow Cylinders": S. R.
Mettu et al; NASA TM- 111707; Prepared by Lockheed Engineering & Science Services; Houston, Texas; July 1992.
: 9) "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 (EPRI); dated November 13, 2002.
 
Engineering Report M-EP-2003-003 Rev. 00 Page 35 of 35
: 10) Mathcad - 11; Data Analysis Products Division; Mathsoft Inc.; Seattle WA; November 2002.
: 11) EPRI NDE Demonstration Report; "MRP Inspection Demonstration Program -
Wesdyne Qualification": Transmitted by e-mail from B. Rassler (EPRI) to K. C.
Panther (Entergy); Dated 3/27/2003.
 
Attachment I to Eng- Report No. M-EP-2003-0003, Rev. 01 Page I of 4 Page 1        of I Design Input Revision 0 DESIGN INPUT RECORD Document Type:
Document Number.                                                    Document Revision:
Design Objective: (Attach additional sheets as required)
The purpose of this Design Input Record is to establish the applicable design inputs associated with the In-Core Instrument (ICI) nozzle configurations at ANO-2 and Waterford-3. This information will be used as input to fracture mechanics evaluations being prepared in accordance with ASME Section Xl, part IWB-3600 to evaluate flaw propagation associated with potential future nozzle repairs due to PWSCC cracking in Alloy 600 material.
Design Inputs: (Identify requirement and how it is applied. Ref. DC-141, Sec. 5.1.2)
See attached sheets Contributing Disciplines:
NOTE I Mechanical I&C Electfical civil Piping Structures Engineering programs Other NOTE 1: The contributing discipline engineer shall provide his/her name beside the appropriate block.
-Lead Discipline Mechanical
-Prepared by (DA)      Jamie GoBell        ,                                        Date    07121/03 Lead Design/Responsible Engineer I        3  ,  OR/RIA  SA 1P                    Date Lead Discipline Reviewer                    Nara Ray    N:tED.A Ear                Dae      7- 403
-Lead Discipline Supervisor                William Sims lcl-,>                      Date 7_3Q3
 
Attachment I to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 2 of 4 The NDE limitations for the ICI nozzles are provided relative to the point at which the blend radius begins on the inside surface of the bottom of the nozzle. The dimensions provided for the head cladding surface to the bottom of the ICI nozzle are provided relative to the "sharp corner" points before the points are blended to a 1/16 inch radius. To define the NDE limitations, the vertical distance from the "sharp corner" points up to the tangent point of the blend radius with the vertical face of the nozzle have to be considered. The sketch below shows those dimensions for the zero and 180 degree azimuth positions on the nozzle. At the 90 and 270 degree azimuth positions, the dimension is 1/16 inch. The calculations of the values in the figure below are shown on the following page. It should be noted that on the low hill side, the smaller cutoff angle from the Waterford 3 ICI nozzle configuration was more conservative and was used, and on the upper hill side, the larger cutoff angle from the ANO-2 ICI nozzle configuration was more conservative and was used.
0.206 inches from sharp comer to radius tangent
 
Attachment I to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 3 of 4 xrcr    donztcfr
        ~/ts  el b4 pM4irrht#
A ji    so-0-633.7167 '
c-BO;2"F0.02SC.s      4=    i1 4S fz.O042 Sw  Sj:.O3147 At:      rc/,  =0 .17o1G'
                                        .~re + r    O 0t6 2 X:4,O4oS" 7-  1,30' X=OO/ Is "
 
Attachment I to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 4 of 4 The dimensions of the ICI nozzles relative to the J-groove welds and cladding surface inside the head were calculated relative to the "tangent line" that defines the radius of curvature of the head. These dimensional references are depicted in the sketch below.
Top of counter bore Bottom of counter bore        -
Top of J-weld at 180 deqrees        -
Claddinq at 180                      D Nozzle bottom at OD at 180        -
Nozzle bottom at IDat 180        -
F-Noz bot at IDat00 xKNoz bat OD at 0 --3
                                                      -Cladding      at 0 deg e-)
Top J-weld at 0 deg -D Tangent line datum plane        -
Because there is a slight variation in the location of the ICI nozzles at Waterford 3 relative to the centerline of the head, there is a very slight variation in the values calculated from nozzle to nozzle. Because the variation is very small, only one set of values is reported in the tabulated data. If desired, the specific values for a specific nozzle can be extracted from the Excel spreadsheet that calculated the values. The values for ANO-2 and Waterford 3 were calculated using Excel spreadsheets, and the results are summarized in the table below.
Dimension from the tangent line datum plane to:                              ANO-2      W-3 (inches)  (inches)
Top of counter bore transition                                              48.625    55.094 Bottom of counter bore transition                                          48.375    54.844 Top of J-weld at the 180 degree (high hill side)azimuth location            46.998    53.440 Intersection of the projected cladding surface and the nozzle OD            46.211    52.655 at the 180 degree (high hill side) azimuth location Bottom (sharp corner) of the nozzle at the OD surface at the 180            44.211    50.618 degree (high hill side) azimuth location Bottom (sharp corner) of the nozzle at the ID surface at the 180            43.602    50.031 degree (high hill side) azimuth location Top of J-weld at the 0 degree (low hill side)azimuth location              38.283    45.008 Intersection of the projected cladding surface and the nozzle OD            37.875    44.589 at the 0 degree (low hill side) azimuth location Bottom (sharp corner) of the nozzle at the ID surface at the 0              36.484    43.180 degree (low hill side) azimuth location Bottom (sharp corner) of the nozzle at the OD surface at the 0              35.875    42.594 degree (low hill side) azimuth location
 
Attachment 2 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 1 of 2 Page 1      of      2.
Design Input Revision 0 DESIGN INPUT RECORD Document Type:                                                        N/A Document Number.                            N/A                      Document Revision:        N/A Design Objective: (Attach additional sheets as required)
The following dimensions of the ultrasonic (UT) examination blind zone associated with the counterbore region at the 1800 high hillside location of the incore instrumentation (ICI) nozzles at ANO-2 were obtained based on a review of UT data obtained during 2R1 5 for 7 of 8 ICI nozzles. These dimensions represent worst case measurements.
Dimension from Top of J-weld to Bottom of Counterbore Blind Zone: 1.080" Axial Length of UT Blind Zone: 0.880" Arc Length or Circumferential Extent of Counterbore Blind Zone: 820 Attached to this coversheet is a sketch which identifies the UT "blind zone" of the counterbore region at the 180&deg; high hillside location of the ICI nozzles at ANO-2. The sketch provided is only meant to aid in visualizing the location of the blind zone, and is not meant to be taken as an accurate depiction of the nozzle configuration. The sketch is not to scale.
Design Inputs: (Identify requirement and how it is applied. Ref. DC-141, Sec. 5.1.2)
(See attached sheets, drawings, and photographs)
Contributing Disciplines:
NOTE 1 Mechanical                                    N/A                            N/A 1&C                                          N/A                            N/A Electrical                                    N/A                            N/A Civil                                        N/A                            N/A Piping                                        N/A                            N/A Structures                                    N/A                            N/A Engineering programs                          N/A                            N/A Other                                        N/A                            N/A NOTE 1: The contributing discipline engineer shall provide his/her name beside the appropriate block.
-Lead Discipline Mechanical                                  .            i    A
-Prepared by (DA)      Ronnie Swain (Entergy Level l1l) 11  d            A4                  Date yr,/-o zoS~~nse ol!lfl2 Lead Design/Responsible Engineer                                  N/Y                        Date      N/A Lead Discipline Reviewer                                          N/A                        Date      N/A
-Lead Discipline Supervisor                                        N/A                        Date      N/A
 
Attachment 2 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 2 of 2 COUNTERBORE AT HIGH HILLSIDE POSITION UT blind zone starting point = 1.080" above top of weld Axial length of UT blind zone = 0.880" Arc length of limitation for 2" scanning above the weld = 82 degrees The counterbore limits our ability to ultrasonically scan 2" above the j-weld for a circumferencial distance of as much as 82 degrees on the ICI nozzles.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 GRAY, BRIAN C                                                            Page I of 18 From:                            Stephen Ahnert [sahnert~domeng.com]
Sent:                            Monday, August 25, 2003 1:18 PM To:                              GRAY, BRIAN C
 
==Subject:==
E-4162-00-4 ANO2 ICI Results Above Weld AN02ICIC.ICIdata    Ia Uphill Hoop post.results.t... Stress Plot.pd...
Bri an -
Attached are the AN02 ICI hoop stress results, reported in the nozzle coordinate system, for the uphill half of the nozzle (40,000's - 80,000's planes) above the top of the weld. The axial heights shown in the attachment are measured from the lowest point on the tube at the node's circumferential plane (e.g. node 71403's axial height is measured from node 70001).
Since the ICI nozzle model includes an ID counterbore, the wall thickness is not constant along the nozzle axis. Furthermore, because of the angle of the element mesh, the ID transition does not occur between the same two nodes at every circumferential plane. For the 5 planes included in this transmittal, the ID transition occurs between the following nodes.
40,000's      plane                  41901    - 42001 50,000's      plane                  51801    - 51901 60,000's      plane                  61701    - 61801 70,000's      plane                  71601    - 71701 80,000's      plane                  81601    - 81701 Below the transition, the inner radius is 2.375", while above the transition, the radius shrinks to 2.3125". Between the nodes, the radius shrinks linearly. I've also attached a plot focusing on the uphill portion of the nozzle above the weld.
If you have any questions or comments, please do not hesitate to contact me or John at 703-437-1155.
Sincerely, Stephen Ahnert I
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 2 of 18 AN02ICIC 40000's Plane  (90 degrees from downhill)
Hoop Stresses              % Through Wall NODE      ID        25        50        75    OD 41401. 16446. 15541. 13421. 12339. 12594.
41501. 14314. 13452. 11688. 10418. 10601.
41601. 8445.      9350.      9998. 11033. 13072.
41701. 1075.      5098.      8684. 12018. 14641.
41801. 1335.      5111.      9178. 12550. 14555.
41901. 3151.      6164.      9256. 12135. 13611.
42001. 1484.      5279.      8515. 11674. 14273.
42101. 3802.      6228.      8417. 10542. 12607.
42201. 13096. 12072. 11966. 11842. 11007.
ANO2ICIC 50000's Plane  (112.5 degrees from downhill)
Hoop Stresses              % Through Wall NODE      ID        25        50        75    OD 51401. 13439. 11150. 11288. 12991. 19269.
51501. 12560. 10399.      9501. 9540. 9172.
51601. 6466.      7661.      9531. 11608. 13143.
51701.      866.      4582.      8870. 12570. 14646.
51801.      906.      5050.      9540. 13377. 15336.
51901. 2748.      6200.      9745. 13166. 15292.
52001. 3543.      6551.      9276. 12078. 14330.
52101. 7325.      8780. 10127. 11427. 12628.
52201. 13142. 11794. 11231. 10665. 9629.
AN02ICIC 60000's Plane  (135 degrees from downhill)
Hoop Stresses              % Through Wall NODE      ID        25        50        75    OD 61401. 15760. 12973. 11684. 10977. 12678.
61501. 12143. 11320. 11164. 11425. 12767.
61601. 5816.      7062.      8246. 9521. 10482.
61701. 6278.      8097. 10246. 11831. 12131.
61801. 8396.      9921. 11212. 12104. 12473.
61901. 8947.      9990. 10471. 11176. 11617.
62001. 10693. 10537. 10595. 10597. 10475.
62101. 11570. 11146. 10777. 10457. 10165.
62201. 12332. 11207. 10505. 9847. 9088.
ANO2ICIC 70000's Plane  (157.5 degrees from downhill)
Hoop Stresses              % Through Wall NODE      ID        25        50        75    OD 71401. 21920. 18904. 16819. 15479. 10386.
71501. 17603. 15506. 13062. 9850. 8222.
71601. 12704. 12514. 11586. 8619. 5497.
71701. 13761. 13841. 13644. 10194. 6625.
71801. 15399. 15288. 13268. 9179. 5658.
71901. 15955. 15242. 11918. 8363. 5274.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 3 of 18 72001. 15901.      13994.      11179.      8633. 6165.
72101. 14346.      12527.      10824.      9449. 8173.
72201. 11030.      10495.      10124.      9793. 9527.
AN02ICIC 80000's Plane  (180 degrees from downhill)
Hoop Stresses                % Through Wall NODE        ID        25          50        75      OD 81401. 23147.      2155S        19292. 16085. 9729.
81501. 19425.      1818EB.      15780. 11381. 8207.
81601. 15065.      1458)        13132.      6189.    -109.
81701. 16707.      161755.      15560.      8890. 2754.
81801. 17399.      1717i        15044.      8136. 2316.
81901. 17412.      1748X7.      12883.      7180. 2298.
82001. 17115.      15799L.      11377.      7821. 4387.
82101. 15304.      13024V.      10766.      9067. 7453.
82201. 10308.      11ol  9. 10032.      9951. 9936.
AN02ICIC Node Locations W Through Wall NODE        ID        25          50        75      OD 41401. 3.8310      3.83).0      3.8310    3.8310  3.8310 41501. 4.3383      4.33E13      4.3383    4.3383  4.3383 41601. 5.0383      5. 03E33    5.0383    5.0383  5.0383 41701. 6.0041      6 . 004L1    6.0041    6.0041  6.0041 41801. 7. 3368    7.33668      7.3368    7.3368  7.3368 41901. 8.6238      8 .761.8    8.8998    9.0378  9.1757 42001. 11.7131    11.71331    11.7131    11.7131  11.7131 42101. 15.2141    15.2141      15.2141    15.2141  15.2141 42201. 21.2702    21.27C02    21.2702    21.2702  21.2702 51401. 4.0867      4 . 08667    4.0867    4.0867  4.0867 51501. 4.5620      4 .56220    4.5620    4.5620  4.5620 51601. 5.2230      5 .22330    5.2230    5.2230  5.2230 51701. 6.1423      6.27228      6.4034    6.5339  6.6645 51801. 7.3069      7.33E54      7.3638    7.3923  7.4208 51901. 9.1989      9. 19E39    9.1989    9.1989  9.1989 52001. 11.6719    11.673.9    11.6719    11.6719  11.6719 52101. 15.1113    15. 11113    15.1113    15.1113  15.1113 52201. 19.9532    19.95332    19.9532    19.9532  19.9532 61401. 4.2688      4.26E38      4.2688    4.2688  4.2688 61501. 4.7171      4. 71,71    4.7171    4.7171  4.7171 61601. 5.3452      5.39E59      5.4466    5.4973  5.5480 61701. 6.1904      6. 19S92    6.2079    6.2167  6.2255 61801. 7.4589      7.45E39      7.4589    7.4589  7.4589 61901. 9. 1874    9. 18174    9.1874    9. 1874  9. 1874 62001. 11. 6096    11.60S96    11.6096    11.6096  11.6096 62101. 15.0039    15.00339    15.0039    15.0039  15. 0039 62201. 18.8368    18. 83( 68  18.8368    18.8368  18.8368 71401. 4.3860      4. 38(60    4.3860    4.3860  4.3860 71501. 4.8127      4. 81C)0    4.8074    4.8047  4.8020 71601. 5.4444      5.43, 70    5.4297    5.4223  5.4149 71701. 6.2649      6.269L9      6.2649    6.2649  6.2649
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 4 of 18 71801. 7.4647  7.4647  7.4647  7.4647  7.4647 71901. 9.1581  9.1581  9.1581  9.1581  9.1581 72001. 11.5484 11.5484 11.5484 11.5484 11.5484 72101. 14.9222 14.9222 14.9222 14.9222 14.9222 72201. 18.0908 18.0908 18.0908 18.0908 18.0908 81401. 4.4536  4.4536  4.4536  4.4536  4.4536 81501. 4.8639  4.8639  4.8639  4.8639  4.8639 81601. 5.1825  5.2486  5.3148  5.3810  5.4472 81701. 6.2761  6.2761  6.2761  6.2761  6.2761 81801. 7.4543  7.4543  7.4543  7.4543  7.4543 81901. 9.1289  9.1289  9.1289  9.1289  9.1289 82001. 11.5090 11.5090 11.5090 11.5090 11.5090 82101. 14.8917 14.8917 14.8917 14.8917 14.8917 82201. 17.8288 17.8288 17.8288 17.8288 17.8288
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 GRAY, BRIAN C                                                            Page 5 of 18 From:                        Stephen Ahnert [sahnert~domeng.com]
Sent:                        Monday, August 25, 2003 1:58 PM To:                          GRAY, BRIAN C
 
==Subject:==
E-4162-00-5 AN02 ICI Results up to Weld Top ANO2IcC.nodeloc. AN02ICIC.datapos results.bct (... results.t ...
Brian-Here is the data for the ICI nozzle up to the weld top. This info was previously sent to Jai, which is why I thought you might have it already.
I've also included the detailed node locations for the nozzle below the bottom of the weld, where the element mesh is not straight across the wall of the nozzle.
Stephen 1
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 6 of 18 AN02ICIC Node Locations Below Weld Bottom
* Through Wall NODE      ID      25      50        75    OD
: 1. 0.6979  0.5235  0.3490    0.1745 0.0000 101. 0.8029  0.7201  0.6372    0.5543 0.4715 201. 0.8633  0.8330  0.8028    0.7726 0.7423 301. 0.8979  0.8979  0.8979    0.8979 0.8979 10001. 0.6448  0.4836  0.3224    0.1612 0.0000 10101. 0.8557  0.7791  0.7026    0.6260 0.5494 10201. 0.9768  0.9489  0.9209    0.8930 0.8651 10301. 1.0464  1.0464  1.0464    1.0464 1.0464 20001. 0.4935  0.3701  0.2468    0.1234 0.0000 20101. 0.8988  0.8402  0.7816    0.7231 0.6645 20201. 1.1317  1.1103  1.0889    1.0675 1.0462 20301. 1.2654  1.2654  1.2654    1.2654 1.2654 30001. 0.2671  0.2003  0.1335    0.0668 0.0000 30101. 0.9090  0.8773  0.8456    0.8139 0.7821 30201. 1.2777  1.2662  1.2546    1.2430 1.2315 30301. 1.4896  1.4896  1.4896    1.4896 1.4896 40001. 0.0000  0.0000  0.0000    0.0000 0.0000 40101. 0.8726  0.8726  0.8726    0.8726 0.8726 40201. 1.3739  1.3739  1.3739    1.3739 1.3739 40301. 1.6618  1.6618  1.6618    1.6618 1.6618 50001. 0.0000  0.0668  0.1335    0.2003 0.2671 50101. 1.0655  1.0972  1.1289    1.1606 1.1923 50201. 1.6776  1.6891  1.7007    1.7123 1.7239 50301. 2.0292  2.0292  2.0292    2.0292 2.0292 60001. 0.0000  0.1234  0.2468    0.3701 0.4935 60101. 1.2091  1.2677  1.3263    1.3848 1.4434 60201. 1.9036  1.9250  1.9464    1.9678 1.9891 60301. 2.3026  2.3026  2.3026    2.3026 2.3026 70001. 0.0000  0.1612  0.3224    0.4836 0.6448 70101. 1.3062  1.3828  1.4593    1.5359 1.6124 70201. 2.0566  2.0845  2.1124    2.1404 2.1683 70301. 2.4876  2.4876  2.4876    2.4876 2.4876 80001. 0.0000  0.1745  0.3490    0.5235 0.6979 80101. 1.3646  1.4475  1.5303    1.6132 1.6961 80201. 2.1485  2.1787  2.2090    2.2392 2.2695 80301. 2.5988  2.5988  2.5988    2.5988 2.5988
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 7 of 18 AN02ICIC O's Plane  (0 degrees from downhill)
                                        % Through Wall NODE      HEIGHT        ID        25          50          75        OD
: 1. 0.3490        330.  -16634      -22706.    -21399.    -19763.
101. 0.6372      15313.    -4281      -17786.    -14429.    -10809.
201. 0.8028      26820. 187693.      -3643.      -5548.        397.
301. 0.8979      27575. 27463        11589.      12114. 23130.
401. 1. 1242      26017. 27633        24092.      27004. 45053.
501. 1.3505      28242. 28868        30962.      40738. 54823.
601. 1. 5768      20921. 27864        35821.      45523. 53450.
701. 1.8031      11964. 23787        33856.      42567. 51113.
801. 2.0295        9687. 17779        27821.      30215. 40313.
901. 2.2558      19668. 19737        25207.      27694. 34390.
1001. 2.4821      37434. 31888        27565.      24410. 27638.
1101. 2.7084      43325. 40161        32465.      26020. 30372.
1201. 2.9347      40046. 40036        37953.      30641. 32887.
1301. 3.1610      35368. 35925        38751.      36110. 38087.
AN02ICIC 10000's I?lane  (22.5 degrees from downhill)
                                        % Through Wall NODE      HEIGHT        ID        25          50          75        OD 10001. 0.3224      11817.    -300( D.    -15292.    -17046.    -14741.
10101. 0.7026      23129.      894( P.    -4634.      -7335.      -4914.
10201. 0. 9209      26611. 198144.        8851.      6956. 15400.
10301. 1.0464      25592. 221931.      16673.      20834. 32108.
10401. 1.2671      23008. 214759.      22537.      28149. 43356.
10501. 1.4878      14243. 1818XF.      24429.      31101. 45101.
10601. 1.7085        5755. 145922.      23974.      31574. 40756.
10701. 1.9292        984. 12514 L. 24300.      33893. 38241.
10801. 2.1499        5267. 13512        21660.      26329. 31416.
10901. 2.3706      16884. 18312        19651.      22167. 28262.
11001. 2.5913      26961. 2284E6.      19899.      18757. 23492.
11101. 2.8120      32152. 2908E6.      25470.      21444. 27068.
11201. 3.0327      32793. 33052        30915.      26565. 30561.
11301. 3.2534      31892. 3213CD.      31968.      28400.      35085.
ANO2ICIC 20000's Plane    (45 degrees from downhill)
                                        % Through Wall NODE      HEIGHT        ID        25          50          75        OD 20001. 0.2468      20018. 12176,.        2142.    -4565.      -4829.
20101. 0.7816      17823. 13195,.        8703.      7199. 11360.
20201. 1.0889      13018.      983CI. 11177.      16535.      29313.
20301. 1.2654        8173.      7762      11434.      21752.      29049.
20401. 1.4771        2810.      643E3. 11829.      18313.      24836.
20501. 1.6888      -2122.      3625i. 11444.      19199.      25718.
20601. 1.9005      -6511.      -383        9736. 18601.      26353.
20701. 2.1122      -7277.    -1422        7250.      16568. 19341.
20801. 2.3239      -1618.      3555;.      9846. 16479.      19018.
20901. 2.5356        5060.      8571      11061.      13316.      13608.
21001. 2.7474      10775. 113533.      11467. 13710.      15707.
21101. 2.9591      17210. 16185;.      13444.      12720.      18141.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 8 of 18 21201. 3.1708      22055. 21876.      19604. 17419.      19194.
21301. 3.3825      22420. 22298.      20957. 19614.      22892.
ANO2ICIC 30000's Plane  (67.5 degrees from downhill)
                                      % Through Wall NODE      HEIGHT        ID      25          50        75          OD 30001. 0.1335        8133. 7529.      8405.      8807.      9444.
30101. 0.8456        2509. 4841.      8075. 13153.      14854.
30201. 1.2546      -3159.      185.      6565. 15336.      19781.
30301. 1.4896      -8698.  -3807.        4486. 15633.      21762.
30401. 1.6905    -10607.    -5127.        4368. 16593.      23105.
30501. 1.8915    -11697.    -6146.        3629. 14221.      21065.
30601. 2.0924    -12130.    -5767.        3348. 11915.      24052.
30701. 2.2934    -10623.    -4097.        2790.      9076. 14421.
30801. 2.4943      -6605.  -1271.        4055. 10985.      18666.
30901. 2.6953        -846. 1412.      5279.      8673. 12195.
31001. 2.8963        5966. 4457.      6294.      8822. 10450.
31101. 3.0972      12453. 8583.      8083.      7942.      9098.
31201. 3.2982      17413. 13069.      11816.      9951.      7765.
31301. 3.4991      19608. 16481.      14640. 15484.      12007.
AN02ICIC 40000's Plane  (90 degrees from downhill)
                                        % Through Wall NODE      HEIGHT        ID      25          50        75          OD 40001. 0.0000        5256. 624'        9996. 13433.      14867.
40101. 0.8726      -3168. 110:        7186. 13071.      17896.
40201. 1.3739    -10727.    -380(6.      6415. 17046.      27965.
40301. 1.6618    -15878.    -731,7.      4861. 18322.      29000.
40401. 1.8519    -16192.    -73141.      4927. 19781.      31004.
40501. 2.0421    -15973.    -698E6.      3677. 16010.      23384.
40601. 2.2322    -15040.    -618'3.      2945. 11781.      22918.
40701. 2.4223    -12838.    -554'        3656. 10925.      15784.
40801. 2.6124      -9517.  -579E8.      1581.      9281. 16033.
40901. 2.8026      -4550.  -403(        1975.      7726. 11560.
41001. 2.9927        1807.    -21lF.      3770.      8108.      7520.
41101. 3.1828        6378. 3653L.      5439.      8875.      4032.
41201. 3.3729      10031. 675)L.      6671.      6664.      1885.
41301. 3.5631      13966. 1249EB.      11967. 14062.        6061.
ANO2ICIC 50000's Plane (112.5 degrees from downhill)
                                        % Through Wall NODE      HEIGHT        ID      25          50        75          OD 50001. 0.1335        1855. 4938.      9186. 12671.      15099.
50101. 1.1289        -3205. 1648.      8628. 15241.      19737.
50201. 1.7007      -10751.    -4274.      5271. 16542.      24718.
50301. 2.0292      -15595.    -6154.      6009. 20523.      29654.
50401. 2.2096      -17582.  -8682.        3168. 15984.      27678.
50501. 2.3900      -16129.    -8492.      3069. 14915. 22125.
50601. 2.5704      -14648.    -7789.      3245. 13265.      20801.
50701. 2.7508      -13026.    -7342.      3631. 13180.      19786.
50801. 2.9312      -11837.    -6347.      2955. 12010.      19650.
50901. 3.1116      -10397.    -4769.      2256. 10236.      16691.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 9 of 18 51001. 3.2920      -7427.    -2667.      3304.      7906. 12458.
51101. 3.4724      -2850.      583.      4589. 10291.      8319.
51201. 3.6528        2957. 3567.      5248.      8049.      4998.
51301. 3.8332        9365. 8955. 10723. 13578.      7031.
ANO2ICIC 60000's 1?lane  (135 degrees from downhill)
                                      % Through Wall NODE      HEIGHT        ID      25        50        75        OD 60001. 0.2468        7021. 5842.      5526.      6093.      7368.
60101. 1.3263        3640. 3465.      5318.      7600. 11311.
60201. 1.9464        -905. 1001.      5440. 12219. 21693.
60301. 2.3026      -3267. 2518.      8632. 17598. 31596.
60401. 2.4751      -6647.      884.      9919. 20233. 34996.
60501. 2.6476      -5744.      986. 10615. 22120. 33405.
60601. 2.8200      -5329. 2056. 10825. 22691. 31650.
60701. 2. 9925      -4932. 2805. 11187. 22210. 31425.
60801. 3.1650      -4264. 3369. 11827. 19607. 30392.
60901. 3.3374      -2796. 4582. 11807. 20853. 29935.
61001. 3.5099            30. 5642. 12469. 18196. 26233.
61101. 3.6824        4197. 7650. 12858. 18879. 21916.
61201. 3.8549        9685. 10612. 13445. 16308. 19536.
61301. 4.0273      14607. 13634. 15404. 17649. 19056.
ANO2ICIC 70000's IPlane  (157.5 degrees from downhill)
                                      % Through Wall NODE      HEIGHT        ID      25        50        75        OD 70001. 0.3224        1473.  -3036.    -6641.    -12104.    -17020.
70101. 1.4593      20460. 16006. 11035.      2785.    -6169.
70201. 2.1124      21212. 17465. 16798. 18497. 17342.
70301. 2.4876      22297. 22154. 23184. 29005. 38650.
70401. 2.6542      21709. 23715. 25857. 31252. 45358.
70501. 2.8208      20455. 24110. 27879. 33527. 45849.
70601. 2.9874      19387. 24320. 28835. 34759. 46036.
70701. 3.1541      18829. 24621. 28661. 36197. 47360.
70801. 3.3207      18551. 24450. 28707. 32753. 47292.
70901. 3.4873      18254. 23886. 28207. 33211. 44358.
71001. 3.6539      18196. 23178. 27689. 31919. 41466.
71101. 3.8205      19769. 23334. 27730. 34376. 41884.
71201. 3.9871      22441. 23108. 26486. 30105. 41124.
71301. 4. 1537      23836. 22198. 21340. 20204. 32077.
ANO2ICIC 80000's Plane    (180 degrees from downhill)
                                      % Through Wall NODE      HEIGHT        ID      25        50        75        OD 80001. 0.3490      -11742.  -11463    -12940.    -22469.  -28317.
80101. 1.5303      32201. 29001      20291.      4279.  -13369.
80201. 2.2090      30297. 28052      24882. 23328. 16928.
80301. 2.5988      32705. 32454      32437. 35963. 40476.
80401. 2.7617      35478. 35651      35700. 37186. 47454.
80501. 2.9246      35664. 35774      37391. 40265. 51097.
80601. 3.0875      35636. 36135i. 38433. 41721. 53338.
80701. 3.2503      35307. 366751. 38189. 44045. 56253.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 10 of 18 80801. 3.4132 34605. 35864. 37199. 40276. 55808.
80901. 3.5761 33503. 34531. 36673. 40156. 51744.
81001. 3.7390 32045. 32671. 34572. 38781. 48869.
81101. 3.9018 30301. 31492. 34115. 41212. 53934.
81201. 4.0647 28270. 28386. 32739. 36470. 51629.
81301. 4.2276 26390. 25687. 24607. 22680. 44523.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 GRAY, BRIAN C                                                                      Page 11 of 18 From:                      Stephen Ahnert [sahnert@domeng.com]
Sent:                      Tuesday, August 26, 2003 1:34 PM To:                        GRAY, BRIAN C
 
==Subject:==
E-4162-00-6 ANO2 ICI Results Above Weld (Downhill Plane)
AN02ICIC.ICIdata post2.results....
Brian-Attached are the hoop stress results and node locations for the ICI nozzle at the downhill (0's) plane above the top of the weld . The axial heights shown in the attachment are measured from the lowest point on the tube at the node's circumferential plane (node 5 for the downhill plane). The ID counterbore transition occurs between nodes 2001 and 2101.
Stephen I
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 12 of 18 AN02ICIC O's Plane (0 degrees from downhill)
Hoop Stresses              % Through Wall NODE      ID        25          50        75      OD 1401. 31359. 2990EB.      29337. 29599. 28489.
1501. 26330. 2378e5.      21351. 19924. 17183.
1601. 22264. 20265        17426. 11969.  -417.
1701. 17018. 1532S        12768.      6665.  -2122.
1801. 15282. 1489(        13020.      9080. 4869.
1901. 16043. 154959.      13486.      9127. 5185.
2001. 16153. 1478E3.      10629.      6368. 2547.
2101. 14853. 10204I.      5245.      1131.  -2825.
2201. 13403. 128959.      12285. 11712. 11405.
ANO2ICIC Node Locations
                            % Through Wall NODE      ID        25          50        75      OD 1401. 3.4831    3.48331      3.4831    3.4831  3.4831 1501. 4. 1328  4. 132 28    4.1328    4.1328  4.1328 1601. 4. 9976  4. 99776    4.9976    4.9976  4.9976 1701. 6. 1486  6.14836      6.1486    6.1486  6.1486 1801. 7.6805    7.68C15      7.6805    7.6805  7.6805 1901. 9.7195    9.715'5      9.7195    9.7195  9.7195 2001. 12.7631  12.60225    12.4419    12.2813 12.1207 2101. 16. 0453  16.045,3    16.0453    16.0453 16.0453 2201. 25.4095  25.40935    25.4095    25.4095 25.4095
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 GRAY, BRIAN C                                                                          Page 13 of 18 From:                    John Broussard [jbroussard@domeng.comJ Sent:                    Wednesday, September 03, 2003 11:00 AM To:                      GRAY, BRIAN C
 
==Subject:==
E-4162-00-9, Axial Stresses in the ICI nozzle at and above the weld ANO2ICIC.axial.res ults.txd (13...
Brian, Per our conversation, attached is a text file containing through-wall axial stresses (cylindrical coordinate system centered on the nozzle) and node elevations (relative to the lowest point on the nozzle) for every circumferential plane around the nozzle. If you have any questions or require further information, do not hesitate to call or e-mail.
John Broussard, P.E.
Dominion Engineering, Inc.
E-mail: jbroussardsdomeng.com Phone : 703-437-7826 x236 Fax        : 703-437-0780 1
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 14 of 18 ANO2ICIC - Stresses Above the Weld O's Plane (0 degrees from downhill)
Axial Stresses            % Through Wall NODE      ID        25        50        75    OD 1301. 19134. 19841. 23185. 23594. 23602.
1401. 21283. 22477. 23786. 24530. 26400.
1501. 24244. 23406. 22564. 19655. 15696.
1601. 21617. 21652. 21873. 20331. 10326.
1701. 15755. 17788. 20296. 20152. 14481.
1801. 14607. 16765. 19586. 19917. 19366.
1901. 13693. 15556. 17456. 17722. 17673.
2001. 11799. 12422. 12271. 12235. 12122.
2101. 9528. 8143.      6757.      5463. 4009.
2201. 7582. 6930.      5926.      4908. 4268.
ANO2ICIC - Stresses Above the Weld 10000's Plane (22.5 degrees from downhill)
Axial Stresses            % Through Wall NODE      ID        25        50        75    OD 11301. 22586. 22533. 23312. 23359. 25490.
11401. 23861. 23539. 24158. 26607. 33571.
11501. 23450. 22379. 21257. 19017. 16595.
11601. 21170. 20405. 20232. 18786. 12381.
11701. 16771. 17940. 19555. 19168. 15399.
11801. 15537. 17110. 19041. 19315. 18815.
11901. 14317. 15543. 16831. 17585. 17957.
12001. 11514. 11890. 11821. 11647. 11801.
12101. 8776. 7616.      6655.      5694. 4550.
12201. 6698. 6114.      5295.      4480. 3935.
ANO2ICIC - Stresses Above the Weld 20000's Plane (45 degrees from downhill)
Axial Stresses            % Through Wall NODE      ID        25        50        75    OD 21301. 32078. 30339. 27899. 25016. 23002.
21401. 32246. 29745. 27938. 28428. 31653.
21501. 28287. 26285. 24046. 22044. 21592.
21601. 21901. 20929. 19971. 18562. 16355.
21701. 17934. 18215. 18706. 17913. 16267.
21801. 15767. 16723. 17588. 17926. 17999.
21901. 13734. 14661. 15815. 16924. 18084.
22001. 10646. 10362. 10036.      9985. 10015.
22101. 5882. 5455.      5297.      5132. 4810.
22201. 5389. 5108.      4877.      4619. 4334.
ANO2ICIC - Stresses Above the Weld 30000's Plane (67.5 degrees from downhill)
Axial Stresses            % Through Wall NODE      ID        25        50        75    OD 31301. 33568. 30437. 28273. 26492. 21121.
31401. 32613. 29501. 25741. 23410. 20830.
31501. 27804. 26658. 25076. 23609. 24053.
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 15 of 18 31601. 20992. 20323.      19276. 18062. 16687.
31701. 14110. 14247.      14670. 14920. 14942.
31801. 10324. 11615.      13167. 14307. 15302.
31901. 9890. 10413.      11095. 11524. 11672.
32001. 7802. 8304.      8650.      8901. 9102.
32101. 3146. 3772.      4392.      4997. 5563.
32201. 4854. 4611.      4694.      4781. 4601.
ANO2ICIC - Stresses Above the Weld 40000's Plane (90 degrees from downhill)
Axial Stresses              % Through Wall NODE      ID        25          50        75    OD 41301. 27693. 26366.      24818. 23340. 16693.
41401. 27076. 25745.      22225. 20007. 19364.
41501. 21642. 20426.      18131. 16185. 16290.
41601. 15264. 15112.      14377. 13926. 14193.
41701. 5004. 6885.      8509. 10424. 12026.
41801. 4640. 6420.      8493. 10387. 11537.
41901. 6519. 7330.      8271.      9065. 9330.
42001. 4302. 5572.      6738.      7940. 8892.
42101. 2449. 3416.      4343.      5245. 6088.
42201. 5189. 4721.      4770.      4821. 4469.
ANO2ICIC - Stresses Above the Weld 50000's Plane (112.5 degrees from downhill)
Axial Stresses              % Through Wall NODE      ID        25          50        75    OD 51301. 16932. 15839.      16310. 16729. 13390.
51401. 17627. 14595.      12835. 12324. 17720.
51501. 13191. 10239.      7842.      6261. 5158.
51601. 5842. 6039.      6398.      6923. 7504.
51701.      -27. 1914.      4198.      6352. 7716.
51801. 1264. 2980.      4949.      6577. 7463.
51901. 3160. 4250.      5485.      6675. 7363.
52001. 2524. 3586.      4636.      5927. 6956.
52101. 3505. 4084.      4668.      5242. 5741.
52201. 5464. 4957.      4932.      4859. 4472.
ANO2ICIC - Stresses Above the Weld 60000's Plane (135 degrees from downhill)
Axial Stresses              % Through Wall NODE      ID        25          50        75    OD 61301. 3896. 2573.      4347.      6737. 10416.
61401. 4814. 1456.      -147.    -1041. -1614.
61501. 1261.        65.      -337.      -772.  -206.
61601.    -4868.    -4016.      -3343.    -2306. -1074.
61701.    -3529.    -2279.      -543.      975. 1729.
61801.      245. 1119.      2071.      2887. 3455.
61901. 2525. 3025.      3391.      3945. 4307.
62001. 4204. 4306.      4570.      4750. 4811.
62101. 4855. 4863.      4957.      5065. 5104.
62201. 5488. 5162.      5144.      5053. 4823.
ANO2ICIC - Stresses Above the Weld 70000's Plane (157.5 degrees from downhill)
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 16 of 18 Axial Stresses                % Through Wall NODE        ID        25            50          75        OD 71301.      454.  -2163.        -4850.      -6703.      7792.
71401.      1834.  -2115.        -5846.      -9511.  -16830.
71501.      -421.  -3135.        -6430.      -9855.  -11198.
71601.    -2819.    -3261.        -4224.      -5131.    -5407.
71701.      -456.    -938.      -1350.      -1472.    -1504.
71801.      2658. 1946.        1324.        405.    -449.
71901.      4736. 4256.        3468.      2646. 1820.
72001.      5760. 5395.        4874.      4328. 3705.
72101.      5827. 5450.        5223.      5032. 4769.
72201.      5466. 5304.        5258.      5137. 5049.
ANO2ICIC - Stresses Above the Weld 80000's Plane (180 degrees from downhill)
Axial Stresses                % Through Wa:Ll NODE        ID        25          50          75        OD 81301.      238.  -3173.        -8173.    -11550. 15902.
81401.      2159.  -1729.        -7605.    -15001.    -24613.
81501.      -662.  -3054.        -7027.    -11418.    -13552.
81601.    -1163.  -2032.        -4603.      -6545.    -7444.
81701.      1946.      456.      -1865.      -3592.    -4364.
81801.      4652. 3396.        1590.        - 159.  -1737.
81901.      6022. 5282.        3800.        2360. 1009.
82001.      6542. 6050.        5056.        4230. 3328.
82101.      6161. 5674.        5320.        5006. 4621.
82201.      5431. 5323.        5257.        5112. 5062.
AN02ICIC Node Elevations Above the Weld
                            % Through Wall NODE        ID        25          50          75      OD 1301. 3.1610    3.16) LO      3.1610      3.1610    3.1610 1401. 3.4831    3. 48 31      3.4831      3.4831    3.4831 1501. 4.1328    4. 13 28      4.1328      4.1328    4.1328 1601. 4. 9976  4. 99, 76    4.9976      4. 9976  4. 9976 1701. 6.1486    6. 14E16      6.1486      6.1486    6.1486 1801. 7.6805    7. 68()5      7.6805      7.6805    7.6805 1901. 9.7195    9. 71 95      9.7195      9.7195    9.7195 2001. 12.7631  12.60225      12.4419    12.2813    12.1207 2101. 16.0453  16. 04!i3    16.0453    16.0453    16.0453 2201. 25.4095  25 .40595    25.4095    25.4095    25.4095 11301. 3.2534    3.25314      3.2534      3.2534    3.2534 11401. 3.5665    3. 56665      3.5665      3.5665    3.5665 11501. 4.1839    4. 18319      4.1839      4.1839    4.1839 11601. 5.0137    5.01: 37      5.0137      5.0137    5.0137 11701. 6.1290    6. 125)0      6.1290      6.1290    6.1290 11801. 7.6279    7.62979      7.6279      7.6279    7.6279 11901. 9.6425    9.64225      9.6425      9.6425    9.6425 12001. 12.3503  12.21411      12.0780    11. 9418  11.8056 12101. 15.9895  15. 985 95    15.9895    15.9895    15.9895 12201. 25. 0944  25.094 ~4    25.0944    25.0944    25.0944
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 17 of 18 21301. 3.3825  3.3825  3.3825  3.3825  3.3825 21401. 3.6821  3.6821  3.6821  3.6821  3.6821 21501. 4.2630  4.2630  4.2630  4.2630  4.2630 21601. 5.0509  5.0509  5.0509  5.0509  5.0509 21701. 6.1198  6.1198  6.1198  6.1198  6.1198 21801. 7.5697  7.5697  7.5697  7.5697  7.5697 21901. 9.5365  9.5365  9.5365  9.5365  9.5365 22001. 12.2045 11.8805 11.5564 11.2324 10.9084 22101. 15.8235 15.8235 15.8235 15.8235 15.8235 22201. 24.1971 24.1971 24.1971 24.1971 24.1971 31301. 3.4991  3.4991  3.4991  3.4991  3.4991 31401. 3.7829  3.7829  3.7829  3.7829  3.7829 31501. 4.3262  4.3262  4.3262  4.3262  4.3262 31601. 5.0695  5.0695  5.0695  5.0695  5.0695 31701. 6.0867  6.0867  6.0867  6.0867  6.0867 31801. 7.4786  7.4786  7.4786  7.4786  7.4786 31901. 9.3834  9.4289  9.4744  9.5199  9.5655 32001. 11.9898 11.9898 11.9898 11.9898 11.9898 32101. 15.5564 15.5564 15.5564 15.5564 15.5564 32201. 22.8542 22.8542 22.8542 22.8542 22.8542 41301. 3.5631  3.5631  3.5631  3.5631  3.5631 41401. 3.8310  3.8310  3.8310  3.8310  3.8310 41501. 4.3383  4.3383  4.3383  4.3383  4.3383 41601. 5.0383  5.0383  5.0383  5.0383  5.0383 41701. 6.0041  6.0041  6.0041  6.0041  6.0041 41801. 7.3368  7.3368  7.3368  7.3368  7.3368 41901. 8.6238  8.7618  8.8998  9.0378  9.1757 42001. 11.7131 11.7131 11.7131 11.7131 11.7131 42101. 15.2141 15.2141 15.2141 15.2141 15.2141 42201. 21.2702 21.2702 21.2702 21.2702 21.2702 51301. 3.8332  3.8332  3.8332  3.8332  3.8332 51401. 4.0867  4.0867  4.0867  4.0867  4.0867 51501. 4.5620  4.5620  4.5620  4.5620  4.5620 51601. 5.2230  5.2230  5.2230  5.2230  5.2230 51701. 6.1423  6.2728  6.4034  6.5339  6.6645 51801. 7.3069  7.3354  7.3638  7.3923  7.4208 51901. 9.1989  9.1989  9.1989  9.1989  9.1989 52001. 11.6719 11.6719 11.6719 11.6719 11.6719 52101. 15.1113 15.1113 15.1113 15.1113 15.1113 52201. 19.9532 19.9532 19.9532 19.9532 19.9532 61301. 4.0273  4.0273  4.0273  4.0273  4.0273 61401. 4.2688  4.2688  4.2688  4.2688  4.2688 61501. 4.7171  4.7171  4.7171  4.7171  4.7171 61601. 5.3452  5.3959  5.4466  5.4973  5.5480 61701. 6.1904  6.1992  6.2079  6.2167  6.2255 61801. 7.4589  7.4589  7.4589  7.4589  7.4589 61901. 9.1874  9.1874  9.1874  9.1874  9.1874 62001. 11.6096 11.6096 11.6096 11.6096 11.6096 62101. 15.0039 15.0039 15.0039 15.0039 15.0039 62201. 18.8368 18.8368 18.8368 18.8368 18.8368 71301. 4.1537  4.1537  4.1537  4.1537  4.1537 71401. 4.3860  4.3860  4.3860  4.3860  4.3860 71501. 4.8127  4.8100  4.8074  4.8047  4.8020 71601. 5.4444  5.4370  5.4297  5.4223  5.4149 71701. 6.2649  6.2649  6.2649  6.2649  6.2649 71801. 7.4647  7.4647  7.4647  7.4647  7.4647
 
Attachment 3 to Eng. Report No. M-EP-2003-0003, Rev. 01 Page 18 of 18 71901. 9.1581  9.1581  9.1581  9.1581  9.1581 72001. 11.5484 11.5484 11.5484 11.5484 11.5484 72101. 14.9222 14.9222 14.9222 14.9222 14.9222 72201. 18.0908 18.0908 18.0908 18.0908 18.0908 81301. 4.2276  4.2276  4.2276  4.2276  4.2276 81401. 4.4536  4.4536  4.4536  4.4536  4.4536 81501. 4.8639  4.8639  4.8639  4.8639  4.8639 81601. 5.1825  5.2486  5.3148  5.3810  5.4472 81701. 6.2761  6.2761  6.2761  6.2761  6.2761 81801. 7.4543  7.4543  7.4543  7.4543  7.4543 81901. 9.1289  9.1289  9.1289  9.1289  9.1289 82001. 11.5090 11.5090 11.5090 11.5090 11.5090 82101. 14.8917 14.8917 14.8917 14.8917 14.8917 82201. 17.8288 17.8288 17.8288 17.8288 17.8288
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 1 of 42 Arkansas Nuclear One Unit 2 Primary Water Stress Corrosion Crack Growth Analysis for an ICI ID Surface Flaw Uphill (1800), in the Blind Zone above the Top of the J-Groove Weld Developed by CentralEngineering Programs, Entergy Operations Inc.
Flaw Case 1: 25% Through-Wall Flaw with a 6-to-1 Flaw Length-to-Depth Aspect Ratio, Located at the Center of the Blind Zone Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -tog Thickness Ratio:- "Rmlt" - between 1.0 and 300.0 Note:    The Metric fonn of the equation from EPRI MRP was used 55-Rev. I . A correction factor is applied in the determination of the crack extension to convert the units of meters per second to the            ID Surface Flaw value in inches per hour.
User Input:
The Dominion Engineering Inc. (DEI) finite element model nodal elevations and hoop stresses for the uphill side (1800 azimuth) of the ICI nozzle are brought into the Mathcad worksheet from data supplied in Reference 6d. The data are composed of the nodal elevations (in inches), along with the ID, 25%
through-wall (tw), 50% tw, 75% tw, and OD hoop stresses, beginning at the top of the weld (nodal line 81301) and extending to the top of the nozzle in the FEA model, which is at the point where the nozzle intersects the reactor vessel head.
The DEI FEA data has elevation referenced from the bottom of the ICI nozzle. The elevations of the node points in the DEI FEA model, beginning at the top of the weld (nodal line 81301), are as follows:
i := 0..9 Nodelinei := IDelev feai := QTelev-feai := MD-elev-feai                        TQ elev-feai := ODelevfeai :=
81301              4.2276              4.2276              4.2276              4.2276      4.2276 81401              4.4536              4.4536              4.4536              4.4536      4.4536 81501              4.8639              4.8639              4.8639              4.8639      4.8639 81601              5.1825              5.2486              5.3148              5.3810      5.4472 81701              6.2761              6.2761              6.2761              6.2761      6.2761 81801              7.4543              7.4543              7.4543              7.4543      7.4543 81901              9.1289              9.1289              9.1289              9.1289      9.1289 82001              11.5090            11.5090              11.5090            11.5090      11.5090 82101              14.8917            14.8917              14.8917            14.8917      14.8917 82201              17.8288            17.8288              17.8288            17.8288      178288
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 2 of 42 The corresponding stresses at these nodes are IDstress feai :=    QTstress-fea1 :=      MDstressfeai :=    TQ_stressfea :=      ODstressfeai :=
26.390                25.687                24.607              22.680                44.523 23.147                21.559                19.292              16.085                9.729 19.425              18.188                15.780              11.381                8.207 15.065              14.581                13.132                6.189                -0.109 16.707              16.175                15.560                8.890                2.74 17.399              17.177                15.044                8.136                2.316 17.412              17.487                12.883              7.180                  2.298 17.115              15.794                11.377                7.821                4.387 15.304              13.024                10.766                9.067                7.453 10.308              10. 119              10.032                9.951                9.936 Blind Zone and Counterbore Reference dimensions:
From design drawings (Ref 2a and 2b) and the design input of Attachment 1, the following dimensions are used to locate the counterbore bottom and blind zone locations (bottom, top, and middle) as referenced from the nodal coordinates of the DEI FEA model.
Actualcborebottomelev := IDelev feao + 1.377 Actual cbore bottom elev = 5.6046 topweld-to bottom BZ := 1.08 BZ_length:= 0.88 elev_tomidBZ := IDelev feaO + topweldtobottomBZ + BZ length elevtomidBZ = 5.7476 bottomof BZ := ID_elev_feao + topweldtobottomBZ bottomof BZ = 5.3076
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 3 of 42 topof BZ := IDelev-feao + topweldtobottomBZ + BZlength top_of BZ =      6.1876 For stress averaging and fracture mechanics purposes, the reference coordinate system--with a "0" elevation at the bottom of the nozzle, at the ID corner--must be converted into a new coordinate system with the top of the nozzle (nodal line 82201) as the new "0" elevation.. The positive direction along this new coordinate system will be towards nodal line 81301, which is the top of the weld. This modification facilitates a fracture mechanics model more ammenable to the surface flaw loop structure previously developed in Reference 7.
The following iterative loops convert the five (5) through-wall stress components--ID, 25% tw (QT),
50% tw (MD), 75% tw (TQ), and OD--and the associated elevations, initially given in the DEI FEA model, into the "new" coordinate system, referenced from the top of the nozzle where it meets the reactor vessel head.
IDconv          Top e- ID_elevfea9 while j 2 0 IDelevconvi      v- Top - ID-elev-feaj ID stressi v-  ID_stress feaj output(j, 0) v- IDelevyconvi output(i, I) - IDstressi i(-  i+ I output ID elev      ID convy)
IDstress := ID conv(y
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 4 of 42 QT-conv := Top +- QTelev-fea 9 j<-9 i*-o while j 2 0 QT_elev-conv; +- Top - QT-elev-feaj QTstressi    -  QT-stressjfeaj output(i, 0) -  QT_elev-convi output(i, I) -  QTstress; j*-j-I i-- i+I output QTelev := QTconv(&deg;)
QT stress := QT conv~ )
MDconv := Top <- MDelev-feag while j 2 o MDelevconv; +- Top - MD-elev-feaj MDstress; <- MD stress feaj outputi, 0)    - MD elevconvi output(i, 1)  - MD-stressi j*-j-I ioui+t output MDelev:= MD convy()
MDstress := MD conv(y)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 5 of 42 TQ~conv :    Top v- TQ0elev-fea 9 while j 2 0 TQelev convi v- Top - TQelev feaj TQstressi      -  TQstressjfeaj output(i, 0) v- TQelev-convi output~j, I) <- TQstressi i*- i+ I output TQelev := TQ_conv(o)
TQ-stress := TQ-conv(1)
OD_conv :=    Top v- OD_elevfeag while j 2 0 OD_elevconvi +- Top - OD-elev-feaj ODstressi      -  OD stress fea-output(i, 0) +- OD elevconvi output(i, I) - OD-stressi j*-j-1 i<- i+I output OD_elev := ODconv(o)
OD_stress := OD conv(l)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 6 of 42 ID-elevi =            QT_elevi =          MDelevi =          TQelevi =            OD-elevi 0                    0                    0                  0                    0 2.9371                2.9371              2.9371              2.9371                2.9371 6.3198                6.3198              6.3198              6.3198                6.3198 8.6999                8.6999              8.6999              8.6999                8.6999 10.3745              10.3745              10.3745            10.3745              10.3745 11.5527              11.5527              11.5527            11.5527              11.5527 12.6463              12.5802              12.514            12.4478              12.3816 12.9649              12.9649              12.9649            12.9649              12.9649 13.3752              13.3752              13.3752            13.3752              13.3752 13.6012              13.6012              13.6012            13.6012              13.6012 IDstressi            QTstressi            MDstressi          TQstressi            OD-stressi 10.308                10.119              10.032              9.951                9.936 15.304                13.024              10.766              9.067                7.453 17.115                15.794              11.377              7.821                4.387 17.412                17.487              12.883                7.18                2.298 17.399                17.177              15.044              8.136                2.316 16.707                16.175                15.56                8.89                  2.74 15.065                14.581              13.132              6.189                -0.109 19.425                18.188                15.78              11.381                8.207 23.147                21.559              19.292              16.085                9.729 26.39                25.687              24.607                22.68                44.523 The two sets of five arrays given above are the elevations measured from the top of the ICI nozzle from the FEA model down to the top of the J-weld and the corresponding hoop stresses in the modified coordinate system (MCS).
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 7 of 42 Additional Geometry in Modified Coordinate System The top of the J-groove weld in the MCS is equal to the last entry in the IDelev array:
Top Jweld := ID-elevg Top Jweld = 13.6012 The location of the top of the UT blind zone (BZ) in the MCS (as measured from the ID surface) is BZtop := Top_Jweld - (topweld tobottomBZ + BZlength)
BZ-top = 11.6412 The midpoint of the BZ in the MCS is BZ mid:= BZ top + BZilength 2
BZ mid = 12.0812 The bottom of the BZ in the MCS is BZbottom := BZ top + BZ-length BZbottom = 12.5212 The location of the actual counterbore (from design drawings) in the MCS:
cbore elev := Top Jweld - 1.377 cboreelev = 12.2242
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 8 of 42 From the MCS, the stress distribution from elevation 0 (the top of the ICI nozzle where it intersects the RV head) to the top of the weld is graphically shown below.
Stress Distribution to Top of Weld
::)
C._
0 0
Ir
      -10                        '
0            2        4            6          8            10    12          14 Dist. from Top of nozzle to top weld-in.
          -        ID stress
              ----- 25% tw stress
          ----    50% tw stress 75% tw stress
          -        OD stress For the ID surface flaw model, the reference point is the location along the axis of the nozzle used to locate the flaw. For this analysis, the reference point is considered at the mid-height of the blind zone.
Refpoint := BZ mid c.OCG
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 9 of 42 To place the flaw with respect to the reference point, the flaw tips and center can be located as follows:
: 1) The Upper "c- tip" located at the reference point (Enter 1)
: 2) The Center of the flaw at the reference point (Enter 2)
: 3) The lower "c- tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the point below the blind zone region where stresses will be considered for curve-fitting. This point is taken as the top of the weld, since the stress distribution changes drastically within the weld region Enter this dimension or variable below.
EleVStrs.Dist := Top Jweld        The elevation to the point of maximum stress to consider (Axial distance from elevation 0 in the MCS).
ICI Nozzle Geometry Input Data:
od := 5.563 - 0.001            Tube OD, in inches (The value from Ref. 2a, is 5.563" +0.00/-0.001) idI := 4.625 + 0.01            Maximum Tube ID above counterbore, in inches (The value from Ref. 2b is 4.625" +/- 0.010")
id2 := 4.750 + 0.01            Maximum Tube ID below counterbore, in inches (The value from Ref. 2b is 4.750" +1- 0.0 10")
tI _ (od - idl) 2 Minmum wall thickness above the counterbore, in inches tl = 0.4635 Q := (od - id2) t2~~
Minimum wall thickness below the counterbore, in inches t2 = 0.401 R od Ro = 2.781 id 1 idl Rid I := 2                Ridl  = 2.3175
 
Attachment 4 to Eng. Report No. M-EP-2003-003. Rev. 0 Page 10 of 42 id2 Rid2 =    2              Rid2 = 2.38 ti Rmi := Ridl + -2          Rmi = 2.54925 Rm2 := Rid2 + 2          Rm2 = 2.5805 Rm2 Rt :=                      Rt = 6.43516 t2 Ro
            = 6.93516 Q
Flaw Geometry Input Data:
A postulated flaw could exist in the 0.88" UT Blindzone that occurs 1.08" above the top of the J-weld at the uphill (1800) location. The flaw length (c) and depth (a) constitute the input parameters. This flaw represents an internal surface crack in a cylinder, as described in Reference 8.
ARO := 6              The flaw length-to-depth aspect ratio. This is a ratio common to ASME Section XI, and one sufficient to promote flaw growth through the thickness.
t2-.25 = 0.10025 a    = 0.1            Initial Flaw Depth of the ID surface flaw in the blind zone above the top of the weld on the uphill side. The minimum detectable depth of a surface flaw from UT demonstrations [Ref. 11] was 8% throughwall. Conservatively, a 25%
throughwall flaw is assumed. This flaw is sufficiently deep to see the stress field developed through the thickness.
L.= aO-AR 0            Initial Flaw Length of an ID surface flaw in the counterbore region, in inches.
The length was determined by assuming a 6-to-I flaw length-to-depth aspect ratio. Half the flaw length (0.3 inch) was placed the below the mid-height of L = 0.6                the blind zone, while the other half was placed above the mid-height.
L co := 2                The half flaw length used in the fracture mechanics model
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 11 of 42 Additional Input Data:
Pint := 2.235                  Design Operating Pressure (internal) [Ref. 3]
Years := 40                    Number of Operating Years Ilim = 8000                    Iteration limit for Crack Growth loop IL:= 604                        Conservative Operating Temperature for the head, in degrees F. Ref. 4 gives a value of 594.8 deg. F following power uprate.
aoc := 2.67 12            Constant in MRP-55 PWSCC Model for 1-600 Wrought @ 617 deg. F
[Ref. 9]
Qg = 31.0                      Thermal activation Energy for Crack Growth {MRP) [Ref. 9]
Tref := 617                    Reference Temperature for normalizing Data deg. F [Ref. 9]
Timopr:= 365.2422-24-Years              Numer of operating hours in a year CFinhr := 1.417- 105                    Correction factor to convert meters per second to inches per hour Timop Cblk:      -oIimpr                      Calculation block size for the crack growth iteration loop
              =4im Chlk =43.82906
_    =    lim Prntblk :=50
                -Qg co 1 :=e1103*10 3T
(        7    re T.~+596)
Temperature Correction for Coefficient Alpha from EPRI MRP-55, Revision 1 [Ref. 9]
Co:= 1.0col              75 th percentile from MRP-55 Revision I [Ref. 9]
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 12 of 42 The flaw model used for a postulated flaw within the counterbore region on the uphill side of the ICI nozzle is an internal surface flaw in a cylinder, subject to an arbitrary stress distribution.
To allow for a "moving average" of through-thickness stress values as the flaw extends along the length of the ICI ID surface, the length from the bottom tip of the of the initial flaw in the blind zone to the stress distribution upper limit--Elevstrs.Dit--is broken into 20 equal segments. Note that due to the MCS used, with a 0 elevation occurring at the TOP of the nozzle, the term "UTip" (implying the upper tip of the flaw) is actually the physical bottom tip of the flaw, closer to the top of the weld. UTip is the term used in Reference 7 for the CEDM nozzles, and thus it will continue to be used in the ICI nozzle evaluation.
FLCntr =      Refpo int c0 if Val = I Flaw center Location at the mid-point of Refpoint if Val = 2                the blind zone region Refp0 int + c 0 otherwise UTip := FLCntr + CO UTip = 12.3812 ElevStrs.Dist - UTip Strs.avg :=            20 IncStrs.avg = 0.061 No User Input is required beyond this Point
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 13 of 42 Regression of Through-Thickness Stresses as a Function of Axial Elevation Because of the minor variation in stresses occuring at the top of the nozzle where it intersects the reactor head and the need to accurately curve fit stresses in the region of interest in the BZ, the entire range of stresses is not appropriate to curve fit. To accomodate an area below and above the BZ region, the first two data points in each of the elevation and stress arrays were removed from consideration in the curve fitting equations. This is a reasonable assumption, given that in the completely through-wall tensile stress field that exists in the nozzle above the top of the J-weld, a flaw centered in the BZ region is likely to grow through the thickness entirely (in addition to growth along the surface of the nozzle) rather than grow very long into an area close to the top of the head or below the top of the J-weld (i.e., elevation ranges not included in the stress polynomial curve fit).
Initially, a fourth (4th) order polynomial was chosen for axial stress regression. After regression, the stress at the mid-height of the blind zone (12.0812 inches in the MCS) is checked.
Regression for ID stresses:
k := O.. 6 8.6999 17.412) 10.3745 17.399 11.5527 16.707 IDelevcf :=      12.6463 IDstresscf := 15.065 12.9649 19.425 13.3752 23.147 13.6012) 26.39 )
IDelevi =      ID_stressi 3
0        10.308 3
2.9371          15.304 RID := regress(IDelevcf,IDstresscf,4)                              4                6.3198          17.115 2920.01158            8.6999          17.412 RID =                            10.3745          17.399
                                                              -1120.32621 11.5527          16.707 161.1276 12.6463          15.065 ZID := 8.6999,8.701 .. Top Jweld                          -10.23275 12.9649          19.425 0.24206    )    ~~13.3752        23.147 13.6012          26.39 bD(zllD) := interp(RID, ID elevcf, ID_stress cf,ZID)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 14 of 42 28 26 24 22 flD(ZID)
IDstresscf Oef3        20 18  -
16 14 L 8.5    9  9.5    10  10.5    11      11.5 12 12.5 13 13.5 14 zID, IDelevcf fID(12.0812) = 15.66367 Regression for 25% throughwall stresses:
8.6999 )                          17.487) 10.3745                            17.177 11.5527                            16.175 QTrelev-cf :    12.5802          QTstresscf :=    14.581 12.9649                            18.188 13.3752                            21.559 13.6012)                          25.687)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 15 of 42 QT_elevi    QTstressi =
(        3 0      10.119 3
2.9371      13.024 RQT := regress(QT_elevcf,QTstresscf,4)                        4              6.3198      15.794 3362.70255            8.6999      17.487 RQT =                            10.3745      17.177 ZQT := 8.6999,8.701 .. TopJweld                      -1281.45936 11.5527      16.175 182.93207 12.5802      14.581
                                                      -11.53275 12.9649      18.188 0.27085    )      13.3752      21.559 13.6012      25.687 fQT( ZQT)  := interp( RQT, QTelevcf, QT_stress_cf, zQT) 26 24 22 fQT(ZQT) 20 QTstresscf oeee 18  -
16 14 _
8.5  9    9.5 10  10.5    11      11.5    12  12.5  13    13.5 14 ZQT, QTelevcf fT( 12.0812) = 15.09487
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 16 of 42 Regression for 50% throughwall stresses:
8.6999 )                      12.883) 10.3745                        15.044 11.5527                        15.56 MDelev cf :=      12.514          MDstresscf :=  13.132 12.9649                        15.78 13.3752                        19.292 y13.6012)                      24.607)
MD-elevi  MDstressi =
3 0    10.032 3
2.9371    10.766 RMD := regress(MDelevcf , MDstresscf,      4)                4        6.3198    11.377 6270.57353    8.6999    12.883 RMD =                    10.3745    15.044 ZMD := 8.6999,8.701 .. Top Jweld                        -2357.44561 11.5527      15.56 330.23769 12.514    13.132
                                                          -20.39106 12.9649      15.78
                                                      \1 0.46849    )  13.3752    19.292 13.6012    24.607 fMD(ZMD) := interp(RMD,MD elevcf,MD stress_cf,zMD)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 17 of 42 26 fMD(ZMD)
MDstresscf oee
                        -8.5  9  9.5  10    10.5    11    11.5 12 12.5 13 13.5    14 ZMD, MDelevcf fMD(1 2 .0812) = 14.11569 Regression for 75% throughwall stresses:
I/ 8.6999 )                          7.18 )
10.3745                            8.136 11.5527                            8.89 TQelev-cf :=      12.4478        TQ_stresscf :=    6.189 12.9649                          11.381 13.3752                          16.085 13.6012)                          22.68 )
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 18 of 42 TQelevi        TQstressi =
3 0          9.951 3
2.9371          9.067 RTQ := regress(TQelev cf, TQstresscf , 4)                4              6.3198          7.821 6772.44513          8.6999            7.18 RTQ =                        10.3745          8.136 ZTQ := 8.6999,8.701 .. TopJweld                    -2552.34739 11.5527            8.89 358.42617 12.4478          6.189
                                                    -22.21167 12.9649          11.381 0.51271  )      13.3752          16.085 13.6012          22.68 fTQ(zTQ) := interp( RTQ, TQelev cf, TQstress cf, ZTQ) 25 22.5 20 17.5 fTQ(ZTQ) 15 TQstress cf eee 12.5  -
10 _
7.5    <
8.5  9  9.5 10  10.5    11  11.5    12  12.5  13    13.5    14 ZTQ, TQ_elevcf fTQ(12.08 12) = 7.37343
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 19 of 42 Regression for OD stresses:
kk := o.. 5 r 10.3745")                      2.316 )
11.5527                          2.74 12.3816                        -0.109 ODelev cf :=                      ODstresscf :=
12.9649                        8.207 13.3752                        9.729 Y13.6012)                      44.523 )
I-                OD-elevi  OD-stressi =
3 0      9.936 3
2.9371      7.453 4                      4.387 ROD := regress(ODelevcf, ODstress_cf,4                                6.3198 1.83727x 105    8.6999      2.298 10.3745      2.316 ZOD := 10.3745,10.376.. Top_Jweld          ROD =      -62394.03658 11.5527        2.74 7925.4618 12.3816      -0.109
                                                        -446.31291    12.9649      8.207 9.40247  )  13.3752      9.729 13.6012    44.523 fOD(zOD) := interp(ROD,OD elevcf,ODstress-cf ,zOD)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 20 of 42 50 40 30 fOD(ZOD) 20 ODstresscf 6Eee 10 0-
                  -10 _
10  10.5 11 11.5      12      12.5 13 13.5  14 ZOD, OD elev cf foD(12 .0 8 1 2 ) = 5.39079
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 21 of 42 Calculation to develop Stress Profiles for Analvsis This analysis for the axial stress regression and the through-wall stress regression is the same as that used for the CEDM Nozzles (in Ref. 7) with the exception that the axial stresses are fit with a fourth-order polynomial, rather than a third-order polynomial, to accomodate greater precision.
X:iv= 20                  Number of locations for stress profiles Loco := FLCntr - L FLCntr = 12.0812 L = 0.6
        ,:=  1.. N + 3                            Incri :=  co if i < 4 lneStrs.avg otherwise Loci := Loci-, + Incri SID; = RID 3 + RID 4 -Loci + RID .(Loci) 2 + RID 6 (Loci) + RID *(Loc;)4 SQT; := RQT3 + RQT4 LoCi + RQT5 .(Loc1 ) 2 + RQT 6(Locj) 3 + RQT (Loci) 4 SMDi:= RMD + RMD 4Loci + RMDS (Loci) + RMD .(Loc;) 3 + RMD .(Loc;) 4 STQi := RTQ3 + RTQ4 -LOCi + RTQ .(Loci) 2 + RTQ (Loc1 )3 + RTQ. (Loci) 4 SOD; = ROD3 + ROD4 Loci + ROD .(Loci) + ROD *(Loc;)3 + ROD .(Loc;) 4 j  := I..N SIDj + SIDj+j + SIDj+2 if j =                              SQTJ + SQTj+l + SQTj+2 if; =
Sidj =                                                        Sqt. :
                                                                                                      .. I 3                                                          3 Sid    (j + 1) + SIDj+2                                    Sq      ,(j+ 1)+ SQTj+2 J2                    otherwise                          I qtj+21                  otherwise j+2
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 22 of 42 SMDj + SMDj+l + SMDj+2      if j= 1 5 tqj.
STQj + STQj+j + STQj+ 2 5 md.,"                                                                          if j = I J                3                                          3 Smd  *(j + I) + SMDj+2                    Stq.  (j + I) + STQj+2 otherwise              I                    otherwise j+2                                        j+2 SODj + SODj+1 + SODj+.1)
Sod                            - if j = I odJ'              3 Sod  *(j + 1) + SODj+2 otherwise j+2
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 23 of 42 Through-Wall Stress Distribution for ID Flaws (i.e. ID to OD Stress distribution)
U0 := &deg;.000              u 1 := 0.25            u 2 := 0.50  U3 := 0.75                  u 4 = 1.00 Y := stack(uO, u I ,u2 ,u3 ,u 4 )
SIG1 := stack(Sid, sqt1 Smd,      1 Stq1 Sod1 )              SIG 2 := stack (Sid2j 5Sqt q    Smd2 Stq2 Sod2)
SIG 3 = stack(Sid3 , Sqt 1Smd3 Stq3 ' Sod 3 )                  SIG 4 = stack( Sid4 ' Sqt 4 , Smd4'Stq4,Sod4)
SIG 5 = stack(Sid 5Sqt 5 lSmd5 'Stq5 Sod5)                    SIG 6 = stack(Sid 6 Sqt6 Smd6'Stq6 Sod6)
SIG 7 = stack(Sid7'Sqty Smd 7 9Stq 7 ' Sod7 )                  SIG8 := stack( Sid88Sqt8 9Smd 8 IStq8 'Sod 8 )
SIG 9 := stack(Sid9 . Sqt9 .smd, Stq9 ' Sod9 )                SIGo := stack(Sid        'Sqt 10 S'md 10 w Stq10 tSod10 )
SIG II1 := stack ( Sid 11 Sqtl 1 Smdl11' Stq11,l    od 11)    SIG 1 2  = stack(Sid 12 sqt12 'Smd 12 stq12 'Sod 12 )
SIG 13 = stack( Sid, Sqt13 ' Smd 13 ' Stq13 ' Sod )          SIG 1 4 := stack (Sid 14 sqt14 Smd14 Stq 14 Sod14 )
13 SIG 15 = stack( Sid 1'Sqt' 5 'Smd 'Stq15, Sod 15)            SIG    16 = stack (Sid 16 'Sqt16  'Smd 16 'tq 16 ' od 16)
SIG 17 = stack( Sid17'Sqt 17 , Smd17'Stq17' Sod17)            SG 18 := stack (S id 1 8 'Sqt 1 8 ' Smd    '5 tql 'Sod18 )
SIG 19 := stack( Sid ,9Sqt 9Smd        '  tq 19q Sod1 9)    SIG 2 0 := stack (Sid 2 0 ' Sqt  0'  Smd2 0 ' tq 2 0 Sod2 0 )
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 24 of 42 Regression of Through-Wall Stress distribution to Obtain Stress Coefficients Using a Third Order Polynomial IDRGI      regress(Y, SIG , 3)                                  IDRG 2    regress(Y, SIG 2 ,3)
IDRG 3    regress(Y, SIG 3 , 3)                                IDRG4      regress(Y,SIG 4 ,3)
IDRG5      regress(Y, SIG5 , 3)                                IDRG6      regress(Y,SIG 6 ,3)
IDRG 7    regress(Y,SIG 7 ,3)                                  IDRG 8    regress(Y,SIG 8 ,3)
IDRG9      regress(Y,SIG 9 ,3)                                  IDRGo:      regress(Y,SIG 1 0 ,3)
IDRG I      regress(Y, SIG I1 , 3)                              IDRG1 2    regress(Y,SIG 1 2 ,3)
IDRG1 3    regress(Y,SIG 1 3 ,3)                              IDRG 14    regress(YSIG 14 ,3)
IDRG 1 5    regress( Y, SIG 15 ,3)                              IDRG1 6 := regress(Y,SIG 1 6 ,3)
IDRG 1 7    regress(Y,SIG 17 ,3)                                IDRG1 8 : regress(Y,SIG 1 8 ,3)
IDRG 1  :  regress(Y,SIG 1 9 ,3)                              IDRG 2 0 := regress(YSIG 2 0 ,3)
Stress Distribution in the tube. Stress influence coefficients obtainedfrom thrid-orderpolynomial curvefit to the through/wallstress distribution
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 25 of 42 Data Files for Flaw Shape Factors from NASA SCO4 Model [Ref. 8]
{NO INPUT Required)
Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=
0          1        2 0        1.000    0.200      0.000 1        1.000    0.200      0.200 2        1.000    0.200      0.500 3        1.000    0.200      0.800 4        1.000    0.200      1.000 5        1.000    0.400      0.000 6        1.000    0.400      0.200 7        1.000    0.400      0.500 8        1.000    0.400      0.800 9        1.000    0.400      1.000 10        1.000    1.000      0.000 11        1.000    1.000      0.200 12        1.000    1.000      0.500 13        1.000    1.000      0.800 14        1.000    1.000      1.000 15      2.000      0.200      0.000 15        2.000      0.200      0.200 17        2.000      0.200      0.500 18        2.000      0.200      0.800 19        2.000      0.200      1.000 20        2.000      0.400      0.000 21        2.000      0.400      0.200 22        2.000      0.400      0.500 23        2.000      0.400      0.800 24        2.000      0.400      1.000 25        2.000      1.000      0.000 26        2.000      1.000      0.200 27      2.000      1.000      0.500 28        2.000      1.000      0.800 29        2.000      1.000      1.000 30        4.000      0.200      0.000 31        4.000      0.200      0.200 33 32        4.000      0.200      0.500 0.800 33        4.000      0.200      0.800
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 26 of 42 34      4.000  0.200 1.000 35      4.000  0.400 0.000 36      4.000  0.400 0.200 37      4.000  0.400 0.500 38      4.000  0.400 0.800 39      4.000  0.400 1.000 40      4.000  1.000 0.000 41      4.000  1.000 0.200 2      4.000  1.000 0.500 43      4.000  1.000 0.800 44      4.000  1.000 1.000 45    10.000  0.200 0.000 410.000 0.200 0.200 47    10.000  0.200 0.500 86    10.000  0.200 0.800 49    10.000  0.200 1.000 48    10.000  0.400 0.000 I    10.000  0.400 0.200 2    10.000  0.400 0.500 3    10.000  0.400 0.800 10.000  0.400 1.000 5    10.000  1.000 0.000 10.000  1.000 0.200 55    10.000  1.000 0.500 I  10.000  1.000 0.800 57    10.000  1.000 1.000 1300.000 0.200 0.000 1300.000 0.200 0.200 62    300.000  0.200 0.500 63    300.000  0.200 0.800 42  300.000  0.200 1.000 63  300.000  0.400 0.000 6    300.000  0.400 0.200 75  300.000  0.400 0.500 8    300.000  0.400 0.800 69    300.000  0.400 1.000 70    300.000  1.000 0.000 71    300.000  1.000 0.200 72    300.000  1.000 0.500 73    300.000  1.000 0.800 7-4  300.000  1.000 1.000
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 27 of 42 Sambi :=
0          1      2        3        4        5          6              7 0    1.076    0.693  0.531  0.434    0.608    0.083    0.023          0.009 1    1.056    0.647  0.495  0.408    0.615    0.085    0.027          0.013 2    1.395    0.767  0.557    0.446    0.871    0.171    0.069          0.038 3      2.53    1.174  0.772    0.58    1.554    0.363    0.155          0.085 4    3.846    1.615  0.995    0.716    2.277    0.544    0.233          0.127 5    1.051    0.689  0.536    0.444    0.74    0.112    0.035          0.015 6    1.011    0.646  0.504    0.421    0.745    0.119      0.041          0.02 7    1.149    0.694  0.529    0.435    0.916    0.181      0.073          0.04 8        1.6    0.889  0.642    0.51    1.334    0.307      0.132          0.073 9    2.087    1.093  0.761    0.589    1.752    0.421      0.183          0.101 10    0.992    0.704  0.534    0.506    1.044    0.169      0.064          0.032
        .11    0.987    0.701  0.554    0.491      1.08  0.182    0.067          0.034 12      1.01    0.709  0.577    0.493    1.116      0.2    0.078          0.041 13      1.07    0.73  0.623    0.523    1.132    0.218    0.095          0.051 14    1.128      0.75  0.675    0.556    1.131    0.229      0.11          0.06 15    1.049    0.673  0.519    0.427      0.6  0.078    0.021          0.008 16    1.091    0.661  0.502    0.413    0.614    0.083      0.025          0.012 17    1.384    0.764  0.556    0.446    0.817    0.15      0.058          0.031 18    2.059    1.033  0.708    0.545      1.3  0.291      0.123          0.067 19    2.739    1.301  0.858    0.643    1.783    0.421      0.18          0.099 20    1.075    0.674  0.527    0.436    0.73    0.072    0.044          0.021 1    1.045    0.659  0.511    0.425    0.76    0.122    0.043          0.021 22      1.16    0.71  0.536    0.441    0.919    0.197      0.064          0.034 23      1.51    0.854  0.623    0.498    1.231    0.271      0.114          0.062 24    1.876    0.995    0.71  0.555    1.519    0.317      0.161          0.089 25    1.037    0.732  0.594    0.505    1.132    0.192      0.07          0.035 26    1.003    0.707  0.577    0.493    1.113    0.19      0.071          0.036 27    1.023    0.714    0.58  0.495    1.155    0.207      0.08          0.042 28    1.129    0.774  0.619    0.521    1.286    0.247      0.098          0.052 29    1.242      0.84  0.661    0.549    1.416    0.285    0.115          0.061 30    1.003    0.649  0.511    0.43    0.577    0.07      0.015          0.005 31    1.097    0.666  0.511    0.426    0.606    0.079      0.023          0.01 32    1.405    0.776  0.567    0.46    0.797    0.141      0.054          0.028 33    1.959    0.996  0.692    0.542    1.201    0.262      0.108          0.059 34    2.461    1.197  0.808    0.619    1.586    0.37      0.154          0.085 35    1.024    0.668  0.528    0.451    0.737    0.11      0.033          0.015 36*  1.057    0.666    0.52  0.439    0.77    0.123      0.042          0.021 37    1.193    0.715  0.545    0.454    0.924    0.174      0.068          0.036 38    1.443    0.828  0.614    0.509    1.219    0.263      0.109          0.059 39    1.665    0.934  0.681    0.565    1.487    0.339      0.143          0.078 Ml    1 nn  I  n 7    n a.7 1      sl1a    110    n1    I  n nRA          n naA
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 28 of 42 41      1.009  0.713      0.588    0.511    1.128      0.194 0.072          0.037 42      1.041  0.726      0.594    0.515    1.191      0.214 0.082          0.043 43      1.105  0.768      0.623    0.536    1.316      0.248 0.097          0.05 44      1.162  0.81      0.653    0.558    1.428      0.277 0.109          0.055 45      0.973  0.635      0.499    0.446    0.579        0.07 0.016          0.005 46      1.115  0.673      0.514    0.438    0.607      0.079 0.023          0.01 47      1.427  0.783      0.571    0.462    0.791      0.138 0.052          0.027 48      1.872  0.96      0.671    0.529    1.179      0.253 0.104          0.056 49      2.23  1.108      0.757    0.594    1.548      0.356 0.149          0.081 0      0.992  0.656        0.52    0.443    0.733      0.109 0.032          0.014 1      1.072  0.672      0.523    0.441    0.777      0.125 0.043          0.021 52      1.217  0.723      0.549    0.456    0.936      0.176 0.069          0.036 53      1.393  0.806      0.601    0.493    1.219      0.259 0.106          0.056 54      1.521  0.875      0.647    0.528    1.469      0.328 0.135          0.071 55      0.994  0.715        0.59    0.518    1.114      0.187 0.068          0.035 56      1.015  0.715      0.588    0.512      1.14      0.197 0.074          0.038 57        1.05 0.729      0.596    0.515    1.219      0.221 0.085          0.044 8        1.09  0.76      0.618    0.532    1.348      0.255 0.099          0.051 59      1.118  0.788      0.639    0.55    1.456      0.282 0.109          0.056 60      0.936  0.62      0.486    0.405    0.582      0.068 0.015          0.005 1      1.145  0.681      0.514    0.42    0.613      0.081 0.024          0.011 62      1.459  0.79      0.569    0.454    0.79      0.138 0.051          0.026 63      1.774  0.917      0.641    0.501    1.148      0.239 0.096          0.051 64      1.974  1.008      0.696    0.537    1.482      0.328 0.134          0.07 5      0.982  0.651      0.512    0.427    0.721      0.103 0.031          0.013 66      1.095  0.677        0.52    0.431    0.782      0.127 0.045          0.022 67      1.244  0.727      0.546    0.446    0.946        0.18 0.071          0.037 68        1.37 0.791      0.585    0.473    1.201      0.253 0.102          0.054 69      1.438  0.838      0.618    0.496    1.413        0.31 0.126          0.066 A:= Jsb(o)                X := Jsb(l)          Y := Jsb(2) aU := Sambi(O)              aL := Sambi          aQ := Sambi(2)      ac := Sambi(3)
Cu := Sambi(4)              CL := Sambi(5)      cQ := Sambi(6)      CC := Sambi(7)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 29 of 42 n :=  3 if Rt < 4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W, X, Y)      VaU := aU      RaU := regress(MauVaU,n)
XY):=interp RaU, MaU, VaU{ xI1 faU(W faU(WXY)~,Y) faU(4,.4,.S) = 1.7089          Check Calculation Linear Term MaL := augment(W,X,Y)          VaL := aL              RaL := regress( MaL, VaL, n) faL(W, X,Y) :
IKY)]
faL(4,.4,.8) = 0.93393  Check Calculation Quadratic Term MaQ:= augment(W,X,Y)          VaQ := aQ            RaQ := regress(MaQ,VaQ,n)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 30 of 42
                                                'W)-
faQ(W, X, Y) := interp        ,MaQ, VaQy X I MY) faQ(4,.4,.S) = 0.67668        Check Calculation Cubic Term MaC := augment(W, X, Y)              VaC := aC        RaC := regress( MaC , VaC, n)
_a(,X,  )itrlRCM~KVC !
faC (Ws,XY) := interp RaC, MaC VaC,            X I faC(4,.4,.8) = 0.54151        Check Calculation "C" Tip Coefficients Uniform Term MCU := augment(W, X, Y)                VCU := CU      RcU :=regress( McU, VcU, n) fcU(W XY):=interp RcU, Mcu, VCU!x I1 f~~u~~w~~xY)                                )
fcu(4,.4,.8) = 1.31015        Check Calculation Linear Term McL := augment(W, X, Y)              VCL := CL        RCL := regress( McL, VcL, n)
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 31 of 42 fcLW,~y):=interp{RcLMcLVcL{ xI1
      ~~zL(WXY)y                          )
fCL(2,.4,.8) = 0.28509      Check Calculation Quadratic Term McQ := augment(W,X,Y)                  VCQ := CQ RCQ := regress(McQVCQ,n)
                                        'WY fcQ(WX,Y) := interp        MCQ,  c    X CY) fCQ(4,.4,.8) = 0.11797    Check Calculation Cubic Term MCC := augment(W, X, Y)                          R~CC= regress( M~C. VCn) fcC(W, X, Y) := interp{RCC. McC, VcC,    X  I L              ' Y)_
fcc(4,.4,-8) = 0.06384    Check Calculation Calculations: Recursive calculations to estimate flaw growth
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 32 of 42 Recursive Loop for Calculation of PWSCC Crack Growth CGRsam bi :  j-O o ao -ao aO    CO co - Co t*-t2 NCBo    - Cblk while j < 'Jim a0o-    IDRG3 if cj < CO IDRG2      if co < cj < co + InCStrs.avg IDRG 3 3 if C 0+IlnCstis.avg <    Cj < CO+ 2InCS trs.avg IDRG4      if Co + 2IflCstrs avg < Cj < Co + 3 1nc,Strs.avg IDRG53 if co + 3 Incstrs.avg < Cj <    Co + 4 Inc'Strs.avg IDRG6 33 if    c 0+ 4 Incstrs.avg < Cj < co + s Inc Strs.avg IDRG7 3 if C0 + 4flncstrs.avg < Cj < c 0 + 6 1nc'Strs.avg IDRG 8 3 if CO + 6-lnCstrs.avg < Cj < Co + 7 Inc 'Strs.avg IDRG9 3 if Co + 7 Incstrs.avg < Cj < Co + 8 Inc'Strs.avg IDRG1 0      if Co + 8 InCStrs.avg < Cj _ co +91I  1Cstrs.avg IDRGI3 if Co+9 IncStrs.avg < Cj _ co+ &deg;-lnCstrs.avg IDRGI 2      if co+ 10 lncStrs.avg < Cj _co+ 1 *InCstrs.avg 3
[DRG 1 3    if CO+ lfl nCstrs.avg < Cj < Co+ 122InCStrs.avg 3
IDRG 14 3if Co+ 12 InCStrs.avg < Cj _ co+ 133-InCStrs.avg IDRG 15      if CO+ l3 InCstrs.avg < Cj _ Co+ 144-InCStrs.avg
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 33 of 42 IDRG 16 3 if co+ 14- Incstrs.avg < Cj < C + 15- IncStrs.avg IDRG 17 3 if Co+ l5-lnCStrs.avg < cj < Co + 16- lncSfts avg IDRG 18 3 if CO + 16- lncstrs.avg < Cj < Co + 17- IncStrs avg IDRG 19      if Co+ l7- ICStrs.avg < cj < co+ 18 InSltrs.avg IDRG 2 0    otherwise 3
1 F IDRG  4  if cj < co IDRG 2    if co < Cj < co + InSltrs.avg IDRG 3    if co + Incstrs avg < Cj < Co + 2-InCStrs.avg IDRG4      if Co + 2-Incstrs.avg < Cj < Co + 3 IfnCStrs.avg IDRG 5    if Ce + 3 Ilncstrs.avg < Cj < co + 4-InCStrs.avg IDRG 6    if Co + 4-Ilncstrs.avg < Cj  < C0 + 5-InCStrs.avg IDRG 7    if CO + 5- Ilncstrs.avg < Cj < c 0 + 6-IncSrs.avg IDRG 8    if CO + 6- InCStrs.avg < cj < C0 + 7 InCStrs.avg IDRG 9    if co + 7-Inestrs.avg < Cj < c 0 + 8 fCStrs.avg IDRG 10 4 if Co+8.InCStrs.avg < cj < Co + 9-ICStrs.avg IDRG 1 14 if c 0 + 9flncStrs.avg < cj < co + I IlnCStrs.avg IDRG 1 2    if cO + 10 Incstrs.avg < cj < CO + I-lncstrs.avg IDRG 1 3    if co + I I-l CStrs.avg < Cj < co+ 12 InCStrs.avg IDRG 1 4    if cO + 12 IfncStrs.avg < Cj < co + 13 IfnCStrs.avg IDRG 15      if cO+ 13- InCStrs avg < cj < co + 14- Ilnstrs.avg IDRG 16 4 if CO+ 14 IncStrs.avg < Cj < co+ 15I lnCStrs.avg
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 34 of 42 IIJKU 1 7    it Co + l5-lnCstrs.avg < Cj < Co + 16 lncStrs.avg IDRG1 84 if CO + 16 lncStrs avg < Cj < Co + 17 IlncStrs avg IDRG 19 4 ifCo+        7-lnCStrs.avg < cj < Co+ 18-  lncStrs avg IDRG 2 0    otherwise 4
02<- IDRG I      if Cj <CO IDRG 2      ifco < cj < co + InCStrs.avg IDRG 3      if co + Incstrs.avg < Cj < Co + 21Incstrs.avg IDRG 4      if CO + 2-InCstrs.avg < cj < Co + 3-IfCStrs.avg IDRG 5      if CO + 3flncStrs.avg < cj 5 Co + 4fIncStrs.avg IDRG 6      if CO + 4- IncStrs.avg < Cj < co+ 5lncstrs.avg IDRG 7      if c 0 + 5 lncstrs.avg < Cj < co+ 61Incstrs.avg IDRG 8      if Co + 6flncstrs.avg < cj < C0 + 7flncStrs.avg IDRG 9      if co + 7fInCStrs.avg < Cj < CO + 8IflCStrs.avg IDRG1 0      if CO + 8 lnfstrs.avg < cj < Co + 9llncStrs.avg IDRGI 1 5 if CO + 9Ilncstrs.avg < cj < cO + 10-IncStrs avg IDRG 12 5 if cO + 10o    InCstrs.avg < cj < co + II-Incstrs.avg IDRG 13 5 ifco+ IllnCStrs.avg < Cj < Co+ 12'IfncStrs avg IDRG 14 5 ifco + 12-Incsttrs.avg < cj < co + 13.Ilncstrs.avg IDRG 1 5 5 if co + 13. 1fnstrs.avg < cj      co C  + 14IncStrs avg IDRG 1 6 5 if cO + 14 InCStrs.avg < Cj < Co + 15-IncStrs avg IDRG 1 7      if co+ 15 Incstrs.avg < c< co + 16 1fncStrs.avg IDRG 1 x      if cO + 16- Incetr, n,<e < cj  c + 17- InfCStrz nv
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 35 of 42 IDRG 19 5 if Co+ 17dlncstrs.avg < Cj < Co+ 18 lncStrs.avg IDRG 20      otherwise 5
IDRGI      if Cj < Co IDRG 2    if co < Cj < co + InCStrs.avg IDRG 3    if CO + InCStrs.avg < cj < Co + 2 InCStrs avg IDRG 4    if Co + 2 IncstrS.avg < Cj < Co + 3I lCStrs.avg IDRG 5 if Co + 3dcStrs.avg      < Cji  Co + 4InCStrs.avg 6
IDRG 6 6 if Co+ 4dcStrs.avg      < Cj - Co+ 5dfICStrs.avg IDRG76 if CO + 5flncStrs.avg < Cj < co+ 6-InCStrs.avg IDRG 8 6 if co + 6 InCStrs.avg < Cj < co + 7.flCStrs avg IDRG 9 6 if Co + 7- fCStrs.avg < Cj < co + SlfCStrs.avg IDRG 10 6 if co + 8.lcStrs.avg < Cji      co + 9dflcStrs.avg IDRG1 16 if Co + 9. lCStrs.avg < Cj < Co + OtlnCStrs.avg IDRG 12 6 if co+ 10 InCStrs.avg < ej < co + Ill nCStrs.avg IDRG 1 3 6 if co+ II IncStrs.avg <cj        co+ 12 InCStrs.avg IDRG 1 4 6 if co+ 12 InlCStrs.avg < cj < Co+    3- lncStrs.avg IDRG1 5 6 if co+ 13lncStrs.avg < cj < co + l4 Incstrs.avg IDRG 1 6 6 if co + l4 lncStrs.avg < Cj < co + 1S-lncStrs.avg IDRG1 7 6 if co+ 15sInCStrs.avg < Cj < C + 16 InCStrs.avg IDRG 1 8 6 if co+ 16 lStrs.avg < Cj _ co+ 17olCStrs.avg IDRG19 6 if Co+ 17 IncStrs.avg < Cj < co + I8 IncStrs.avg
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 36 of 42 IIDRG2 0          otherwise 40o- GO 41 +-Go+ CTI -          0.25-3j)  + 0 2 ~0.25*aj>) 2 + 0 O.25 aj'3 t  )
42 +    F      C                  027 .5 j2
                                  +j.i 3 +- CFO      + icy I - 0.75 -aj )
                                    + 02- 0.75- aj)2 + 03{ 0.75.aj)'
t  )            t )
0.0.o-ajA        ( l~o-aj)2      1.0-aj)3
~4 <-- GO      ICI        t )+ C2'        t ) +YY      t J X +- 0.25 x2    0 0.5 x3 - 0.75 X*+ stack(x 0 xI x2 ,x 3 ,x 4 )
ST +- stack(40,t l 42 ^43 '4)
RG *- regress(X, ST, 3)
OO +- RG3 + PInt 10- RG4 0y20 <- RG5 030 <- RG 6 ARj _-
cj aj AT- +      J (GX_  +-f  1    R. AR; .AT;+
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 37 of 42
-auj          a    -X--R-J Gal <- faL(RtARjATj)
Gaqj - faQ (Rt, ARj, ATj)
Gacj        fac(RtARjATJ)
G.cu      - fcU (RtARj, ATj)
GC1 <i*-fcL(Rt, ARjATj)
Gcq +- fcQ(Rt ARj,ATj)
G cci - fcC(Rt, ARj,ATj)
Q    -        I II+1.464{    (t~~~16      if cjaj I + 1.464{2 1.5otherwise Kaj        (t              OOGauj +          O'Galj +  20 Gaqj + (Y30OGacj)
K*Ci +--                *(    00  Gcuj + a O1G0cl + 0 2 0*Gcqj + 030aGcci)
  'l K*a        Kaj l.099 K          Kc; 1Yj1.099 K a <-        9.0 if Ka < 9.0 Ka    otherwise KY      -    9.o if KY < 9.0 Ky l      otherwise Daj        Co(Kai          9.0)1.16 T11 -. In        p.CF. r.        ;f k    '- enn
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 38 of 42 agj      I-a      i-inhr -blk
* jv~
14-10        *CFinhr-Cblk otherwise Dc;i <-- Co0 (K Yj      9.0)1.16 Dcgj 4-      DCCFiinhrdCblk if K          < 80.0 l4      CFilnhr-Cblk otherwise Output(j,o) <- j output(j, 1)    -  aj OUtPUt(j , 2)  *-  Cj - CO OUtPUt(j, 3) 4- Dagj OUtPUt(j,4) - Dcgj OUtPUt(j, 5) 4- Ka.
OUtPUt(j, 6) - KC NCBj OUtPUt(j 7)4- 365-24 OUtPUt(j, 8)  4-  Gau output~j, 9) <- Gal output~j, 10) +- Gaqj output~j, II) <- Gacj outPUt(j, 12) <- Gcuj OUtPUt(j, 13)        Gcl.
OUtPUt(j, 14)4- Gcqj OUtPUt(j, 15) <      Gcc Oj tP-tjy+I)4 a; 4- ai- 1 + Dac0
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 39 of 42 cj v-- cj_. + Dcg.j_
aj*-    t if aj&#x17d;t aj otherwise NCBj v- NCBj-j + Cblk output O.. Ilim The curve below shows the flaw growth through-wall and the operating time (in years) it takes to go through-wall.
Flaw Growth in Depth Direction II            I      I      I      I      IlI 0.6                                                    131.74
.        0.5 _
                                                                  '&0.401
.        0.4 g        0.3 -
0 0
    .~0.2 0.1 0    2          4      6      8      10    12      14    16 18  20 Operating Time {years}
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 40 of 42 The propagation length for the ICI nozzles is defined as the length for which the initial flaw in the blind zone would extend out of the blind zone and grow to a detectable flaw. Reference 11 gives the minimum detectable flaw size of 4 mm (0.16) in length; thus, 0.16 inch was considered as this minimum detectable flaw length. This dimension is added to the end of the blind zone.
BZ length PropLength :=                  - Co + 0.16 2
PropLength = 0.3 This implies that a flaw initially within the blindzone must grow 0.3 inch to become detectable via UT.
The curve below shows the flaw growth along the length of the ICI nozzle and the operating time (in years) it takes to reach the Prop Length value defined above.
1.5 0.5 5-
      -0.5
        -I  -
0      2      4        6        8        10      12  14      16      18      20 Operating Time {years}
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 41 of 42 Stress Intensity Factors 100 80 0
C)  60 Ws usd 40 a
20 -
0  2        4  6    8        10      12  14 16 18    20 Operating Time {years}
        - Depth Point Surface Point
 
Attachment 4 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 42 of 42 Influence Coefficients - Flaw 3
2.5 2
E 1.5 0
0.5~~~~~~~~~                                        ~~~~~~
O __________-              -        ~--    _        __    ___    _-----___            __
0            2            4            6          8        10      12      14          16 18        20 Operating time {years}
                "a" - Tip -- Uniform
      -----    "a" - Tip -- Linear
          -      a" - Tip -- Quadratic
      --  -    '"a" - Tip -- Cubic
                -c" - Tip -- Uniform
              '---'"c'
                      - Tip -- Linear
      --      "c" - Tip -- Quadratic
                -"c" - Tip -- Cubic c-2
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 1 of 42 Arkansas Nuclear One Unit 2 Primary Water Stress Corrosion Crack Growth Analysis for an ICI ID Surface Flaw Uphill (1800), in the Blind Zone above the Top of the J-Groove Weld Developed by Central Engineering Programs, Entergy Operations Inc.
Flaw Case 2: 0.4-inch Long Flaw with a 10-to-1 Flaw Length-to-Depth Aspect Ratio, Located at the Center of the Blind Zone Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to- Thickness Ratio:- "Rmtt"    - between 1.0 and 300.0 Note:    The Metric form of the equation from EPRI MRP was used 55-Rev. I . A correction factor is applied in the determination of the crack extension to convert the units of meters per second to the            ID Surface Flaw value in inches per hour.
User Input:
The Dominion Engineering Inc. (DEI) finite element model nodal elevations and hoop stresses for the uphill side (1800 azimuth) of the ICI nozzle are brought into the Mathcad worksheet from data supplied in Reference 6d. The data are composed of the nodal elevations (in inches), along with the ID, 25%
through-wall (tw), 50% tw, 75% tw, and OD hoop stresses, beginning at the top of the weld (nodal line 81301) and extending to the top of the nozzle in the FEA model, which is at the point where the nozzle intersects the reactor vessel head.
The DEI FEA data has elevation referenced from the bottom of the ICI nozzle. The elevations of the node points in the DEI FEA model, beginning at the top of the weld (nodal line 81301), are as follows:
i := O.. 9 Nodelinei :=      ID-elev-feai := QT_elev feai :=          MDelev feai := TQelev-feai :=        ODelevfea:
81301              4.2276              4.2276              4.2276              4.2276        4.2276 81401              4.4536              4.4536              4.4536              4.4536        4.4536 81501              4.8639              4.8639              4.8639              4.8639        4.8639 81601              5.1825              5.2486              5.3148              5.3810        5.4472 81701              6.2761              6.2761              6.2761              6.2761        6.2761 81801              7.4543              7.4543              7.4543              7.4543        7.4543 81901              9.1289              9.1289              9.1289              9.1289        9.1289 82001              11.5090            11.5090              11.5090            11.5090        11.5090 82101              14.8917            14.8917              14.8917              14.8917        14.8917 82201              17.8288            17.8288              17.8288            17.8288        17.8288
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 2 of 42 The corresponding stresses at these nodes are IDstress feai :=    QTstress-feai :=      MDstress feat :=    TQ_stressfeai :=    ODstressfea- :=
26.390                25.687                24.607              22.680                44.523 23.147                21.559                19.292              16.085                9.729 19.425                18.188                15.780              11.381                8.207 15.065                14.581                13.132                6.189                -0.109 16.707                16.175                15.560                8.890                  2.74 17.399                17.177                15.044                8.136                2.316 17.412                17.487                12.883                7.180                2.298 17.115                15.794                11.377                7.821                4.387 15.304                13.024                10.766                9.067                7.453 10.308                10.119                10.032                9.951                9.936 Blind Zone and Counterbore Reference dimensions:
From design drawings (Ref. 2a and 2b) and the design input of Attachment 1, the following dimensions are used to locate the counterbore bottom and blind zone locations (bottom, top, and middle) as referenced from the nodal coordinates of the DEI FEA model.
Actual cborebottomelev := IDelevfeao + 1.377 Actualcbore bottom elev = 5.6046 topweldtobottom BZ := 1.08 BZ_length := 0.88 elevtomidBZ := IDelev feao + topweld to bottomBZ +              -BZlength elevto midBZ = 5.7476 bottomof BZ := IDelevfeao + topweldtobottomBZ bottomof BZ = 5.3076
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 3 of 42 topof BZ := IDelev feao + topweldtobottom_BZ + BZlength top_of BZ = 6.1876 For stress averaging and fracture mechanics purposes, the reference coordinate system--with a "0" elevation at the bottom of the nozzle, at the ID corner--must be converted into a new coordinate system with the top of the nozzle (nodal line 82201) as the new "0" elevation.. The positive direction along this new coordinate system will be towards nodal line 81301, which is the top of the weld. This modification facilitates a fracture mechanics model more ammenable to the surface flaw loop structure previously developed in Reference 7.
The following iterative loops convert the five (5) through-wall stress components--ID, 25% tw (QT),
50% tw (MD), 75% tw (TQ), and OD-and the associated elevations, initially given in the DEI FEA model, into the "new" coordinate system, referenced from the top of the nozzle where it meets the reactor vessel head.
IDconv := Top 4- IDelevfeag il-o while j > 0 IDelevconvi v- Top - ID-elev-feaj ID-stressi +- IDstressjfeaj output(^0) 4- IDelev-convi output(i, I) - IDstressi j4-j-I i+- i+ I output IDelev := ID convy" IDstress := ID conv(y
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 4 of 42 QT-conv := Top      *-  QT elev-feag i*-0 while j 2 o QT-elev-convi    -  Top - QT-elev-feaj QT_stressi <- QTstressjfeaj output(i, 0) - QT elevconvi output(i, 1) <- QTstressi j*-j-I i*- i+ 1 output QT-elev := QTconvy&deg;)
QT-stress := QT-conv()
MDconv := Top        *-  MD-elev-feag i*-0 while j 2 0 MDelev convi        *- Top - MDelevfeaj MDstressi      - MDstressfeaj output(i, 0)
* MD elevconvi output(i, I) <- MD-stressi j<-j-i*- i+
output MDelev:= MDconv(&deg;)
MDstress:= MD conv( )
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 5 of 42 TQ conv := Top <- TQelevfeag j<-9 i*-o while j 2 0 TQ-elevconvi      <-  Top - TQelev-feaj TQstressi    *-  TQstressfeaj output(i, 0) <- TQelev_convi output(i, 1) <- TQstressi i    i+I output TQ elev := TQ_ con()
TQstress := TQ convI)
OD conv := Top      - OD-elevfea9 j*-9 i-  0 while j 2 0 OD_elev convi      *- Top - OD elev feaj OD_stress;  <- OD_stressfeaj output(i, 0) <- OD_elev_convi output(i, I) - OD_stressi J B J -I i*- i+ 1 output OD_elev := OD conv(y)
OD_stress := OD conv(y)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 6 of 42 IDelevi =            QT_elevi =          MDelevi =          TQelevi =            OD-elevi 0                    0                    0                  0                      0 2.9371                2.9371              2.9371              2.9371                2.9371 6.3198                6.3198              6.3198              6.3198                6.3198 8.6999                8.6999              8.6999              8.6999                8.6999 10.3745              10.3745              10.3745            10.3745              10.3745 11.5527              11.5527              11.5527            11.5527              11.5527 12.6463              12.5802              12.514            12.4478              12.3816 12.9649              12.9649              12.9649            12.9649              12.9649 13.3752              13.3752              13.3752            13.3752              13.3752 13.6012              13.6012              13.6012            13.6012              13.6012 IDstressi            QTstressi            MDstressi          TQstressi            OD-stressi 10.308                10.119              10.032              9.951                  9.936 15.304                13.024              10.766              9.067                  7.453 17.115                15.794              11.377              7.821                  4.387 17.412                17.487              12.883                7.18                  2.298 17.399                17.177              15.044              8.136                  2.316 16.707                16.175                15.56                8.89                  2.74 15.065                14.581              13.132              6.189                -0.109 19.425                18.188                15.78              11.381                  8.207 23.147              21.559                19.292              16.085                  9.729 26.39              25.687                24.607              22.68                44.523 The two sets of five arrays given above are the elevations measured from the top of the ICI nozzle from the FEA model down to the top of the J-weld and the corresponding hoop stresses in the modified coordinate system (MCS).
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 7 of 42 Additional Geometry in Modified Coordinate System The top of the J-groove weld in the MCS is equal to the last entry in the IDelev array:
Top Jweld := ID-elevg Topjweld = 13.6012 The location of the top of the UT blind zone (BZ) in the MCS (as measured from the ID surface) is BZ top := Top_Jweld - (topweld to bottomBZ + BZ_length)
BZ top = 11.6412 The midpoint of the BZ in the MCS is BZ length BZ mid := BZtop + - 2 BZ mid = 12.0812 The bottom of the BZ in the MCS is BZbottom := BZ top + BZ length BZbottom = 12.5212 The location of the actual counterbore (from design drawings) in the MCS:
cbore elev := Top Jweld - 1.377 cboreelev =    12.2242
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 8 of 42 From the MCS, the stress distribution from elevation 0 (the top of the ICI nozzle where it intersects the RV head) to the top of the weld is graphically shown below.
Stress Distribution to Top of Weld 40 30
:Z~    20
  =0 10 0
      -10 0            2        4            6            8            10    12          14 Dist. from Top of nozzle to top weld-in.
            -      ID stress
            -----  25% tw stress
              ---- 50% tw stress 75% tw stress
            -      OD stress For the ID surface flaw model, the reference point is the location along the axis of the nozzle used to locate the flaw. For this analysis, the reference point is considered at the mid-height of the blind zone.
Refpoint := BZ-mid Coto
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 9 of 42 To place the flaw with respect to the reference point, the flaw tips and center can be located as follows:
: 1) The Upper "c- tip" located at the reference point (Enter 1)
: 2) The Center of the flaw at the reference point (Enter 2)
: 3) The lower "c- tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the point below the blind zone region where stresses will be considered for curve-fitting. This point is taken as the top of the weld, since the stress distribution changes drastically within the weld region Enter this dimension or variable below.
ElevStrs.Dist := TopJweld        The elevation to the point of maximum stress to consider (Axial distance from elevation 0 in the MCS).
ICI Nozzle Geometry Input Data:
od := 5.563 - 0.001            Tube OD, in inches (The value from Ref. 2a, is 5.563" +0.00/-0.001) idI := 4.625 + 0.01            Maximum Tube ID above counterbore, in inches (The value from Ref. 2b is 4.625" +/- 0.0 10")
id2 := 4.750 + 0.01            Maximum Tube ID below counterbore, in inches (The value from Ref. 2b is 4.750" +/- 0.0 10")
tl    (od - idI) 2 Minmum wall thickness above the counterbore, in inches tI = 0.4635 t2      (od - id2) 2 Minimum wall thickness below the counterbore, in inches t2 = 0.401
__od RoO*:= 2d  2 Ro = 2.781 idl Ridl := 2                Ridl = 2.3175
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 10 of 42 id2 Rid2 = 2                  Rid2 = 2.38 Rml := Rdl +              Rmi = 2.54925 Rm2      Rid2 +2          Rm2 = 2.5805 Rm2 Rt :=                    Rt = 6.43516 Ro
              - 6.93516 t2 Flaw Geometrv Input Data:
A postulated flaw could exist in the 0.88" UT Blindzone that occurs 1.08" above the top of the J-weld at the uphill (1 800) location. The flaw length (c) and depth (a) constitute the input parameters. This flaw represents an internal surface crack in a cylinder, as described in Reference 8.
ARO:= 10                The flaw length-to-depth aspect ratio. This is a ratio common to ASME Section XI, and one sufficient to promote flaw growth through the thickness.
t2*.1i  = 0.0401 I.^:= 0.4                Initial Flaw Length of an ID surface flaw in the counterbore region, in inches.
The length was based on a sufficiently long flaw (10-to-I aspect ratio) with enough depth into the thickness (10%) to precipitate growth in both the depth and length directions. Half the flaw length (0.2 inch) was placed the below the mid-height of the blind zone, while the other half was placed above the mid-height.
0.4            Initial Flaw Depth of the ID surface flaw in the blind zone above the top of the a0 :=-
      &deg;ARO              weld on the uphill side. The minimum detectable depth of a surface flaw from UT demonstrations [Ref. 11] was 8% throughwall. This flaw is 10%
ao = 0.04                throughwall.
L c 0 := -                The half flaw length used in the fracture mechanics model
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 11 of 42 Additional Input Data:
PInt = 2.235                Design Operating Pressure (internal) [Ref. 3]
Years := 40                  Number of Operating Years Ilim = 8000                  Iteration limit for Crack Growth loop L,:= 604                    Conservative Operating Temperature for the head, in degrees F. Ref. 4 gives a value of 594.8 deg. F following power uprate.
aOC := 2.67. 10- 12          Constant in MRP-55 PWSCC Model for 1-600 Wrought @ 617 deg. F
[Ref. 9]
Qg    31.0                  Thermal activation Energy for Crack Growth {MRP) [Ref. 9]
Tref := 617                  Reference Temperature for normalizing Data deg. F [Ref. 9]
Timopr      365.2422 Years      Numer of operating hours in a year CFinhr      1.417- 105              Correction factor to convert meters per second to inches per hour Timop Cblk          opr                  Calculation block size for the crack growth iteration loop h4im Cblk  = 43.82906 Prntblk        lm 0=
e    _Qg        ( i            1I                    Temperature Correction for Coefficient Alpha C.103 10 3 T+459.67 Tref+459.67)j                  from EPRI MRP-55, Revision I [Ref. 9]
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 12 of 42 Co      1.0Lco I      75  t percentile from MRP-55 Revision 1 [Ref. 9]
The flaw model used for a postulated flaw within the counterbore region on the uphill side of the ICI nozzle is an internal surface flaw in a cylinder, subject to an arbitrary stress distribution.
To allow for a "moving average" of through-thickness stress values as the flaw extends along the length of the ICI ID surface, the length from the bottom tip of the of the initial flaw in the blind zone to the stress distribution upper limit--Elevstrs.Dist--is broken into 20 equal segments. Note that due to the MCS used, with a 0 elevation occurring at the TOP of the nozzle, the term "UTip" (implying the upper tip of the flaw) is actually the physical bottom tip of the flaw, closer to the top of the weld. UTip is the term used in Reference 7 for the CEDM nozzles, and thus it will continue to be used in the ICI nozzle evaluation.
FLCntr =      Refp 0 i t - c 0 if Val =
Flaw center Location at the mid-point of RefPoint if Val = 2                the blind zone region
                          + c 0 otherwise UTip := FLCntr + c0 UTip = 12.2812 ElevStrs.Dist - UTip lctrs.avg :-20 Incstr.avg =0.066 No User Input is required beyond this Point
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 13 of 42 Regression of Throul!h-Thickness Stresses as a Function of Axial Elevation Because of the minor variation in stresses occuring at the top of the nozzle where it intersects the reactor head and the need to accurately curve fit stresses in the region of interest in the BZ, the entire range of stresses is not appropriate to curve fit. To accomodate an area below and above the BZ region, the first two data points in each of the elevation and stress arrays were removed from consideration in the curve fitting equations. This is a reasonable assumption, given that in the completely through-wall tensile stress field that exists in the nozzle above the top of the J-weld, a flaw centered in the BZ region is likely to grow through the thickness entirely (in addition to growth along the surface of the nozzle) rather than grow very long into an area close to the top of the head or below the top of the J-weld (i.e., elevation ranges not included in the stress polynomial curve fit).
Initially, a fourth (4th) order polynomial was chosen for axial stress regression. After regression, the stress at the mid-height of the blind zone (12.0812 inches in the MCS) is checked.
Regression for ID stresses:
k := O.. 6 8.6999 )
(17.412) 10.3745 17.399 11.5527 16.707 ID_elevcf := 12.6463                IDstress cf := 15.065 12.9649 19.425 13.3752 23.147 13.6012)
Y 26.39 )
IDelevi =      IDstressi =
3 0        10.308 3
2.9371        15.304 RID := regress(IDelevcf,IDstresscf,4)                            4                6.3198        17.115 2920.01158            8.6999        17.412 RID =                            10.3745        17.399
                                                              -1120.32621 11.5527        16.707 161.1276 12.6463        15.065 ZID := 8.6999,8.701..Top Jweld                            -10.23275 12.9649        19.425 0.24206  )        13.3752        23.147 13.6012          26.39 fID(zID) := interp(RID,ID elevcf, IDstress cf ,zID)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 14 of 42 28 26 24 22 fID(ZID)
ID stresscf 6E~e        20 18  -
16 14 _
8.5    9  9.5    10  10.5    11      11.5 12 12.5 13 13.5 14 ZID, ID elevcf flD(12.0812) = 15.66367 Regression for 25% throughwall stresses:
8.6999 )                            17.487) 10.3745                              17.177 11.5527                            16.175 QTelev-cf :      12.5802          QTstresscf :=    14.581 12.9649                            18.188 13.3752                            21.559 13.6012)                          25.687)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 15 of 42 QT-elevi    QTstressi =
3 0      10.119 3
2.9371      13.024 RQT := regress(QT_elevcf, QTstresscf, 4)                    4              6.3198      15.794 3362.70255            8.6999      17.487 RQT =                          10.3745      17.177 ZQT :=  8.6999,8.701.. Top_Jweld                  -1281.45936 11.5527      16.175 182.93207 12.5802      14.581
                                                      -11.53275 12.9649      18.188 0.27085    )      13.3752      21.559 13.6012    25.687 fQT(ZQT) := interp(RQT, QT_elevcf, QTstresscf,zQT) 26 24 22 fQT(ZQT) 20 QTstresscf oeee 18  -
16 14    -
8.5    9    9.5 10 10.5    11    11.5    12  12.5  13    13.5 14 ZQT* QTelevcf fQT(12.0812) = 15.09487
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 16 of 42 Regression for 50% throughwall stresses:
8.6999  )                    12.883) 10.3745                      15.044 11.5527                        15.56 MDelev cf :=        12.514        MDstresscf := 13.132 12.9649                        15.78 13.3752                      19.292 13.6012)                      24.607)
MD-elevi  MDstressi =
3 0    10.032 3
2.9371    10.766 RMD := regress(MDelevcf, MDstresscf,4)                        4        6.3198    11.377 6270.57353    8.6999    12.883 RMD =                    10.3745    15.044 zMD :=  8.6999,8.701  .. Top Jweld                      -2357.44561 11.5527      15.56 330.23769 12.514    13.132
                                                          -20.39106 12.9649      15.78 0.46849  )  13.3752    19.292 13.6012    24.607 fMD (ZMD) := interp(RMD, MDelevcf, MDstresscf , ZMD)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 17 of 42 26 24 22 20 fMD(ZMD) 18 MDstresscf oeE 16 14  -
12 -
10 .-
8.5  9    9.5  10    10.5    11    11.5  12 12.5 13 13.5    14 ZMD , MD-elev-cf fMD(12.0812) = 14.11569 Repression for 75% throughwaI stresses:
8.6999 )                          7.18 )
10.3745                            8.136 11.5527                            8.89 TQ__0ev-cf      12.4478          TQ~stress-cf :    6.189 12.9649                            11.381 13.3752                            16.085 13.6012)                          22.68 )
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 18 of 42 I-TQelevi        TQstressi =
3 0          9.951 3
2.9371          9.067 RTQ := regress(TQelev cf, TQstresscf, 4)                      4              6.3198          7.821 6772.44513          8.6999            7.18 RTQ =                          10.3745          8.136 ZTQ := 8.6999,8.701 .. Top Jweld                      -2552.34739 11.5527            8.89 358.42617 12.4478          6.189
                                                        -22.21167 12.9649          11.381 0.51271  )      13.3752          16.085 13.6012          22.68 fTQ(zTQ) := interp(RTQ, TQelev cf, TQstress cf,zTQ) 25 22.5 20 17.5 fTQ (ZTQ) 15 TQ stresscf oee 12.5 10  -
7.5 -
5 8.5  9    9.5 10 10.5    11      11.5    12  12.5  13    13.5    14 ZTQ .TQelevcf fTQ(12.0 8 12 ) = 7.37343
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 19 of 42 Regression for OD stresses:
kk := o.. 5 10.3745)                        2.316 )
11.5527                          2.74 12.3816                        -0.109 OD elev cf :=                    ODstresscf :=
_    _      12.9649                        8.207 13.3752                        9.729 13.6012)                      44.523 )
OD-elevi  ODstressi =
('      3 0      9.936 3
2.9371      7.453 4                      4.387 ROD := regress(ODelevcf ,OD_stressCf, 4                                6.3198 1.83727X 10l    8.6999      2.298 ROD =                      10.3745      2.316 ZOD := 10.3745,10.376.. Top Jweld                    -62394.03658 11.5527      2.74 7925.4618 12.3816    -0.109
                                                        -446.31291    12.9649      8.207 9.40247  )  13.3752      9.729 13.6012    44.523 fOD(zOD) := interp(ROD,OD elevcf,ODstress cfzoD)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 20 of 42 50 40 30 foD(ZOD) 20 OD stresscf oeE)6 10 0 -
                -10 _
10  10.5 11 11.5      12      12.5 13 13.5  14 ZOD, OD-elev-cf foD(1 2 .0 8 12) = 539079
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 21 of 42 Calculation to develop Stress Profiles for Analysis This analysis for the axial stress regression and the through-wall stress regression is the same as that used for the CEDM Nozzles (in Ref. 7) with the exception that the axial stresses are fit with a fourth-order polynomial, rather than a third-order polynomial, to accomodate greater precision.
      ,.:=    20                  Number of locations for stress profiles Loco := FLCntr - L FLCntr = 12.0812 L = 0.4
          ,,:=  1..N+3                              Incr; :=  co if i < 4 IncStrs.avg otherwise Loci := Loci-, + Incri SID; = RID3 + RID4Loci + RID .(Loci) 2 + RID *(Loc) 3 + RID *(Loc;)4 SQT;      RQT3 + RQT4 Loci + RQT .(Loci) 2 + RQT *(Loci)3 + RQT. (Loci)4 3
SMD := RMD3+ RMD4Loci + RMD .(Loci) 2 + RMD *(Loc;) + RMD *(Loc;)4 STQ; = RTQ3 + RTQ4- Loci + RTQ5 .(Loc1 ) 2 + RTQ *(Loci)3 + RTQ7*(Loc;) 4 SOD; = ROD + ROD4Loci + ROD .(Loci) 2 + ROD *(Loc;)3 + ROD *(Loc;)4 j:= i..N SIDj + S+Dj+D+ SIDj+2 if . _                              SQTj + SQTj+ 1 + SQTj+2 if j = 1 Sid . =                      3          ifJ-= I              Sqtj :
dJ3                                                                              3 Sid    *(j + I) + SIDj+2                                  sqt (  ij + 1) + SQTj+2 J l                  otherwise                                                    otherwise j+2                                                    j+2
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 22 of 42 Smd  =  SMDj + SMDj+l + SMDj+2 if j = I      St~i = STQj + STQj+1 + STQj+2 if j = I J                ~~~~~3                  tqj                3 Smd    I(j + i) + SMDj+ 2                    Stq.] 4(j + 1) + STQj+2 ji                    otherwise          i-I    ~otherwise j+2                                        j+2 5 od SODj + SODj+l + SODj+ 2
:                                if j = I 3
Sod    *(j + 1)+ SODj+2 otherwise j+2
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 23 of 42 Through-Wall Stress Distribution for ID Flaws (i.e. ID to OD Stress distribution)
U0 := 0.000            U  := 0.25              u 2 := 0.50        U3 := 0.75                  U4  = 1.00 Y := stack(uIuiu          2 ,u 3 ,u 4 )
SIGI    stack(Sid, Sqt 19Smd1 . Stq1 9Sod1)                      SIG 2    stack( Sid2 , Sqty Smd2, Stq2, Sod2)
SIG 3    stack( Sid3 Sqty Smd 3 Stq 3 ' Sod 3 )                    SIG 4    stack( Sid 4 , Sqt4 , Smd 4 , Stq 4 , Sod 4 )
SIG5    stack(Sid5 Sqt5 smd 5 Stq5 S od 5 )                      SIG 6    stack (Sid6    Sqt6 Smd6 Stq 6 ' Sod6)
SIG 7 = stack(    7dSqt7y  Smd7' SStq7 sSod 7 )                  SIG8 := stack (Sid 8 'Sqt8 'Smd 8 'Stq 8 'Sod )
8 SIG 9 := stack(Sid 9 Sqt9 ' Smd9 9Stq 9 -Sod 9 )                  SIG 10 = stack(Sidlo* sqtl0 S'mdl0 Stq I Sod 0)
SIG II := stack(Sid l, Sqtl'l Smd , ' Stq,,'Sod )                  SIG 1 2 := stack(Sid1 2 ' Sqt1 2 ' Smd1 2 ' 5 tq[ 2 ' od 12) 11 SIG 13 = stack(Sid, Sqt 13 ' Smd 13 ' Stq13 ' Sod13 )              SIG 14 := stack(Sid14 ' Sqt14 'Smd1 4 'Stq14 Sod14 )
SIG 15 := stack(Sid  5 Sqtj 5 ISmd 15 ' Stq1I, Sod 15 )          SIG 1 6 := stack (Sid1 6 Sqt 6'Smd1 6 'tq        16  'Sod 16 )
SIG 1 7 = stack(Sid 7'Sqt7'Smd 7'Stq[ 'od                )        SIG 1 8 = stack(Sid18 ' Sqt1 ' Smdl            tq 18 Sod18 )
17 SIGI9 := stack(Sid    ,9Sqt,XSmd 9      Stql 9 sod19)            SIG 2 0 := stack(Sid2 0 ' Sqt2 0 Smd 2 0 ' Stq 2 0 'Sod 2 0 )
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 24 of 42 Regression of Through-Wall Stress distribution to Obtain Stress Coefficients Using a Third Order Polynomial IDRG I    regress(Y, SIG 1 , 3)                                IDRG2      regress(Y,SIG 2 ,3)
IDRG 3    regress(Y, SIG 3 ,3)                                  IDRG 4    regress(Y, SIG 4 ,3)
IDRG 5    regress(Y,SIG 5 ,3)                                  IDRG 6    regress(Y,SIG 6 ,3)
IDRG 7    regress(Y,SIG 7 ,3)                                  IDRG 8    regress(Y,SIG 8 ,3)
IDRG 9    regress(Y, SIG 9 , 3)                                IDRGio      regress(Y,SIG 1 0 ,3)
IDRG  1    regress(Y,SIGI 1,3)                                IDRG 12      regress( Y, SIG 1 2 ,3)
IDRG 1 3    regress(Y,SIG 1 3 ,3)                              IDRG 1 4    regress(YSIG14,3)
IDRG 1 5    regress(Y,SIG 1 5 ,3)                              IDRG1 6      regress(Y,SIGI 6 ,3)
IDRG17      regress(Y,SIG 1 7 ,3)                              IDRG 1 8    regress(Y,SIG 1 8 ,3)
IDRG1 9    regress(Y,SIG 1 9 ,3)                              IDRG 2 0    regress(Y, SIG 2 0,3)
Stress Distribution in the tube. Stress influence coefficients obtainedfrom thrid-orderpolynomial curvefit to the throughwallstress distribution
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 25 of 42 Data Files for Flaw Shape Factors from NASA SC04 Model [Ref. 8]
(NO INPUT Required)
Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=
0          n1        2 0        1.000      0.200      0.000 1        1.000      0.200      0.200 2        1.000      0.200      0.500
_        1.000      0.200      0.800 4        1.000      0.200      1.000 5        1.000      0.400      0.000 6        1.000      0.400      0.200 7_      1.000      0.400      0.500 8        1.000      0.400      0.800 18        1.000      0.400      1.000 9        TWO0      1.000      0.000
[11        1.000      1.000      0.200 12        1.000      1.000      0.500 3      1.000      1.000      0.800
[4        1.000      1.000      1.000 is        2.000      0.200      0.000 16        2.000      0.200      0.200 17        2.000      0.200      0.500 18l      2.000      0.200      0.800
_19      2.000      0.200      1.000 01      2.000      0.400      0.000 121        2.000      0.400      0.200 12    2.000      0.400      0.500 21        2.000      0.400      0.800 22        2.000      0.400      1.000 2.000      1.000      0.000 2.000      1.000      0.200 127        2.000      1.000      0.500 826      2.000      1.000      0.800
      !27        2.000      1.000      1.000 30        4.000      0.200      0.000 31        4.000      0.200      0.200 32        4.000      0.200      0.500 C33-      4.000      0.200      0.800
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 26 of 42 34    4.000 0.200 1.000 35    4.000 0.400 0.000 36    4.000 0.400 0.200 37    4.000 0.400 0.500 37  4.000 0.400 0.800 39    4.000 0.400 1.000 30    4.000 1.000 0.000 41    4.000 1.000 0.200 41  4.000 1.000 0.500 32  4.000 1.000 0.800 44    4.000 1.000 1.000 45    10.000 0.200 0.000 46    10.000 0.200 0.200 47    10.000 0.200 0.500 48    10.000 0.200 0.800 49    10.000 0.200 1.000 50    10.000 0.400 0.000 51    10.000 0.400 0.200 52    10.000 0.400 0.500 63    10.000 0.400 0.800 54    10.000 0.400 1.000 55    10.000 1.000 0.000 56    10.000 1.000 0.200 57    10.000 1.000 0.500 58    10.000 1.000 0.800 59    10.000 1.000 1.000 60  300.000 0.200 0.000 61  300.000 0.200 0.200 21  300.000 0.200 0.500 32  300.000 0.200 0.800 64  300.000 0.200 1.000 65  300.000 0.400 0.000 6  300.000 0.400 0.200 67  300.000 0.400 0.500 68  300.000 0.400 0.800 69  300.000 0.400 1.000 70  300.000 1.000 0.000 71  300.000 1.000 0.200 72  300.000 1.000 0.500 73  300.000 1.000 0.800
_7  300.000 1.000 1.000
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 27 of 42 Sambi :=
0        1      2      3      4        5        6              7 0    1.076    0.693    0.531  0.434    0.608    0.083    0.023          0.009 1    1.056    0.647    0.495  0.408    0.615    0.085    0.027        0.013 2    1.395    0.767    0.557  0.446    0.871    0.171    0.069        0.038 3      2.53  1.174    0.772    0.58  1.554    0.363    0.155          0.085 4    3.846    1.615    0.995  0.716    2.277    0.544    0.233        0.127 5    1.051    0.689    0.536  0.444    0.74    0.112    0.035        0.015 6    1.011    0.646    0.504  0.421    0.745    0.119    0.041          0.02 7    1.149    0.694    0.529  0.435  0.916    0.181    0.073          0.04 8        1.6  0.889    0.642    0.51  1.334    0.307    0.132        0.073 9    2.087    1.093    0.761  0.589    1.752    0.421    0.183        0.101 10    0.992    0.704    0.534  0.506    1.044    0.169    0.064        0.032 11    0.987    0.701    0.554  0.491    1.08    0.182    0.067        0.034 12      1.01  0.709    0.577  0.493    1.116      0.2  0.078        0.041 13      1.07    0.73  0.623  0.523    1.132    0.218    0.095        0.051 14    1.128      0.75  0.675  0.556    1.131    0.229    0.11          0.06 15    1.049    0.673    0.519  0.427      0.6  0.078    0.021        0.008 16    1.091    0.661    0.502  0.413  0.614    0.083    0.025        0.012 17    1.384    0.764    0.556  0.446  0.817      0.15    0.058        0.031 18    2.059    1.033    0.708  0.545      1.3  0.291    0.123        0.067 19    2.739    1.301    0.858  0.643    1.783    0.421    0.18        0.099 20  1.075    0.674    0.527  0.436    0.73    0.072    0.044        0.021 21    1.045    0.659    0.511  0.425    0.76    0.122    0.043        0.021 22      1.16    0.71  0.536  0.441  0.919    0.197    0.064        0.034 23      1.51  0.854  0.623  0.498  1.231    0.271    0.114          0.062 24    1.876    0.995    0.71  0.555  1.519    0.317    0.161          0.089 25    1.037    0.732  0.594  0.505  1.132    0.192      0.07        0.035 26    1.003    0.707    0.577  0.493  1.113      0.19    0.071        0.036 27    1.023    0.714    0.58  0.495  1.155    0.207      0.08        0.042 28    1.129    0.774    0.619  0.521  1.286    0.247    0.098        0.052 29    1.242    0.84    0.661  0.549  1.416    0.285    0.115        0.061 30    1.003    0.649    0.511    0.43  0.577      0.07    0.015        0.005 31    1.097    0.666  0.511  0.426  0.606    0.079    0.023            0.01 32    1.405    0.776  0.567    0.46  0.797    0.141    0.054          0.028 33 0  1.959    0.996  0.692  0.542    1.201  0.262    0.108          0.059 34    2.461    1.197  0.808  0.619    1.586    0.37  0.154          0.085 35    1.024    0.668  0.528  0.451  0.737      0.11  0.033          0.015 36    1.057    0.666    0.52  0.439    0.77  0.123    0.042          0.021 37    1.193    0.715  0.545  0.454  0.924    0.174    0.068          0.036 38    1.443    0.828  0.614  0.509    1.219  0.263    0.109          0.059 39    1.665    0.934  0.681  0.565    1.487  0.339    0.143          0.078 1 nnn    A79    nro7    n n1Q  1110a    n 1RP    n nlAR        nunqA
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 28 of 42
      }>41*  1.009  0.713        0.588  0.511      1.128        0.194 0.072          0.037 42    1.041  0.726        0.594  0.515      1.191        0.214 0.082        0.043 3    1.105  0.768        0.623  0.536      1.316        0.248 0.097          0.05 1.162    0.81        0.653  0.558      1.428        0.277 0.109        0.055 5    0.973  0.635        0.499  0.446      0.579          0.07 0.016        0.005 6    1.115  0.673        0.514  0.438      0.607        0.079 0.023          0.01 7    1.427  0.783        0.571  0.462      0.791        0.138 0.052        0.027 8    1.872  0.96        0.671  0.529      1.179        0.253 0.104        0.056 49    2.23  1.108        0.757  0.594      1.548        0.356 0.149        0.081 50      0.992  0.656          0.52  0.443      0.733        0.109 0.032          0.014 51    1.072  0.672        0.523  0.441      0.777        0.125 0.043          0.021 52      1.217  0.723        0.549  0.456      0.936        0.176 0.069          0.036 53      1.393  0.806        0.601  0.493      1.219        0.259 0.106        0.056 54      1.521  0.875        0.647  0.528      1.469        0.328 0.135        0.071 55      0.994  0.715          0.59  0.518      1.114        0.187 0.068        0.035 6    1.015  0.715        0.588  0.512        1.14        0.197 0.074        0.038 57        1.05 0.729        0.596  0.515      1.219        0.221 0.085        0.044 58      1.09  0.76        0.618  0.532      1.348        0.255 0.099        0.051
      ;59    1.118  0.788        0.639    0.55    1.456        0.282 0.109        0.056 60      0.936  0.62        0.486  0.405      0.582        0.068 0.015        0.005 61      1.145  0.681        0.514    0.42    0.613        0.081 0.024        0.011
      '62    1.459  0.79        0.569    0.454      0.79        0.138 0.051        0.026 63      1.774  0.917        0.641    0.501      1.148        0.239 0.096        0.051 64      1.974  1.008        0.696  0.537      1.482        0.328 0.134          0.07 65      0.982  0.651        0.512    0.427      0.721        0.103 0.031        0.013 1.095 I66    0.677          0.52  0.431      0.782        0.127 0.045        0.022 7    1.244  0.727        0.546    0.446      0.946          0.18 0.071        0.037 68      1.37  0.791        0.585    0.473      1.201        0.253 0.102        0.054 69    1.438  0.838        0.618    0.496      1.413          0.31 0.126        0.066 aQ :=    (2) (2) tW:= Jsb(0)                  X := Jsb'l) au := Sambi(0)              aL := Sambi6 '        aQ := Sambi 2)          ac := Sambi(3)
CU := Sambi(4)              CL := Sambi(5)        cQ := Sambi(6)          cc := Sambi(7)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 29 of 42 n:=    3 if Rt<4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W, X, Y)      VaU := aU      RaU := regress(Mau XVaU, n) faU(WXY):= interp[RaU      ,MaJ, VaU{ xI]
faU(4,.4,'8) = 1.7089            Check Calculation Linear Term MaL := augment(W,X,Y)          VaL := aL              RaL := regress( MaL VaL, n) faL(W, X, Y) := interp{RaL, MaL , VaL, X I1 faL(4,.4,.8) = 0.93393  Check Calculation Quadratic Term MaQ := augment(W, X, Y)      VaQ := aQ              RaQ := regress(MaQ, VaQ, n)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 30 of 42
                                        'W)-
faQ(WX,Y) := interp      IMaQ, VaQ, X CaY)c faQ(4,.4,.8) = 0.67668  Check Calcul/ation Cubic Term MaC := augment(W, X, Y)      VaC := aC        RaC :=regress( MaC,VaC,n)
(W)-
faC(W, X, Y) := interp    MaCVaCsX I faC(4,.4,-8) = 0.54151    Check Calculation
    'IC" Tip Coefficients Uniform Term MCU := augment(W,X,Y)          VCU := CU        RcU :=regress( Mcu,Vcu,n)
            ~~u(WXY)~~W) fcu(4,.4,.8) = 1.31015  Check Calculation Linear Term M& := augment(W, X, Y)        VCL := CL        RcL := regress(McLVcLn)
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 31 of 42 YW)-
fcL(W, X, Y) := interF RcL , McL , VcL , X I
                            -          ~~~y )
fCL( 2 ,.4,.8) = 0.28509        Check Calculation Quadratic Term McQ := augment(W, X, Y)                VCQ := CQ  RcQ := regress( MCQ. VCQ. n)
W)-
fcQ(WX,Y) := interp          McQI VCQ    X I Y)h fCQ(4,.4,.8) = 0.11797      Check Calculation Cubic Term M~c := augment(W, X, Y)                            R~c := regress( Mcc, VcC, n)
KWY fcC(WXY) := interp RcCMCCVCC,            x I
                          -              y )-
Check Calculation
                =0.06384 fCC(4,.4,.8)
Calculations : Recursive calculations to estimate flaw growth
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 32 of 42 Recursive Loop for Calculation of PWSCC Crack Growth CGRsam bi:  j* o ao - ao CO +- CO t *- t2 NCBo +- Cblk while j < Ilim 0 o -  IDRG 1      if cj < co IDRG 2      if co < cj < co + InCStrs.avg IDRG 3 3 if cO + Incstrs.avg < cj < Co + 2-IncS trs.avg IDRG 4 3 if Co + 2 Incstrs.avg < cj < Co + 3 Inc'Strs.avg IDRG5 3 if Co + 3 Incstrs.avg < cj < Co + 4 Inc'Strs.avg IDRG6      if co + 4 InCstrs.avg < Cj _ co + 5-l( 'Strs.avg IDRG 7 33 if CO + 5 IflCstrs avg < Cj < co + 6 Inc'Strs.avg IDRG 8      if cO + 6 InCstrs.avg < cj < cO +  7 Inc'Strs.avg 3
IDRG 9      if C 0 + 7-Incstrs.avg < cj < co + 8fIn( 'Strs.avg 3
IDRGIO        if co + 8 InCStrs.avg < cj _ co +91 IcStrs.avg IDRG 1 1      if co + 9dfCStis.avg < Cj _ co +i1 InlcStrs.avg 3
IDRG 12      if Co+ 10 InCStrs.avg < Cj _Co+1 *Iftrst.avg IDRG 1 3      if co+ 12 Incstrs avg < cj    co +  1  *IflcStrs.avg IDRG 1 4      if co + l2iflCStrs.avg < cj _co +l      *IflcStrs.avg IDRG15        if Co+ 13 flCStrs.avg < cj _ c o + 14IflcStrs.avg 3
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 33 of 42 IDRG 163if      C0 + 4f InCstrs.avg < cj < C0 + 15-Incstrs.avg IDRG 17 3if      CO+ l5d fCStrs avg < cj < C + 16 IncStrs avg IDRG 18      if co+ 16- IncStrsavg < cj < CO+ 17-Incstrs.avg IDRG 19      if Co+ l7-lncStrs.avg < cj < co+ i8flncStrs.avg IDRG 2 0      otherwise 3
IDRG4 if Cj < Co IDRG 2    if co < cj < co + InCStrs.avg IDRG 3    if co + Incstrs.avg < cj < CO + 2-lnCStrs.avg IDRG 4    if CO + 2 lnCStrs.avg < Cj < Co + 3 InCStrs.avg IDRG 5    if co + 3 InCstrs.avg < Cj < C0 + 4 1lCStrs.avg IDRG 6 4 if CO + 4- lCStrs.avg < Cj < Co + 5- lCStrs.avg IDRG 7    if CO + 5s lCStrs.avg < Cj < CO + 6 InCStrs.avg IDRG 84 if Co+ 6 IfnCStrs.avg < Cji        Co+ 7-I&deg;cStrs.avg IDRG 9    if CO + 7-lnCStrs.avg < cj < co + 8lflCStrs.avg IDRG10 4 if co + 8 IncStrs.avg <Cj < CO + 9 lncStrs.avg IDRG 14 if co + 9IlncStrs.avg < cj < co + 10IlnCStrs.avg IDRG 12      if CO + 10 lnCStrs.avg < cj < co + IIl nCStrs.avg 4
IDRG 13      if Co+ I- InCStrs.avg < Cj _ Co+ 12dflCStrs.avg IDRG 14      if co + 12 lncStrs.avg < Cj < co + 13 IlncStrs.avg IDRG 15 4if      cO + 13 IlncStrs.avg < cj < Co + 14 lncStrs.avg IDRG 16      if co + 14 Incstrs.avg < cj < Co + 15 InCStrs.avg 4_.^
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 34 of 42 IL)KU 1 7    it CO+  5 -lnCstrs.avg < cj < CO+ 16 InCsttrs.avg IDRG 184 ifCO + l6-lnCStrs.avg < Cj < Co + 17- InCStrs avg IDRG 1 4 if Co + 17-lncstrs.avg < cj < co + I llncStrs.avg IDRG 2 0      otherwise 4
02 +- IDRG1      if cj < cO IDRG2      ifco < Cj < co + InCStrs.avg IDRG 3      ifCo+ InCStrs.avg < Cj < Co + 2InCStrs.avg IDRG 4      ifCo + 2-InCStrs.avg < cj _ co + 3 IlncStrs.avg IDRG 5      ifCO + 3flncstrs.avg < Cj _ Co + 4-lncstrs.avg IDRG 6 5 ifC + 4lnCStrs.avg < Cj < Co+ 5-        lncStrs.avg IDRG 7      if co+ 5Incstrs.avg < cj < co + 6flCStrs.avg IDRG 8      if  Co + 6-Incstrs.avg < cj < Co+ 7-Incstrs.avg IDRG 9      ifCo+    7-lncStrs.avg < cj < Co + 8-lCStrs.avg ID RG10      ifco + 8-lneStrs~avg < cj < co + 9.ncStrs.avg IDRG 1 0      if cO+ 9lncStrs.avg < Cj < co+ 9&deg;IncStrsavg IDRG 125 if co+ 9O-IncStrs.avg < Cj < co + lIIlnCStrs.avg ID RG 13 5if co + II-lncStrs~avg < cj _ co + 12 lncStrs~avg IDRG 145 if co+ 12.lncStrsavg < Cj < co+ 13IncStrs.avg IDRG 155 if co + 3I-lncStrsavg < Cj < Co+ 4-      Incstrs.avg IDRG 1 6      if co+ 14-IlncStrsavg < cj 5 co+ 153  IncStrs.avg IDRG 1 7      if co+ 14 InlCStrs avg < Cj < c + 6lSIncStrs.avg IDRG 1 7      if co+ 16-Ilncss avg    < cj  co + 17-Incqstravg
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 35 of 42 IDRG 19 5 if co + 17 IlnCStrs.avg < cj < co + 18 lnCStrs avg IDRG 2 0    otherwise 5
IDRG 1    if Cj < Co IDRG 2    if co < cj < co + InCStrs.avg IDRG 3    if co + Incstrs avg < cj < Co + 2-lCStrs.avg IDRG4 6 if Co + 2 IlnCStrs.avg < Cj < Co + 3 IfncStrs avg IDRG 5    if Co + 3flncstrs.avg < cj < Co + 4 InCStrs.avg IDRG 6 6 if Co      4 InCStrs.avg < Cj  C0 + 5-I&deg;cStrs.avg IDRG 7    if co + s lncstrs.avg < Cj < co + 6 lnCStrs.avg IDRG 8    if CO + 6-Incstrs.avg < cj < Co + 7-lncstrs.avg IDRG 9    if Co + 7-lnCstrS.avg < Cj < co + 8. lCStrs.avg 6
IDRG 10 6 if CO + 8 lnCStrs.avg < Cj < co + 9 flncStrs.avg IDRG 116 if co+ 9llncStrs.avg < cj < co + 10dflCStrs.avg IDRG 12 6 if co + II lnCStrs.avg < Cj < Co+ 11 lnCStrs.avg IDRG 1 3    if Co+ ll-lncsttrs.avg < ej < Co+ 12 IlncStrs.avg IDRG14 6 if Co+ 12 IncStrs.avg <cj* Co+ 1_        3 IncStrs.avg 1DRG 1 56 if co + 13 Ilncstrs avg < Cj < co + l4flnCstrs.avg IDRG 1 6 6 if Co+ 14 lnCStrs.avg < Cj < Co + 15 InlCStrs.avg IDRG 1 7    if Co + 15 lnCStrs avg < Cj < C + 16 InCStrs.avg IDRG 186 if CO+ 16 IncStrs.avg < Cj < Co+ 17 InCStrs.avg IDRG 19 6 if Co+ 17 lncStrs.avg < ej < CO + sf Incstrs.avg
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 36 of 42 I IDRG 2 0  otherwise 40 (-- Go 2
0.25taj)3 4*- Go-+0 I{Oy        .ai 1 + 02    (0.25- aj)
Kt    )
(o5aj2        (o.5saj>) 3 42- G0+ Gy                  ++02.(7            +03-      t  )
2 + CTT 0.75*aj 3
    &3<- 00 + Cy I        ai" + 02.(0.75 aj' 00<- C I1()
(o+                    C2      -      + 0 3.y X0      0.0 xi      0.25 X2      0.5 X3      0.75 X4 <- 1.0 X - stack(xx, x2 ,x 3 , x4 )
ST- stack(40          I      2 3' 4)
RG v regress(X, ST, 3) 000 v RG3 + PInt O104v RG 4 020*      RG5 0Y30      RG6 aj ARj        aj Cj aj t
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 37 of 42
-auj a x        J Gal IE faL(RtARjATj)
Gaq    &      faQ(Rt ARj, ATj)
Gacj < faC (Rt, ARj, ATj)
Gcuj          fcU (Rt, ARj, ATJ)
GC1j        fcL(RtARjATj)
Gcq j        fCQ(Rt, ARj, ATj)
GCC; < fcc(Rt, ARj, ATJ)
Qj        l- Il+ 1.464-{2)        if cj 2 aj 1 + 11.464-K1.65 otherwise 0.5 Kaj F (J                    O 00-Gaui + a 10-Gal + (y20-Gaqj + F303Gacj)
KC    -      -_          .(O0Gcuj + CY  IOGCli + 020oGcqj + 30 Gcc3 Ka <--Kaj 1.099 i            i K yj <- K Ci- 1.099
* ai        l9o if Ka01 < 9-0 Ka K      otherwise K* y          9.0o if K , < 9.0 K      otherwise 6
Da;j      CO(Ka          _9.0) n      d-      In    .rP. . . ... if kC  - Qen A
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 38 of 42 agj  I    a  ` inhr -blk  " *jX 4-1o-1&deg;CFinhr-Cblk otherwise Dc - Co.(KY _9.0)11 6 DC j    -  Dc.-CFinhr.Cblk if K , < 80.0 4 - 10    CFinhr Cblk otherwise output(j,O) - j outpukj, 1)      aj OUtPUt(j, 2 )    Cj -CO OUtpUt(j, 3 )    Dag.
OUtPUtkj,4)-      Dcgj output(j,5)      Kaj OUtpUt(j, 6) - KC NCBj OUtpUt(j    7)4- 365-24 OUtpUt(j, 8) - Gau oUtput(j, 9) - Gal output(j, 10) 4    Gaqj output(j, 11)4- Gac.
OUtpUt(j, 12)    - Gcu OUtpUt(j, 13)4-    GOi OUtpUt(j, 14) 4- Gcqj j4-j+l a; - aj 1 + DI,
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 39 of 42 I    I      "rj-l Cj +  Cjd_ + Dcg._j aj E-  lt if aj &#x17d; t aj otherwise NCBj +- NCBj-j + CbIk output KI:= O.. hjim The curve below shows the flaw growth through-wall and the operating time (in years) it takes to go through-wall.
Flaw Growth in Depth Direction 0.6 -
0.5 -
0                                                                          0.401 0.4 _
-C a
0.3 -
2 cD 3
9    0.2 -
0.1 -
I          I      I          I          I  I        I 0
0    5          10      15        20        25  30      35        40 Operating Time {years}
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 40 of 42 The propagation length for the ICI nozzles is defined as the length for which the initial flaw in the blind zone would extend out of the blind zone and grow to a detectable flaw. Reference 11 gives the minimum detectable flaw size of 4 mm (0.16) in length; thus, 0.16 inch was considered as this minimum detectable flaw length. This dimension is added to the end of the blind zone.
BZ length PropLength :=            2      - co + 0.16 2
PropLength      = 0.4 This implies that a flaw initially within the blindzone must grow 0.4 inch to become detectable via UT.
The curve below shows the flaw growth along the length of the ICI nozzle and the operating time (in years) it takes to reach the PropLength value defined above.
2 1.5 I-,-
0 C
S r_
0
_j 0.5 1
2 0
0 fi.
        -0.5
          -1 0        5          10        15        20        25      30      35        40 Operating Time {years}
Thus, a flaw initially 0.4-inch in length, and 0.04-inch in depth (10% through-wall) will not grow in a 40 year operating period.
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 41 of 42 Stress Intensity Factors 100              I          I                      I          I                      I 801 0
U-0 I._
60 _
N-0 c6 va U.
40 _
20 _
l          l                      l          l                      l A.
0            5          10          15          20          25          30          35          40 Operating Time {years}
        -        Depth Point Surface Point
 
Attachment 5 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 42 of 42 Influence Coefficients - Flaw 0.9 0.8 0.7 I 0
0.6
~.)
0 0.5 r-)
.U E.)
0.4 U
0.3 0.2 0.1 0
0          5            I0          15          20        25          30          35          40 Operating time {years}
                "a" - Tip -- Uniform
                    - Tipa -- Linear
            - "a" - Tip -- Quadratic
        -- - "a" - Tip -- Cubic "c" - Tip -- Uniform
        ----- "c' - Tip -- Linear
        -    - tic" - Tip -- Quadratic
        -- - "c" - Tip -- Cubic
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 1 of 42 Arkansas Nuclear One Unit 2 Primary Water Stress Corrosion Crack Growth Analysis for an ICI ID Surface Flaw Uphill (1800), in the Blind Zone above the Top of the J-Groove Weld Developed by Central Engineering Programs, Entergy Operations Inc.
Flaw Case 3: 25% Through-Wall Flaw with a 4-to-1 Flaw Length-to-Depth Aspect Ratio, Located at the Center of the Blind Zone Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to- Thickness Ratio:- "Rlt"- between 1.0 and 300.0 Note:  The Metric forn of the equation from EPRI MRP was used 55-Rev. 1 . A correction factor is applied in the determination of the crack extension to convert the units of meters per second to the            ID Surface Flaw value in inches per hour.
User Input:
The Dominion Engineering Inc. (DEI) finite element model nodal elevations and hoop stresses for the uphill side (1800 azimuth) of the ICI nozzle are brought into the Mathcad worksheet from data supplied in Reference 6d. The data are composed of the nodal elevations (in inches), along with the ID, 25%
through-wall (tw), 50% tw, 75% tw, and OD hoop stresses, beginning at the top of the weld (nodal line 8130 1) and extending to the top of the nozzle in the FEA model, which is at the point where the nozzle intersects the reactor vessel head.
The DEI FEA data has elevation referenced from the bottom of the ICI nozzle. The elevations of the node points in the DEI FEA model, beginning at the top of the weld (nodal line 8130 1), are as follows:
i := 0.. 9 Nodelinei :=      ID-elev-feai := QT_elevyfeai := MD elev feai := TQelev-feai :=              ODelevfeai 81301              4.2276              4.2276              4.2276  .            4.2276        4.2276 81401              4.4536              4.4536              4.4536              4.4536        4.4536 81501              4.8639              4.8639              4.8639              4.8639        4.8639 81601              5.1825              5.2486              5.3148              5.3810        5.4472 81701              6.2761              6.2761              6.2761              6.2761        6.2761 81801              7.4543              7.4543              7.4543              7.4543        7.4543 81901              9.1289              9.1289              9.1289              9.1289        9.1289 82001              11.5090            11.5090              11.5090            11.5090      11.5090 82101              14.8917            14.8917              14.8917            14.8917      14.8917 82201              17.8288            17.8288              17.8288            17.8288      17.8288
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 2 of 42 The corresponding stresses at these nodes are IDstress feai :=    QTstress-feai :=      MDstressfeai :=    TQstressfea1        OD-stress-feai 26.390                25.687                24.607              22.680                44.523 23.147                21.559                19.292              16.085                9.729 19.425                18.188                15.780              11.381                8.207 15.065                14.581                13.132              6.189                -0.109 16.707                16.175                15.560              8.890                  2.74 17.399                17.177                15.044              8.136                2.316 17.412                17.487                12.883              7.180                2.298 17.115                15.794                11.377              7.821                4.387 15.304                13.024                10.766              9.067                7.453 10.308                10.119                10.032              9.951                9.936 Blind Zone and Counterbore Reference dimensions:
From design drawings (Ref. 2a and 2b) and the design input of Attachment 1, the following dimensions are used to locate the counterbore bottom and blind zone locations (bottom, top, and middle) as referenced from the nodal coordinates of the DEI FEA model.
Actualcbore bottom elev := ID-elev feao + 1.377 Actualcborebottomelev = 5.6046 topweldtobottomBZ := 1.08 BZ_length := 0.88 elevtomidBZ := IDelev feaO + topweld to bottomBZ + BZ ength 2
elev_tomid_BZ = 5.7476 bottom-of BZ := IDelevfeaO + topweldtobottomBZ bottomof BZ = 5.3076
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 3 of 42 topof BZ := IDelevfeao + topweldtobottom_BZ + BZ-length top_of BZ    = 6.1876 For stress averaging and fracture mechanics purposes, the reference coordinate system--with a "0" elevation at the bottom of the nozzle, at the ID corner--must be converted into a new coordinate system with the top of the nozzle (nodal line 82201) as the new "0" elevation.. The positive direction along this new coordinate system will be towards nodal line 81301, which is the top of the weld. This modification facilitates a fracture mechanics model more ammenable to the surface flaw loop structure previously developed in Reference 7.
The following iterative loops convert the five (5) through-wall stress components--ID, 25% tw (QT),
50% tw (MD), 75% tw (TQ), and OD--and the associated elevations, initially given in the DEI FEA model, into the "new" coordinate system, referenced from the top of the nozzle where it meets the reactor vessel head.
IDconv :=      Top    v-  ID_elevfea 9 i*-o while j 2 0 IDelevconvi +- Top - ID-elev-feaj ID stressi  v- IDstress feaj output(i, 0) v- IDelev-convi output(i, 1) v- IDstressi j*-j-1 i-    i+1 output IDelev        IDconv(&deg;)
IDstress := ID convy0
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 4 of 42 QTconv := Top      *-  QT-elev-fea 9 j4-9 while j 2 0 QTelev conv; < Top - QTelev fea-QTstressi - QT_stressjfeaj output(i, 0)    QTelev-conv; output(i, I) <- QTstressi pj-l-i-  i+I output QT elev := QTconv(&deg;)
QT-stress := QTconv MDconv :=    Top    &#xf7;- MDelev-fea 9 while j 2 0 MDelevconvi +- Top - MD-elev-feaj MD stress; <- MD stress feaj output( i, 0) - MDelevyconv outpuk i, 1)  *- MDstress; pj-l-i+- i+I output MDelev:= MD conv(&deg;)
MDstress := MD conv(y)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 5 of 42 TQ-conv := Top      <-  TQ-elev fea9 while j 2 0 TQelev-conv;      *- Top - TQelev-feaj TQstress; <- TQstress_feaj output(i,O)  <-  TQ elev convi output(i, 1) <- TQstressi j-j-I i      i+l output TQ-elev := TQconv(&deg;)
TQstress := TQ_conv(y)
OD_conv :=    Top    <-  ODelev-fea9 j-9 1*-  0 while j 2 0 OD_elev convi    - Top - OD elevfeaj OD_stressi <- OD stress feaj output(i, O) <- OD_elevConvi output(i, I) *- ODstress; j    -j-j i-    i+ 1 output OD_elev := OD conv(&deg;)
OD_stress := ODconvy )
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 6 of 42 IDelevi =            QTelevi =            MDelevi =          TQelevi =            OD-elevi 0                    0                    0                  0                    0 2.9371                2.9371              2.9371              2.9371                2.9371 6.3198                6.3198              6.3198              6.3198                6.3198 8.6999                8.6999              8.6999              8.6999                8.6999 10.3745              10.3745              10.3745            10.3745              10.3745 11.5527              11.5527              11.5527            11.5527              11.5527 12.6463              12.5802              12.514            12.4478              12.3816 12.9649              12.9649              12.9649            12.9649              12.9649 13.3752              13.3752              13.3752            13.3752              13.3752 13.6012              13.6012              13.6012            13.6012              13.6012 ID-stressi            QT stress;          MDstressi          TQstressi            OD-stressi 10.308                10.119              10.032              9.951                9.936 15.304                13.024              10.766              9.067                7.453 17.115                15.794              11.377              7.821                4.387 17.412                17.487              12.883                7.18                2.298 17.399                17.177              15.044              8.136                2.316 16.707              16.175                15.56                8.89                  2.74 15.065                14.581              13.132              6.189                -0.109 19.425                18.188                15.78              11.381                8.207 23.147              21.559                19.292              16.085                9.729 26.39              25.687              24.607                22.68                44.523 The two sets of five arrays given above are the elevations measured from the top of the ICI nozzle from the FEA model down to the top of the J-weld and the corresponding hoop stresses in the modified coordinate system (MCS).
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 7 of 42 Additional Geometry in Modified Coordinate System The top of the J-groove weld in the MCS is equal to the last entry in the IDelev array:
Top Jweld := ID-elevg Top Jweld = 13.6012 The location of the top of the UT blind zone (BZ) in the MCS (as measured from the ID surface) is BZtop := Top_Jweld - (topweld tobottomBZ + BZ length)
BZ-top = 11.6412 The midpoint of the BZ in the MCS is BZ mid:= BZ top-l- BZ length BZ mid =    12.0812 The bottom of the BZ in the MCS is BZ bottom := BZ top + BZilength BZbottom =      12.5212 The location of the actual counterbore (from design drawings) in the MCS:
cboreelev := Top Jweld - 1.377 cboreelev = 12.2242
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 8 of 42 From the MCS, the stress distribution from elevation 0 (the top of the ICI nozzle where it intersects the RV head) to the top of the weld is graphically shown below.
Stress Distribution to Top of Weld 40 30 20 0
0.
10 0
      -10 _
0          2          4            6            8            10      12          14 Dist. from Top of nozzle to top weld-in.
          -    ID stress
          .-... 25% tw stress
          ----  50% tw stress 75% tw stress
          -    OD stress For the ID surface flaw model, the reference point is the location along the axis of the nozzle used to locate the flaw. For this analysis, the reference point is considered at the mid-height of the blind zone.
Refpojnt := BZ-mid cIo
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 9 of 42 To place the flaw with respect to the reference point, the flaw tips and center can be located as follows:
: 1) The Upper "c- tip" located at the reference point (Enter 1)
: 2) The Center of the flaw at the reference point (Enter 2)
: 3) The lower "c- tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the point below the blind zone region where stresses will be considered for curve-fitting. This point is taken as the top of the weld, since the stress distribution changes drastically within the weld region Enter this dimension or variable below.
EleVStrs.Dist := Top_Jweld        The elevation to the point of maximum stress to consider (Axial distance from elevation 0 in the MCS).
ICI Nozzle Geometrv Input Data:
od := 5.563 - 0.001            Tube OD, in inches (The value from Ref. 2a, is 5.563" +0.00/-0.001) idI := 4.625 + 0.01            Maximum Tube ID above counterbore, in inches (The value from Ref. 2b is 4.625" +/- 0.010")
id2 := 4.750 + 0.01            Maximum Tube ID below counterbore, in inches (The value from Ref. 2b is 4.750" +/- 0.010")
tI := (od - idI) 2 Minmnum wall thickness above the counterbore, in inches tl = 0.4635 Q := (od - id2) t2~~~
Minimum wall thickness below the counterbore, in inches t2 = 0.401
__od Ro := 2                    o= 2.781 idl Ridl := 2                Ridl = 2.3175
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 10 of 42 Rjd := id2                Rid2 = 2.38 Rid2 R    :=R ml idi  +-
2        Rmi = 2.54925 R m2~ *-R id2 + t2        Rm2 = 2.5805 Rt :                      Rt = 6.43516 Ro
            -= 6.93516 t2 Flaw Geometry Input Data:
A postulated flaw could exist in the 0.88" UT Blindzone that occurs 1.08" above the top of the J-weld at the uphill (1800) location. The flaw length (c) and depth (a) constitute the input parameters. This flaw represents an internal surface crack in a cylinder, as described in Reference 8.
ARO := 4              The flaw length-to-depth aspect ratio. This ratio (4-to-I) is potentially more conducive for through-wall growth than the 6-to-I ratio used in ASME Section t2 .25 = 0.10025      XI, and one sufficient to promote flaw growth through the thickness.
ao = 0.1              Initial Flaw Depth of the ID surface flaw in the blind zone above the top of the weld on the uphill side. The minimum detectable depth of a surface flaw from UT demonstrations [Ref. I1] was 8% throughwall. Conservatively, a 25%
throughwall flaw is assumed. This flaw is sufficiently deep to see the stress field developed through the thickness.
L:= aO-ARO            Initial Flaw Length of an ID surface flaw in the counterbore region, in inches.
The length was determined by assuming a 4-to-I flaw length-to-depth aspect ratio. Half the flaw length (0.2 inch) was placed the below the mid-height of L = 0.4                the blind zone, while the other half was placed above the mid-height.
L Co := 2                The half flaw length used in the fracture mechanics model
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 11 of 42 Additional Input Data:
PInt = 2.235                  Design Operating Pressure (internal) [Ref. 3]
Years := 40                    Number of Operating Years Ilim    g00 0=                    Iteration limit for Crack Growth loop L^:= 604                      Conservative Operating Temperature for the head, in degrees F. Ref. 4 gives a value of 594.8 deg. F following power uprate.
a0C := 2.67-*l-    12          Constant in MRP-55 PWSCC Model for 1-600 Wrought @ 617 deg. F
[Ref. 9]
Qg = 31.0                      Thermal activation Energy for Crack Growth {MRP) [Ref. 9]
Tref := 617                    Reference Temperature for normalizing Data deg. F [Ref. 9]
Timopr      365.2422-24-Years          Numer of operating hours in a year CFinhr :=  1.417-  105                Correction factor to convert meters per second to inches per hour Timopr Cblk:=                                  Calculation block size for the crack growth iteration loop hlim Cblk  = 43.82906 I lim Pmtblk =      50 Temperature Correction for Coefficient Alpha C0                    ~T+459.67 e1.103* Io0~~-3re+496j                                    from EPRI MRP-55, Revision I [Ref. 9]
co:= Locol              75 th percentile from MRP-55 Revision I [Ref. 9]
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 12 of 42 The flaw model used for a postulated flaw within the counterbore region on the uphill side of the ICI nozzle is an internal surface flaw in a cylinder, subject to an arbitrary stress distribution.
To allow for a "moving average" of through-thickness stress values as the flaw extends along the length of the ICI ID surface, the length from the bottom tip of the of the initial flaw in the blind zone to the stress distribution upper limit--Elevsts.Dist--is broken into 20 equal segments. Note that due to the MCS used, with a 0 elevation occurring at the TOP of the nozzle, the term "UTip" (implying the upper tip of the flaw) is actually the physical bottom tip of the flaw, closer to the top of the weld. UTjp is the term used in Reference 7 for the CEDM nozzles, and thus it will continue to be used in the ICI nozzle evaluation.
FLCntr :=-fon            c 0 if Val 1 FL~ntr Refp 0 int
:= -co  if Val= i          Flaw center Location at the mid-point of Refpoint if Val = 2                the blind zone region Refpoint + c 0 otherwise UTip := FLCntr + co UTip    12.2812 EleVStrs.Dist - UTip IncStrs.avg=              20 lcStrs.avg = 0.066 No User Input is required beyond this Point
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 13 of 42 Regression of Through-Thickness Stresses as a Function of Axial Elevation Because of the minor variation in stresses occuring at the top of the nozzle where it intersects the reactor head and the need to accurately curve fit stresses in the region of interest in the BZ, the entire range of stresses is not appropriate to curve fit. To accomodate an area below and above the BZ region, the first two data points in each of the elevation and stress arrays were removed from consideration in the curve fitting equations. This is a reasonable assumption, given that in the completely through-wall tensile stress field that exists in the nozzle above the top of the J-weld, a flaw centered in the BZ region is likely to grow through the thickness entirely (in addition to growth along the surface of the nozzle) rather than grow very long into an area close to the top of the head or below the top of the J-weld (i.e., elevation ranges not included in the stress polynomial curve fit).
Initially, a fourth (4th) order polynomial was chosen for axial stress regression. After regression, the stress at the mid-height of the blind zone (12.0812 inches in the MCS) is checked.
Regression for ID stresses:
k := O.. 6 (8.6999 A 17.412) 10.3745 17.399 11.5527 16.707 ID_elevcf :=      12.6463 IDstresscf :=      15.065 12.9649 19.425 13.3752 23.147 K13.6012) 26.39 )
IDelevi =      ID stressi =
3 0          10.308 3
2.9371          15.304 RID := regress(ID elevcf,ID_stresscf,4)                            4              6.3198          17.115 2920.01158            8.6999          17.412 RID =                            10.3745          17.399
                                                              -1120.32621 11.5527          16.707 161.1276 12.6463          15.065 ZlD := 8.6999,8.701 .. Top Jweld                          -10.23275 12.9649          19.425 0.24206  )        13.3752          23.147 13.6012          26.39 flDD(zlD) := interp(RID,ID elevcf,IDstress cf,zID)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 14 of 42 fID(ZID)
IDstresscf e~e 14                    !            I        I      l      I_
8.5    9    9.5    10  10.5    11      11.5 12 12.5 13 13.5 14 zID, ID-elevcf fID(2.0812 ) = 15.66367 Regression for 25% throughwall stresses:
17.487' 17.177 16.175 QTelev-cf :                        QTstresscf := 14.581 18.188 21.559 25.687)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 15 of 42 QTelevi      QTstressi =
3 0      10.119 3
2.9371      13.024 RQT := regress(QT_elevcf,QTstresscf,4)                        4              6.3198      15.794 3362.70255            8.6999      17.487 RQT =                            10.3745      17.177 ZQT := 8.6999,8.701.. TopJweld                        -1281.45936 11.5527      16.175 182.93207 12.5802      14.581
                                                      -11.53275 12.9649      18.188 k    0.27085    )      13.3752      21.559 13.6012      25.687 fQT(zQT) := interp( RQT, QT_elev cf, QTstresscf, zQT) 26 -
24 22 _
fQT(ZQT) 20 _
QTstresscf oee 18 _
16 14 5 8.5  9    9.5 10  10.5    11      11.5    12  12.5  13    13.5 14 7ZQT, QTelevcf fQT(12.0812) = 15.09487
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 16 of 42 Regression for 50% throughwall stresses:
I-'8.6999  )                    12.883) 10.3745                      15.044 11.5527                      15.56 MDelev cf :=        12.514        MDstresscf := 13.132 12.9649                      15.78 13.3752                      19.292 13.6012)                    24.607)
MD-elevi  MDstressi =
3 0    10.032 3
2.9371    10.766 RMD := regress(MDelevcf,MDstresscf, 4)                      4        6.3198    11.377 6270.57353    8.6999    12.883 RMD =                    10.3745    15.044 zMD := 8.6999,8.701.. Top Jweld                        -2357.44561 11.5527      15.56 330.23769 12.514    13.132
                                                        -20.39106 12.9649      15.78 0.46849  )  13.3752    19.292 13.6012    24.607 fMD(ZMD) := interp(RMD,MDelevcfMDstresscf, ZMD)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 17 of 42 26 12.0812 24 22                                                                    _  _  _
20 fMD(ZMD) 18 MDstresscf eEe 16                                                                      _  _
12                                  _ _ _  _ _ _  _ _  _
10~
8.5  9    9.5  10  10.5    11      11.5    12      12.5 13 13.5      14 ZMD, MD-elev-cf fMD(12.O812) = 14.11569 Regression for 75% throughwall stresses:
8.6999 )                            7.18 )
10.3745                            8.136 11.5527                            8.89 TQjelev-cf :    12.4478          TQ_stresscf :=  6.189 12.9649                            11.381 13.3752                            16.085 13.6012)                          22.68 )
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 18 of42 TQelevi        TQstressi =
3" 0          9.951 3
2.9371          9.067 RTQ := regress(TQelev cf, TQ_stress cf, 4)                  4              6.3198          7.821 6772.44513          8.6999            7.18 RTQ =                        10.3745          8.136 ZTQ := 8.6999,8.701 .. Top Jweld                    -2552.34739 11.5527            8.89 358.42617 12.4478          6.189
                                                      -22.21167 12.9649          11.381 0.51271  )      13.3752          16.085 13.6012          22.68 fTQ(zTQ) := interp(RTQ,TQelev-cf,TQstress cf,zTQ) 25 -
22.5 20 _
17.5 fTQ(ZTQ) 15 _
TQstresscf eee 12.5 _
10  -
7.5 _
5-8.5 9    9.5 10 10.5    11  11.5    12  12.5  13    13.5    14 ZTQ, TQ_elevcf fTQ(1 2 .0812) = 7.37343
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 19 of 42 Regression for OD stresses:
kk := o.. s (10.3745)                          2.316 )
11.5527                          2.74 12.3816                        -0.109 OD_elevcf :f                      OD_stresscf :=
12.9649                        8.207 13.3752                        9.729 t 13.6012)                      44.523 )
OD-elevi  OD_stressi =
(      3      NI 0      9.936 3
2.9371      7.453 4
ROD := regress(ODelevcf,OD_stress_cf,4                                  6.3198      4.387 1.83727X 105      8.6999      2.298 ROD =                      10.3745      2.316 ZOD := 10.3745,10.376.. TopJweld                    -62394.03658 11.5527        2.74 7925.4618 12.3816      -0.109
                                                        -446.31291      12.9649      8.207 9.40247  )  13.3752      9.729 13.6012    44.523 fOD(zOD) := interp(ROD, ODelevcf, OD_stresscf, ZOD)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 20 of 42 50 40 30 fOD(ZOD) 20 OD stress_cf ee6 10 0
                -10 10  10.5 I1 11.5      12      12.5 13 13.5  14 ZOD, OD-elev-cf fOD(12.081 2 ) = 5.39079
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 21 of 42 Calculation to develop Stress Profiles for Analysis This analysis for the axial stress regression and the through-wall stress regression is the same as that used for the CEDM Nozzles (in Ref. 7) with the exception that the axial stresses are fit with a fourth-order polynomial, rather than a third-order polynomial, to accomodate greater precision.
      ,:= 20                  Number of locations for stress profiles Loco:= FLCntr    - L FLCntr = 12.0812 L = 0.4 i:= 1..N +3                                Incr; :=  co if i < 4 IncStrs.avg otherwise Loc;:= Loci- 1 + Incr; 2      D *(L)      + RID *(Loc;)4 SID; := RID3 + RID4Loci + RID '              +
SQT; = RQT3 + RQT 4-Loci + RQT .(Loci) + RQT .(Loci) 3 + RQT. (Loci) 4 SMD; = RMD + RMD4Loci + RMD .(Loc,) + RMD *(Loc;)3 + RMD *(Loc;)4 STQ := RTQ + RTQ4-Loci + RTQ .(Loci) 2 + RTQ *(Loci)3 + RTQ *(Loci)4 SOD := ROD + ROD4 Loci + ROD .(Loci) 2 + ROD *(Loci) 3 + ROD *(Loc;)4 j:= i..N S. t=      SQTJ+SQTj+j+ SQTj+2 if j              1 Siddj. =    SIDj + SIDj+
3  + SlDj+2 if j                            qtj            ~~~~3 Sid . (j+ l) + SIDj+2                                        Sqt(. )(j + 1)+ SQTj+2 J                    otherwise                                    j+_2)              otherwise j+2                                                          j +2
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 22 of 42 STQj + STQj+l + STQj+2      if j = 1 Smd      SMDj + SMDj+l + SMDj+2 if j = I        Stqj .
mj :=3                                                            3 Smd    U(j +  1) + SMDj+2                    stq.  (j + 1)+ STQj+2 JI                    otherwise              1                  otherwise j+2                                        j+2 SODj + SODj+i + SODj+2 Sod -                                if j = I J                    3 5odj.-  Uj + 1)+ SODj+2
                                    )therwise j+2            I
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 23 of 42 Through-Wall Stress Distribution for ID Flaws (i.e. ID to OD Stress distribution)
U0 := 0.000              Ui := 0.25              U2 := 0.50      U3 := 0.75                  U4 = 1.00 Y := stack(u 0 ,u 1 "u2 ,u 3 ,u 4 )
SIG1 = stack(Sid, sqt 1Smd, IStq        1  Sod1)                SIG2 = stack(Sid 2 9Sqy      Smd2 ' tq 2 ' Sod 2 )
SIG 3 = stack(Sid3 Sqty smd3 Stq 3 ' Sod3 )                      SIG 4 = stack (Sid4'Sqt4 Smd4Stq4 Sod 4 )
SIG 5 = stack(Sid 5 Sqt 5 smd5' Stq 5 ' Sod 5 )                  SIG 6 = stack(Sid 6 , Sqt 6 ,Smd 6 'Stq6'Sod 6 )
SIG7 = stack( Sid 7 'Sqt 7 , Smd7 ' Stq 7 ' Sod 7 )              SIG 8 = stack Sid8, Sqt8 , Smd 8 ' Stq8 'Sod 8 )
SIG 9 := stack( Sid9 ' sqt9 , Smd9 ' Stq9 ' Sod 9 )              SIG 10 = stack(Sidio Sqt1 0 's md10 ' Stq1 0 Sod1 0 )
SIG 1 1 := stack (Sid 1, Sqt    , Smd 1  Stq  1  Sod11 )      SIG12 = stack(Sid12S qt1 2 ' Smd2 Stq 'od12)
SIG 13 = stack(Sid13' Sqt 13 ' Smd113 Stq 3' Sod 13 )          SIG 1 4 = stack (Sid 14 ' Sqt14 'Smd14 'Stq14 'Sod1 4 )
SIG 15 = stack(Sid 5 'Sqt 1'Smd' 5 Stq 'Sod 5)                  SIG 1 6 = stack(Sid 16 'Sqt16 'Smd16 ' Stq 16 'Sod16 )
SIG 1 7 = stack( Sid 1'Sqt17' Smd17 '5 tq                      SIG 1 8 := stack (Sid 1 8 ' qt 8' Smd g8 Stq18 ' Sod, )
7  'Sod17 )                                                                8 SIG,    := stack(Sid    '9Sqt  9'Smd 19Stq qSod19)              SIG 2 0 := stack (Sid 2 0 ' Sqt'Smd20' tq 20 Sod2 0 )
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 24 of 42 Regression of Through-Wall Stress distribution to Obtain Stress Coefficients Using a Third Order Polynomial IDRGI      regress(Y,SIGI ,3)                                  IDRG2      regress(Y, SIG 2 ,3)
IDRG 3    regress(Y, SIG 3 ,3)                                  IDRG 4    regress(Y, SIG 4 ,3)
IDRG 5    regress(Y,SIG 5 ,3)                                  IDRG 6    regress( Y,SIG6 ,3)
IDRG7      regress(Y,SIG 7 ,3)                                  IDRG 8    regress( Y,SIG8,3)
IDRG9    regress(Y,SIG 9 ,3)                                  IDRG 10    regress(Y, SIG 1 0 , 3)
IDRG1 I1 :=regress(Y, SIG 1 1 , 3)                              IDRG 12    regress(Y,SIG 12 ,3)
IDRG1 3    regress( Y,SIG 13 ,3)                              IDRG 1 4    regress(YSIG14 ,3)
IDRG1 5    regress(Y,SIG  5 , 3)                              IDRG 1 6    regress(Y,SIG 1 6 ,3)
IDRG 1 7    regress(YSIG 1 7 ,3)                                IDRG1 8      regress(YSIG1 8 ,3)
IDRG 1 9    regress(Y, SIG 19 , 3)                              IDRG 2 0    regress(YSIG 2 0 ,3)
Stress Distribution in the tube. Stress influence coefficients obtainedfrom thrid-orderpolynomial curvefit to the throughwallstress distribution
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 25 of 42 Data Files for Flaw Shape Factors from NASA SC04 Model [Ref. 8]
(NO INPUT Required)
Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=
0          1        2 0        1.000      0.200      0.000 1        1.000      0.200      0.200 2  ;    1.000      0.200      0.500 3        1.000      0.200      0.800 4        1.000      0.200      1.000 5        1.000      0.400      0.000 6        1.000      0.400      0.200 7-      1.000      0.400      0.500 8        1.000      0.400      0.800 9        1.000      0.400      1.000 lb        1.000      1.000      0.000 11        1.000      1.000      0.200 12        1.000      1.000      0.500 I3        1.000      1.000      0.800 i4        1.000      1.000      1.000 15        2.000      0.200      0.000 16        2.000      0.200      0.200 17        2.000      0.200      0.500 18-      2.000      0.200      0.800 19      2.000      0.200      1.000 20        2.000      0.400      0.000 21        2.000      0.400      0.200 22        2.000      0.400      0.500 23        2.000      0.400      0.800 24        2.000      0.400      1.000 25        2.000      1.000      0.000 26        2.000      1.000      0.200 27        2.000      1.000      0.500 28        2.000      1.000      0.800 29        2.000      1.000      1.000 30        4.000      0.200      0.000 31        4.000      0.200      0.200 32        4.000      0.200      0.500 33        4.000      0.200      0.8001
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 26 of 42 34    4.000  0.200 1.000 35    4.000  0.400 0.000 36    4.000  0.400 0.200 3      4.000  0.400 0.500 38    4.000  0.400 0.800 39    4.000  0.400 1.000 40    4.000  1.000 0.000 41    4.000  1.000 0.200 42    4.000  1.000 0.500 43    4.000  1.000 0.800 44    4.000  1.000 1.000 45    10.000  0.200 0.000 6  10.000  0.200 0.200 47d10.000      0.200 0.500 8  10.000  0.200 0.800 49    10.000  0.200 1.000 10.000  0.400 0.000 50    10.000  0.400 0.200 52    10.000  0.400 0.500 53    10.000  0.400 0.800 54    10.000  0.400 1.000 5  10.000  1.000 0.000 65  10.000  1.000 0.200 57    10.000  1.000 0.500 8  10.000  1.000 0.800 98  10.000  1.000 1.000 1300.000 0.200 0.000 61  300.000  0.200 0.200 62  300.000  0.200 0.500 63  300.000  0.200 0.800 64  300.000  0.200 1.000 64 300.000  0.400 0.000 65 300.000  0.400 0.200 7  300.000  0.400 0.500 68  300.000  0.400 0.800 69  300.000  0.400 1.000 76  300.000  1.000 0.000 71  300.000  1.000 0.200 72  300.000  1.000 0.500 73  300.000  1.000 0.800 7    300.000  1.000 1.000
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 27 of 42 Sambi :=
0      I        2      3      4        5          6              7 O    1.076    0.693    0.531  0.434    0.608    0.083      0.023          0.009 1    1.056    0.647    0.495  0.408    0.615    0.085      0.027          0.013 2    1.395    0.767    0.557  0.446    0.871    0.171      0.069          0.038 3      2.53    1.174    0.772    0.58  1.554    0.363      0.155          0.085 4    3.846    1.615    0.995  0.716    2.277    0.544      0.233          0.127 5    1.051    0.689    0.536  0.444    0.74    0.112      0.035          0.015 6    1.011    0.646    0.504  0.421    0.745    0.119      0.041            0.02 7    1.149    0.694    0.529  0.435    0.916    0.181      0.073            0.04 8        1.6  0.889    0.642    0.51  1.334    0.307      0.132          0.073 9    2.087    1.093    0.761  0.589    1.752    0.421      0.183          0.101 10    0.992    0.704    0.534  0.506    1.044    0.169      0.064          0.032 11    0.987    0.701    0.554  0.491    1.08    0.182      0.067          0.034 12      1.01  0.709    0.577  0.493    1.116      0.2    0.078          0.041 13      1.07    0.73  0.623  0.523    1.132    0.218      0.095          0.051 14    1.128    0.75    0.675  0.556    1.131    0.229      0.11            0.06 15    1.049    0.673    0.519  0.427      0.6  0.078      0.021          0.008 16    1.091    0.661    0.502  0.413    0.614    0.083      0.025          0.012 17    1.384    0.764    0.556  0.446    0.817      0.15    0.058          0.031 18    2.059    1.033    0.708  0.545      1.3  0.291      0.123          0.067 19    2.739    1.301    0.858  0.643    1.783    0.421        0.18          0.099 20  1.075    0.674    0.527  0.436    0.73    0.072      0.044          0.021 21    1.045    0.659    0.511  0.425    0.76    0.122      0.043          0.021 22      1.16    0.71  0.536  0.441    0.919    0.197      0.064          0.034 23      1.51  0.854    0.623  0.498    1.231    0.271      0.114          0.062 24  1.876    0.995      0.71  0.555    1.519    0.317      0.161          0.089 5  1.037    0.732    0.594  0.505    1.132    0.192        0.07          0.035 2-6  1.003    0.707    0.577  0.493    1.113    0.19      0.071          0.036 7    1.023    0.714      0.58  0.495    1.155    0.207        0.08          0.042 28    1.129    0.774    0.619    0.521  1.286    0.247      0.098          0.052 29    1.242      0.84  0.661    0.549  1.416    0.285      0.115          0.061 30    1.003    0.649    0.511    0.43  0.577      0.07    0.015          0.005 31    1.097    0.666    0.511  0.426    0.606    0.079      0.023            0.01 32  1.405    0.776    0.567    0.46  0.797    0.141      0.054          0.028 33    1.959    0.996    0.692  0.542    1.201    0.262      0.108          0.059 34    2.461    1.197    0.808  0.619    1.586      0.37    0.154          0.085 35    1.024    0.668    0.528    0.451  0.737      0.11    0.033          0.015 36    1.057    0.666      0.52  0.439    0.77    0.123      0.042          0.021 37  1.193    0.715    0.545  0.454    0.924    0.174      0.068          0.036 8  1.443    0.828    0.614    0.509  1.219    0.263      0.109          0.059 9  1.665    0.934    0.681  0.565  1.487    0.339      0.143          0.078 1 nnr,    n 7,)  A      n rA        ia  n1 1P It  n1nnaI          n nA
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 28 of 42 ov        .vJ  J.D        U.% - I. V-            .-    J.*U V.    .- V          V.-
41      1.009  0.713        0.588    0.511      1.128      0.194 0.072          0.037 42      1.041  0.726        0.594    0.515      1.191      0.214 0.082          0.043 43      1.105  0.768        0.623    0.536      1.316      0.248 0.097            0.05 4&#xa2;4      1.162  0.81      0.653    0.558      1.428      0.277 0.109          0.055 45      0.973  0.635        0.499    0.446      0.579        0.07 0.016          0.005 46      1.115  0.673        0.514    0.438      0.607      0.079 0.023            0.01 47      1.427  0.783        0.571    0.462      0.791      0.138 0.052          0.027 48      1.872  0.96        0.671    0.529      1.179      0.253 0.104          0.056 9      2.23 1.108        0.757    0.594      1.548      0.356 0.149          0.081 50      0.992  0.656        0.52    0.443      0.733      0.109 0.032          0.014 51      1.072  0.672      0.523    0.441      0.777      0.125 0.043          0.021 52      1.217  0.723        0.549    0.456      0.936      0.176 0.069          0.036 53      1.393  0.806        0.601    0.493      1.219      0.259 0.106          0.056 M4    1.521  0.875        0.647    0.528      1.469      0.328 0.135          0.071 i5      0.994  0.715        0.59    0.518      1.114      0.187 0.068          0.035 56      1.015  0.715        0.588    0.512        1.14      0.197 0.074          0.038 57        1.05 0.729        0.596    0.515      1.219      0.221 0.085          0.044 58        1.09  0.76      0.618    0.532      1.348      0.255 0.099          0.051 59      1.118  0.788      0.639      0.55    1.456      0.282 0.109          0.056 60      0.936  0.62      0.486    0.405      0.582      0.068 0.015          0.005 1    1.145  0.681      0.514      0.42      0.613      0.081 0.024          0.011 62      1.459  0.79        0.569    0.454      0.79      0.138 0.051          0.026 63      1.774  0.917        0.641    0.501      1.148      0.239 0.096          0.051 1.974  1.008        0.696    0.537      1.482      0.328 0.134            0.07 65      0.982  0.651        0.512    0.427      0.721      0.103 0.031          0.013 66      1.095  0.677        0.52    0.431      0.782      0.127 0.045          0.022 67      1.244  0.727      0.546    0.446      0.946        0.18 0.071          0.037 68        1.37 0.791      0.585    0.473      1.201      0.253 0.102          0.054 69      1.438  0.838      0.618    0.496      1.413        0.31 0.126          0.066 WA:= MOb()                  X := Jsb(I)            Y : Jsb"L aU := Sambi(0)              aL := Sambi(l)        aQ := Sambi(2)        ac := Sambi(3)
CU := Sambi(4)              CL := Sambi(5)          CQ := Sambi(6)      CC := Sambi(7)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 29 of 42 n:=    3 if Rt<4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W,X,Y)        VaU := aU      RaU := regress(Mau, VaU, n) eWY faU(W,XY) , interp RaU MaU , VaU,    XI1 ChcClultY)o faU(4, 4,.8) = 1.7089          Check Calculation Linear Term MaL := augment(W,X,Y)        VaL := aL              RaL := regress(MaL, VaL, n) faL(W, X, Y) := interp RaL MaL, VaL,    X I
_            k)-
faL(4,4,.8) = 0.93393  Check Calculation Quadratic Term MaQ := augment(W, X, Y)      VaQ := aQ              RaQ := regress(MaQ,VaQ,n)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 30 of 42 QW) faQ(WXY) :=interp faQ (4,.4,.8)      = 0.67668  Check Calculation Cubic Term MaC := augment(W,X,Y)              VaC := aC        RaC := regress(Mac ,VaC ,n)
Kwy faC (W, X, Y) := interp RaC, MaC, VaC,    X I
                              -          ,y )-
faC(4,.4,.8) = 0.54151        Check Calculation "C" Tip Coefficients Uniform Term MCU := augment(W,X,Y)              VCU := CU      RcU :=regress( MCU,VcU,n) fcU(WXY) = nterp RCU, MCU, VCU{XI]
f~~u~~w~~xY)                          )
fcu(4,.4,.8) = 1.31015        Check Calculation Linear Term MCL := augment(W, X, Y)            VCL := CL      RCL := regress(McLVcLn)
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 31 of 42 YW[
fcL (W. X, Y) := interp RcL sMcL MVcL, x I
                          -            ~y )-
fcL(2,.4,.8) = 0.28509          Check Calculation Quadratic Term McQ := augment(W,X,Y)                  VCQ .- CQ  RcQ := regress(McQgVcQn)
W8-fcQ(W XY) := interpl        !McQ'VCQ    X I CY)a fCQ(4,.4,.8) = 0.11797      Check Calculation Cubic Term MCC := augment(W, X, Y)                            R~c := regress( McCVCCn) fCC~X, Y) = inter{RCC            cc,,x        I fcc(4,.4,.8) = 0.06384      Check Calculation Calculations : Recursive calculations to estimate flaw growth
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 32 of 42 Recursive Loop for Calculation of PWSCC Crack Growth CGRsambi:  j -0 aO - aO CO 4- CO t<- t2 NCBo- Cblk while j < Ilim 00o-    IDRG1    if cj < CO IDRG2    if co < cj < co + InCStrs.avg IDRG 3  if co + IncStrs avg < cj S CO + 2-  Incstrs.avg IDRG 4  if CO + 2-Instrs.avg < cj < Co + 3-lncsttrs.avg IDRG 5  if C0 + 3-Incstrs.avg < cj < CO+ 4-lncstrs.avg IDRG 6 3 if CO + 4 flCStrs.avg < Cj < co+ 5InCStrs avg IDRG 7  if c 0 + 5-lnCsttrs.avg < Cj < co+ 6fInCstrsavg IDRG8    if cO + 6-  ncstrs.avg < cj <  C0 + 7-lncstrs.avg IDRG 9  if c 0 + 7-lncstrs.avg < cj < co + 8fInCstrs.avg 10RIO3 if co + 8-Inc Strs avg < cj <~ co+ 9-ncStrs~avg IR 113 if co + 9- IncStrs avg < cj < co+ 10-IncStrs.avg IDRG 123 if cO+ If lnCStrs.avg < Cj < co + IlncStrs.avg IDRG 13    if cO+ lII-ncStrs.avg < Cj < C0 + l12flncStrs.avg IDRG 1 43 if co+ 12.lncStrs.avg < cj < co + 13IlnCStrs.avg IDRG 1 5  if co+ 13 IncStrs avg < cj < cO + 14 IlncStrs.avg
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 33 of 42 IDRG 1 6 3 if Co + 14-flCStrs.avg < cj < Co + 15 Incstrs.avg IDRG 1 7 3 if Co + 15 Ifncstrs.avg < cj < CO + 16- IncStrs avg IDRG 1 8    if CO+ 16-InCStrs avg < cj < Co+ 17- IlncStrs.avg IDRG 1 9    if Co + 17- Ilncstrs.avg < cj < co + 18 flncStrs.avg IDRG 20      otherwise 3
0 c I v- IDRG  4  if cj < co IDRG 2    if co < cj < co + InCStrs.avg IDRG 3    if co + Incstrs.avg < cj < C0 + 2 lncstrs.avg IDRG 4    if Co + 2-lncstrs.avg < cj < Co + 3-InCStrs.avg IDRG 5    if co + 3-lncStrs.avg < Cj < C0 + 4 lncStrs.avg IDRG 6    if Co + 4-Incstrs.avg < cj  < co + 5 lnCStrs.avg IDRG 7    if Co + 5-IlnCStrs.avg < cj  < co + 6fnCStrs.avg IDRG 8    if co + 6-Incstrs.avg < cj < C0 + 7 lncStrs.avg IDRG 9    if C0 + 7-lncstrs.avg < Cj  < co + 8- fCStrs.avg IDRGIO4 if co + 8.IncStrs.avg < cj < co + 9 IlncStrs.avg IDRGI 14 if cO + 9-IncStrs.avg < cj < co + l olncStrs.avg IDRG124 if co + IOlncStrs.avg < cj < co + 11 I-lCStrs.avg IDRG 13 4 if co + 11 I-lncStrs.avg < cj < C0 + 12 lncStrsavg IDRG 1 4    if cO + 12 lncStrs.avg < Cj < co + 13I lncStrs.avg IDRG 15 4 if co + 13 -lncStrs.avg < Cj < co + 14 lncStrs.avg IDRG 1 6    if c 0 + 14 IlncStrs.avg < cj < co + 15 InCStrs.avg 4
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 34 of 42 Il)KU 1 7  it Co+ 15 flncstrs.avg < Cj < Co+ 16lnCStrs.avg IDRG 1 8    ifCo+ 16 IncStrs avg < Cj < Co+ 17 4lCStrs.avg IDRG1 94 ifCo+ 17-IlncStrsavg < Cj < Co+ 18lncStrs.avg IDRG 2 0    otherwise IDRG 1    if Cj < Co IDRG 2    ifco < cj < co + InCStrs.avg IDRG 3    ifCO + Ilncstrs.avg < Cj < Co + 2 lnCStrs.avg IDRG 4    if Co + 2flncstrs.avg < Cj < co + 3llncStrs.avg IDRG 5    ifCO + 3flncstrs.avg < Cj < Co+ 4flncStrs.avg 5
IDRG 6    if c 0 + 4flncstrs.avg < cj < co+ 5lfncStrs.avg IDRG 7    if Co + 5IlnCstrs.avg < Cj < Co + 6-IfCStrs.avg IDRG 8    ifCo + 6flncstrs.avg < cj < CO + 7lncStrs.avg IDRG 9    if co + 7-Incstrs.avg < cj < co+ 8 Incstr.avg IDRG 10    ifco + 8flncstrs.avg < cj < co + 9flncStrs.avg IDRGI15 ifco+ 9lncStrs.avg < cj < CO + 10IflnCStrs.avg IDRG 1 2 5 if co + 10 IlncStrs.avg < cj < co + lllncStrs avg IDRG1 3 5 if co+ IIIncStrs.avg < cj < Co + 12 IlncStrs.avg IDRG 14 5 if co +      l2IncStrs.avg < cj < cO + 13lncstrs.avg IDRG 1 5    if co+ 13IncStrs avg < Cj < Co+ 14flCStrs.avg IDRG1 6 5 if CO+ 14-lncStrs.avg < Cj < cO+ 15-IncStrs avg IDRG1 7    if co+ 15 Incstrs.avg < cj < co + 16Incstrs.avg IDRGIR      ifco+ 16-I1nCtrq      v < Cj < Co+ 17fnCRtrz vo
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 35 of 42 IDRG 19      if Co + 17  InCstrs.avg < Cj < co + 18- IncStrs.avg IDRG 2 0      otherwise 5
03
* IDRGI      if Cj < Co IDRG 2 6 if eo < Cj < c 0 + IflCstrs.avg 6
IDRG 3      if C0 + IflCstrs avg < Cj < C0 + 2*InCStrs.avg IDRG 4 6 if co + 2-IncStrs.avg < Cj < CO + 3 InCStrs avg IDRG 5      if co+ 3 IncStrs.avg < cj < Co + 4 Infcstrs avg IDRG66 if Co + 4 InCStrs avg < Cj < Co + 5-InCStrs avg IDRG 7      if  co + 5 IfCStrs.avg < Cj < co + 6 1lCStrs.avg IDRG 8 6 if co + 6 IncStrs.avg < cj < Co + 7 Incstrs avg IDRG 9      if co + 7 lncStrs avg < Cj < Co + 8 InCStrs avg 6g IDRG 1 0      if cO+ 8 lnCStrs.avg < Cj < co + 9 lncStrs.avg IDRG I I      if co + 9Ifncstrs avg < Cj < co + i olnCStrs.avg IDRG 1 2      if co + 1.Incstrs.avg I              < cj < co + llInclCstrs.avg IDRG 1 3      if co+ II lncstrs.avg < cj < co+ 12 lncStrs.avg DRG 1 4 6 if CO+ 12 IfncStrs.avg < Cj < c 0 + 13 lncStrs.avg IDRG 1 5      if c 0 + 13 1ncstrs.avg < Cj < co + 14 InCstrs.avg 6
IDRG 1 6      if co+ 14 Incstrs.avg < Cj < co+ 15dlCStrs avg IDRG 17      if Co+ 15lInCStrs.avg < Cj < co+ 16 lncStrs.avg IDRG 18      if CO + 16 IfncStrs.avg < Cj < C0 + 17 IlnCStrs.avg 6
IDRG 1 9      if co + 17dfncStrs.avg < cj
* co + l8 AflcStrs. avg 6
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 36 of 42 IIDRG 2 0      otherwise to-    Go t.25-aj)                    (0.25-aj)3 a1+-CO+(
t)                            t)
I).5-aj)                        0.5-aj)3 42 (-- G~O+ cYI'                  + 02{)+    +
t      )                        t  )
O.5aJ>F2 {t)      + 3 43 (--YO+GI
~44(- G0+ CFI'(    I1_0__j                _ 2_    ( 1.0-aj '3 X0    0.0 x-    0.25 x2    0.5 X3 - 0.75 X+- stack(xO,xI,x          2 ,x 3 x 4 )
STY stack(40,412,43,4)
RG      regress(X, ST, 3) o0 0-    RG3 + PInt 010<- RG4 020--RG5 o 3 0 <- RG6 ARj v-Cj aj t
G+ -f 1 1 ,(R..AR;.AT;A
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 37 of 42
-au.    -
Gal    - faL(Rt, ARj, ATj) j Gaq    &  faQ(RtARj ,ATj)
Gacj.      faC(RtARjATJ)
GCUj      fcU(RtARj,ATj)
Gcl-      fcL(RtARjATj)
Gcq v fcQ(RtARiATj)
GCCj      fCC(Rt, ARj ,ATj)
I +1.464{2aj)      1.65  if cj 2 aj I + 1.464    C1        otherwise Kaj <      (0    O    .-
O0Gaui        +0ciOs Galij+ ay 2O.Gaqj + cy3O-Gacj)
KcCi    (r Qj )      -(OOGcuj+          alOGclj+020      Gcqj +  30 Gccj Ka + Ka; 1.099 KyYJ          i K~C*'1.099 Ka            9.o if Ka < 9.0 Ka    otherwise J
KTi Ky    otherwise Da + Co.(Ka              9.0)    6 n      Z    In    (CF.  .    ... if k-      .- enn
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 38 of 42 Iaa "aj        minhr -blk    "  " X 4- 10  - CFin        Chblk otherwise D~j +-Co (Kj-9.0) 1.16 DCgi -      Dcj CFinhr.Cblk if K            < 80.0 4        10-CF ~inhr -Cblk otherwise output(j, o)    -  j output(j,i ) - aj outputj ,2) - Cj - CO OUtpUt(j, 3) & Dagj OUtPUt(j, 4) & Dcg.
OUtpUt(j, 5) & Ka output(j, 6) - KC NCBj Outpukjs7)    v    -365.24 outpukj, 8) & Gau output(j, 9)        Gai output(j, 10)  <    Gaq.
output(j, I1)& Gac outpukj, 12) < GCuj OUtPUt(j, 13)      - Gcl OUtpUt(j, 14) 4- GCqj output(j, 15)    -    Gcc j4-j+1 aj  - aj.. + DI0
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 39 of 42
                                  ' bj-l Cj E CjI_ + Dcg._j aj  - It  if aj &#x17d; t aj otherwise NCBj  -- NCBjj + Cblk output o.. hrim The curve below shows the flaw growth through-wall and the operating time (in years) it takes to go through-wall.
Flaw Growth in Depth Direction 0.6                                                                      23.34 0.5 Cs                                        ................................            0.401                          '
0.4 0.3 0.2 0.1 0                        I                    I                    I        I 0          5            10                  15                    20      25      30 Operating Time {years}
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 40 of 42 The propagation length for the ICI nozzles is defined as the length for which the initial flaw in the blind zone would extend out of the blind zone and grow to a detectable flaw. Reference 11 gives the minimum detectable flaw size of 4 mm (0.16) in length; thus, 0.16 inch was considered as this minimum detectable flaw length. This dimension is added to the end of the blind zone.
BZ length PropLength        =    2        Co + 016 PropLength = 0.4 This implies that a flaw initially within the blindzone must grow 0.4 inch to become detectable via UT.
The curve below shows the flaw growth along the length of the ICI nozzle and the operating time (in years) it takes to reach the PropLength value defined above.
2 20.98 1.5 0.5                                                                                  0.4-0
      -0.5
        -1 0            5            10            15          20          25                30 Operating Time {years}
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 41 of 42 Stress Intensity Factors 100 80 0
60 (n
cn C
40 U.
20 0        5      10            15          20 25  30 Operating Time {years}
      - Depth Point Surface Point
 
Attachment 6 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 42 of 42 Influence Coefficients - Flaw 3
2.5 2
C:
E 0.L)                                                                          /
0L)
E    1.5
.U E.)
U 0)
C:                                                                            -
                              -~~~~~~~~~~~~~~~~                                    - -
                                                                        ~~~~--      - --  - -  -  - - -
0.5
_ ~ ~ ~    -          -  - - - -  -
0 0              5                10              15            20            25                30 Operating time {years}
                "a" - Tip -- Uniform
          -----  "a" - Tip -- Linear
          -    - "a" - Tip -- Quadratic
          -- - "a" - Tip -- Cubic "c" - Tip -- Uniform
          -----  "c'- Tip -- Linear
          -    - "c" - Tip -- Quadratic
          --  - "c" - Tip -- Cubic
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 1 of 42 Arkansas Nuclear One Unit 2 Primary Water Stress Corrosion Crack Growth Analysis for an ICI ID Surface Flaw Uphill (1800), in the Blind Zone above the Top of the J-Groove Weld Developed by Central Engineering Programs, Entergy Operations Inc.
Flaw Case 4: Flaw Spanning the Full Length of the Blind Zone (0.88 Inch) with a 6-to-1 Aspect Ratio Calculation Basis: MRP 75 th Percentile and Flaw Face Pressurized Mean Radius -to- Thickness Ratio:- "Rm/t" - between 1.0 and 300.0 Note: The Metric form of the equation from EPRI MRP was used 55-Rev. I . A correction factor is applied in the determination of the crack extension to convert the units of meters per second to the            ID Surface Flaw value in inches per hour.
User Input:
The Dominion Engineering Inc. (DEI) finite element model nodal elevations and hoop stresses for the uphill side (1800 azimuth) of the ICI nozzle are brought into the Mathcad worksheet from data supplied in Reference 6d. The data are composed of the nodal elevations (in inches), along with the ID, 25%
through-wall (tw), 50% tw, 75% tw, and OD hoop stresses, beginning at the top of the weld (nodal line 81301) and extending to the top of the nozzle in the FEA model, which is at the point where the nozzle intersects the reactor vessel head.
The DEl FEA data has elevation referenced from the bottom of the ICI nozzle. The elevations of the node points in the DEI FEA model, beginning at the top of the weld (nodal line 81301), are as follows:
i := O.. 9 Nodelinei          ID elev-feai        QTelevfeai := MDelev feai := TQelevfeai :=              ODelev_feai 81301              4.2276              4.2276              4.2276              4.2276        4.2276 81401              4.4536              4.4536              4.4536              4.4536        4.4536 81501              4.8639              4.8639              4.8639              4.8639        4.8639 81601              5.1825              5.2486              5.3148              5.3810        5.4472 81701              6.2761              6.2761              6.2761              6.2761        6.2761 81801              7.4543              7.4543              7.4543              7.4543        7.4543 81901              9.1289              9.1289              9.1289              9.1289        9.1289 82001              11.5090            11.5090              11.5090            11.5090      11.5090 82101              14.89 17            14.8917              14.8917            14.8917      14.8917 82201              17.8288            17.8288              17.8288            17.8288      17.8288
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 2 of 42 The corresponding stresses at these nodes are IDstress-feai :=    QTstress-feai :=      MDstressfeai        TQstressfeai        ODstressfeai :=
26.390                25.687                24.607              22.680                44.523 23.147                21.559                19.292              16.085                9.729 19.425              18.188                15.780              11.381                8.207 15.065              14.581                13.132              6.189                -0.109 16.707              16.175                15.560                8.890                  2.74 17.399              17.177                15.044              8.136                  2.316 17.412                17.487                12.883              7.180                  2.298 17.115                15.794                11.377              7.821                  4.387 15.304                13.024                10.766              9.067                  7.453 10.308                10.119              10.032              9.95 1                9.936 Blind Zone and Counterbore Reference dimensions:
From design drawings (Ref. 2a and 2b) and the design input of Attachment 1, the following dimensions are used to locate the counterbore bottom and blind zone locations (bottom, top, and middle) as referenced from the nodal coordinates of the DEI FEA model.
Actualcborebottomelev := IDelev feao + 1.377 Actual cbore bottom elev = 5.6046 topweldto bottom BZ :=1.08 BZ_length := 0.88 elevtomidBZ := IDelev feaO + topweld to bottomBZ + BZ length 2
elevtomidBZ = 5.7476 bottomof BZ := ID elev feaO + topweld to bottomBZ bottomof BZ = 5.3076
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 3 of 42 topof BZ := IDelev feao + topweldtobottomBZ + BZ-length topof BZ = 6.1876 For stress averaging and fracture mechanics purposes, the reference coordinate system--with a "0" elevation at the bottom of the nozzle, at the ID corner--must be converted into a new coordinate system with the top of the nozzle (nodal line 82201) as the new "0" elevation.. The positive direction along this new coordinate system will be towards nodal line 81301, which is the top of the weld. This modification facilitates a fracture mechanics model more ammenable to the surface flaw loop structure previously developed in Reference 7.
The following iterative loops convert the five (5) through-wall stress components--ID, 25% tw (QT),
50% tw (MD), 75% tw (TQ), and OD--and the associated elevations, initially given in the DEI FEA model, into the "new" coordinate system, referenced from the top of the nozzle where it meets the reactor vessel head.
IDconv :=      Top - ID_elevfeag while j > 0 IDelevconvi      v- Top - ID-elev-feaj ID stressi  v- IDstress feaJ output(i, 0) v- IDelev-convi output(i, 1) v- IDstressi j*-j-1 i-  i+l output IDelev =IDconvo&deg;)
IDstress := ID convy)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 4 of 42 QTconv := Top <- QTelev-fea9 j*-9 while j 2 0 QTelev convi +- Top - QT elev fea-QTstress;i    QTstressjfeaj output( , 0) - QTelev-conv; outputki, 1)  QTstress;
                      -ij-I i- i+
output QTelev := QTconv(&deg;)
QTstress := QTconv(')
MDconv :=    Top +- MDelev-fea 9 j*-9 while j > 0 MDelevconv; +- Top - MD-elev-feaj MDstress; <- MD stress feaj output(iO) < MD_elev-conv; outputk, I) E- MDstress; i<-- i+l output MDelev:= MD conv(o)
MDstress:= MD convy)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 5 of 42 TQconv :=    Top    *- TQelevfea9 while j > o TQelev-conv; <- Top - TQelev-feaj TQstress;    i- TQstressjfeaj output( i 0) <- TQ elevConv; output(i, I) <- TQstressi i-- i+  1 output TQ elev := TQ conv(&deg;)
TQstress := TQconvy)
ODconv :=    Top <- OD-elevfeag j*-9 1i<- 0 while j > 0 OD_elev-convi <- Top - ODelevfeaj ODstressi <- OD_stressfeaj output(i, 0) <- OD elev conv; output(i, 1) <- ODstress; j    j-i-
i*-~i+
output ODelev := OD-convo)
OD stress := OD convy )
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 6 of 42 IDelevi =            QT~e~evi  =          MDelevi =          TQelevi =            OD-elevi 0                                          0                  0                    0 2.9371                                    2.9371              2.9371                2.9371 6.3198                                    6.3198              6.3198                6.3198 8.6999                                    8.6999              8.6999                8.6999 10.3745                                    10.3745            10.3745              10.3745 11.5527                                    11.5527            11.5527              11.5527 12.6463                                    12.514            12.4478              12.3816 12.9649                                    12.9649            12.9649              12.9649 13.3752                                    13.3752            13.3752              13.3752 13.6012                                    13.6012            13.6012              13.6012 IDstressi            QTstressi            MDstressi          TQstressi            OD stress; 10.308                10.119              10.032              9.951                9.936 15.304                13.024              10.766              9.067                7.453 17.115                15.794              11.377              7.821                4.387 17.412                17.487              12.883                7.18                2.298 17.399                17.177              15.044              8.136                2.316 16.707                16.175                15.56                8.89                  2.74 15.065                14.581              13.132              6.189                -0.109 19.425                18.188                15.78              11.381                8.207 23.147                21.559              19.292              16.085                9.729 26.39              25.687              24.607                22.68                44.523 The two sets of five arrays given above are the elevations measured from the top of the ICI nozzle from the FEA model down to the top of the J-weld and the corresponding hoop stresses in the modified coordinate system (MCS).
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 7 of 42 Additional Geometry in Modified Coordinate System The top of the J-groove weld in the MCS is equal to the last entry in the IDelev array:
TopJweld := ID elevg Top jweld = 13.6012 The location of the top of the UT blind zone (BZ) in the MCS (as measured from the ID surface) is BZtop := Top_Jweld - (topweld tobottomBZ + BZ length)
BZ-top = 11.6412 The midpoint of the BZ in the MCS is BZmid := BZ top + BZ length 2
BZ mid = 12.0812 The bottom of the BZ in the MCS is BZbottom := BZ-top + BZilength BZbottom = 12.5212 The location of the actual counterbore (from design drawings) in the MCS:
cboreelev := Top Jweld - 1.377 cboreelev = 12.2242
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 8 of 42 From the MCS, the stress distribution from elevation 0 (the top of the ICI nozzle where it intersects the RV head) to the top of the weld is graphically shown below.
Stress Distribution to Top of Weld 40 30 L... 20 0.
0
  =
10 0
      -10 0            2        4            6            8            10    12          14 Dist. from Top of nozzle to top weld-in.
            -        ID stress
              ----- 25% tw stress
            ---- 50% tw stress 75% tw stress
            -        OD stress For the ID surface flaw model, the reference point is the location along the axis of the nozzle used to locate the flaw. For this analysis, the reference point is considered at the mid-height of the blind zone.
Refpoint := BZ-mid C1Z
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 9 of 42 To place the flaw with respect to the reference point, the flaw tips and center can be located as follows:
: 1) The Upper "c- tip" located at the reference point (Enter 1)
: 2) The Center of the flaw at the reference point (Enter 2)
: 3) The lower "c- tip" located at the reference point (Enter 3).
Val := 2 The Input Below is the point below the blind zone region where stresses will be considered for curve-fitting. This point is taken as the top of the weld, since the stress distribution changes drastically within the weld region Enter this dimension or variable below.
ElevStrsDist := Top Jweld        The elevation to the point of maximum stress to consider (Axial distance from elevation 0 in the MCS).
ICI Nozzle Geometry Input Data:
od := 5.563 - 0.001            Tube OD, in inches (The value from Ref. 2a, is 5.563" +0.00/-0.001) idI := 4.625 + 0.01            Maximum Tube ID above counterbore, in inches (The value from Ref. 2b is 4.625" +/- 0.010")
id2 := 4.750 + 0.01            Maximum Tube ID below counterbore, in inches (The value from Ref. 2b is 4.750" +/- 0.010")
tl :(od - idi) 2 Minmum wall thickness above the counterbore, in inches tl = 0.4635 Q :=(od - id2) t2~~~
Minimum wall thickness below the counterbore, in inches a    = 0.401 od Ro = 2.781 id 1 Ridi :=2                  Ridl  = 2.3175
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 10 of 42 id2 Rid2 = 2                Rid2 = 2.38 RmlR:=    R + ~~ti2
:=Rdl              Rmi = 2.54925 R m2 *- R id2 + 22      Rm2 = 2.5805 Rm2 Rt :=                    Rt = 6.43516 Ro
            = 6.93516 t2 Flaw Geometry Input Data:
A postulated flaw could exist in the 0.88" UT Blindzone that occurs 1.08" above the top of the J-weld at the uphill (1800) location. The flaw length (c) and depth (a) constitute the input parameters. This flaw represents an internal surface crack in a cylinder, as described in Reference 8.
ARij:= 6              The flaw length-to-depth aspect ratio. This is a ratio common to ASME Section XI, and one sufficient to promote flaw growth through the thickness.
I.:= BZiength          Initial Flaw Length of an ID surface flaw in the counterbore region, in inches.
The length was set equal to the full length of the UT blind zone (0.88 inch).
Flaw depth was based on a common length-to-depth aspect ratio of 6-to-1.
Half the flaw length (0.44 inch) was placed the below the mid-height of the L = 0.88            blind zone, while the other half was placed above the mid-height.
L a( :=    -            Initial Flaw Depth of the ID surface flaw in the blind zone above the top of the AR0            weld on the uphill side. The minimum detectable depth of a surface flaw from UT demonstrations [Ref. I 1] was 8% throughwall. This flaw equates to ao = 0.14667 36.58% through-wall. This flaw is sufficiently deep to see the stress field developed through the thickness.
t2-.36575 = 0.14667
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 11 of 42 Co  := 2              The half flaw length used in the fracture mechanics model Additional Input Data:
PInt := 2.235            Design Operating Pressure (internal) [Ref. 3]
Years := 40              Number of Operating Years Ilim = 8000              Iteration limit for Crack Growth loop IL:= 604                Conservative Operating Temperature for the head, in degrees F. Ref. 4 gives a value of 594.8 deg. F following power uprate.
a0c := 2.67 12      Constant in MRP-55 PWSCC Model for 1-600 Wrought @ 617 deg. F
[Ref. 9]
Qg := 31.0              Thermal activation Energy for Crack Growth {MRP) [Ref. 9]
Tref := 617              Reference Temperature for normalizing Data deg. F [Ref. 9]
Timopr:= 365.2422-24-Years      Numer of operating hours in a year CFinhr := 1.417-105              Correction factor to convert meters per second to inches per hour Timopr Cblk:= - Iim                      Calculation block size for the crack growth iteration loop
            =4im Chik = 43.82906
                'urn Prntblk :=      50 Col :
11Qg        _      - re  1
          .O3 101 3T+459.67 Tref+459.67)J Temperature Correction for Coefficient Alpha from EPRI MRP-55, Revision I [Ref. 9]
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 12 of 42 C0 := Loc    1        75  t  percentile from MRP-55 Revision I [Ref. 9]
The flaw model used for a postulated flaw within the counterbore region on the uphill side of the ICI nozzle is an internal surface flaw in a cylinder, subject to an arbitrary stress distribution.
To allow for a "moving average" of through-thickness stress values as the flaw extends along the length of the ICI ID surface, the length from the bottom tip of the of the initial flaw in the blind zone to the stress distribution upper limit--Elevsts.Dit--is broken into 20 equal segments. Note that due to the MCS used, with a 0 elevation occurring at the TOP of the nozzle, the term "UTip" (implying the upper tip of the flaw) is actually the physical bottom tip of the flaw, closer to the top of the weld. UTip is the term used in Reference 7 for the CEDM nozzles, and thus it will continue to be used in the ICI nozzle evaluation.
FLCntr =-e~on                c 0 if ValiX FL~ntr Refp 0 int
:= -co    if Val          Flaw center Location at the mid-point of Refpoint if Val = 2                the blind zone region Refpoint + c 0 otherwise UTip := FLCntr +co UTip      12.5212 ElevStrs.Dist    - UTip ncStrs.avg                  20 IncStrs.avg = 0.054 No User Input is required beyond this Point
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 13 of 42 Regression of Through-Thickness Stresses as a Function of Axial Elevation Because of the minor variation in stresses occuring at the top of the nozzle where it intersects the reactor head and the need to accurately curve fit stresses in the region of interest in the BZ, the entire range of stresses is not appropriate to curve fit. To accomodate an area below and above the BZ region, the first two data points in each of the elevation and stress arrays were removed from consideration in the curve fitting equations. This is a reasonable assumption, given that in the completely through-wall tensile stress field that exists in the nozzle above the top of the J-weld, a flaw centered in the BZ region is likely to grow through the thickness entirely (in addition to growth along the surface of the nozzle) rather than grow very long into an area close to the top of the head or below the top of the J-weld (i.e., elevation ranges not included in the stress polynomial curve fit).
Initially, a fourth (4th) order polynomial was chosen for axial stress regression. After regression, the stress at the mid-height of the blind zone (12.0812 inches in the MCS) is checked.
Regression for ID stresses:
k := O.. 6 8.6999 )
17.412) 10.3745 17.399 11.5527 16.707 IDelev cf := 12.6463                IDstresscf :=      15.065 12.9649 19.425 13.3752 23.147 13.6012) 26.39 )
IDelevi =      ID-stressi =
3 0          10.308 3
2.9371          15.304 RID := regress(IDelevcf, ID_stresscf, 4)                          4              6.3198          17.115 2920.01158            8.6999          17.412 RID =                            10.3745          17.399
                                                              -1120.32621 11.5527          16.707 161.1276 12.6463          15.065 ZID := 8.6999,8.701.. Top Jweld                          -10.23275 12.9649          19.425 0.24206  )        13.3752          23.147 13.6012          26.39 flD(zID) := interp(RID,ID elevcf, IDstresscf,zID)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 14 of 42 fID(ZID)
IDstresscf E3e 8.5    9  9.5    10  10.5    11      11.5 12 12.5 13 13.5 14 ZID, ID elev-cf frD(1 2 .0812) = 15.66367 Regression for 25% throughwall stresses:
8.6999 )                          17.487) 10.3745                            17.177 11.5527                            16.175 QTelev-cf :=      12.5802          QT~stress-df      14.581 12.9649                            18.188 13.3752                            21.559 13.6012)                          25.687)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 15 of 42 QTstressi =
* 3 10.119 3
13.024 RQT := regress(QT_elevcfQTstress-cf,4)                    4                      15.794 3362.70255                    17.487 RQT =                                  17.177 ZQT := 8.6999,8.701.. Top_Jweld                    -1281.45936 16.175 182.93207 14.581
                                                    -11.53275 18.188 0.27085    )                21.559 25.687 fQT(zQT) := interp(RQT,QT elevcf,QT stresscf,zQT) 26 fQT(ZQT)
QTstresscf eee 14 .5 8.5  9    9.5 10 10.5    11    11.5    12  12.5 13 13.5 14 zQT, QT_elevcf fQT(02.0812 ) = 15.09487
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 16 of 42 Regression for 50% throuahwall stresses:
8.6999 )                      12.883) 10.3745                      15.044 11.5527                        15.56 MDelev cf :=      12.514          MDstresscf := 13.132 12.9649                        15.78 13.3752                      19.292 13.6012)                      24.607)
MD-elevi  MDstressi =
                                                        '      3 0    10.032 3
2.9371    10.766 RMD := regress(MDelevcf, MDstresscf, 4)                        4        6.3198    11.377 6270.57353    8.6999    12.883 RMD =                      10.3745    15.044 zMD := 8.6999,8.701.. Top Jweld                          -2357.44561 11.5527      15.56 330.23769 12.514    13.132
                                                          -20.39106 12.9649      15.78 0.46849  )  13.3752    19.292 13.6012    24.607 fMD(zMD) := interp(RMD,MDelevcf ,MDstress_cf          ,zMD)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 17 of 42 fMD(ZMD)
MDstresscf oeee 10    - .L.
1 8.5    9    9.5  10  10.5    11    11.5  12 12.5 13 13.5      14 ZMD, MD-elev-cf fMD(12.0812) = 14.11569 Regression for 75% throuahwall stresses:
8.6999 )                            7.18 )
10.3745                            8.136 11.5527                            8.89 TQjelev-cf :    12.4478          TQstresscf :=    6.189 12.9649                            11.381 13.3752                            16.085 13.6012)                          22.68 )
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 18 of 42 TQelevi        TQstressi =
3 0            9.951 3
2.9371            9.067 RTQ := regress(TQelev-cf,TQ~stresscf, 4)                  4              6.3198            7.821 6772.44513          8.6999            7.18 RTQ =                      10.3745            8.136 zTQ := 8.6999,8.701 .. Top Jweld                    -2552.34739 11.5527            8.89 358.42617 12.4478            6.189
                                                    -22.21167 12.9649          11.381 0.51271  -)      13.3752          16.085 13.6012            22.68 fTQ(zTQ) := interp(RTQ, TQelev cf, TQstresscf, zTQ) 25 22.5 20 17.5 fTQ (ZTQ) 15 TQstresscf oee 12.5  -
10 7.5 _
5-8.5  9    9.5 10 10.5    11  11.5    12    12.5  13    13.5    14 ZTQ, TQelevcf fTQ(12.0812) = 7.37343
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 19 of 42 Regression for OD stresses:
kk := o.. 5 10.3745)                        2.316 )
11.5527                        2.74 12.3816                        -0.109 ODelev cf :=                    ODstress_cf :=
12.9649                        8.207 13.3752                        9.729 13.6012)                      44.523 )
OD-elevi  OD_stressi =
3 0      9.936 3
2.9371      7.453 4          6.3198      4.387 ROD := regress(ODelevcfODstress_cf,4 1.83727X 105    8.6999      2.298 ROD =                    10.3745      2.316 ZOD := 10.3745,10.376.. TopJweld                    -62394.03658 11.5527      2.74 7925.4618 12.3816    -0.109
                                                      -446.31291    12.9649      8.207 9.40247  )  13.3752      9.729 13.6012    44.523 foD(zoD) := interp(ROD,OD elevcf, OD stresscf,ZOD)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 20 of 42 fOD(ZOD)
ODstresscf 6Eee
_10      ,  _    I,_II 1o    10.5    11 11.5      12      12.5 13 13.5  14 ZOD, OD elevcf foD(12.0812) = 5.39079
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 21 of 42 Calculation to develop Stress Profiles for Analysis This analysis for the axial stress regression and the through-wall stress regression is the same as that used for the CEDM Nozzles (in Ref. 7) with the exception that the axial stresses are fit with a fourth-order polynomial, rather than a third-order polynomial, to accomodate greater precision.
    ,,:=    20                  Number of locations for stress profiles Loco:= FLCntr - L FLCntr = 12.0812 L = 0.88 i:= i..N+3                                  Incr := lco if i < 4 Incstrs.avg    otherwise Loci := Loci-, + Incri SIDi = RID3 + RID 4 -Loci + RID .(Loci) + RID 6(Loci) 3 + RID *(Loc;)4 SQTJ = RQT3 + RQT 4-Loci + RQT 5(Locj) 2 + RQT *(Loc;) + RQT *(Loc;)4 SMD := RMD3+ RMD 4Loci + RMD5 (Loci)            2 + RMD *(Loci)3 + RMD *(Loc;)4 STQ; = RTQ3 + RTQ4 -Loci + RTQ5 (Loci) 2 + RTQ .(Loc;) 3 + RTQ. (Loci) 4 SODi = ROD + ROD *Loci + ROD *(Loci) + ROD6 (Locj)                3 + ROD (Loc;) 4 3        4            5.6N j:=1.. N SIDj + SlDj+j + SIDj+2                            S    ;=    SQTJ + SQTj+1 + SQTj+2 if j =
Sid. =3if                                J=I                  qt=                    3 j            ~~~~~3 Sid  *(j + I) + SIDj+2                                      Sqt      (j + 1) + SQTj+2 (J_1)                    otherwise J  ~          ~      otherwise j+2                                                            j+2
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 22 of 42 SMDj + SMDj+l + SMDj+2 if j = 1            STQj + STQj+l + STQj+2 S md- :-                                      Stqj =                              if j = I J                    3                                        3 Smd    *(j + I) + SMDj+2                  stq  G(j +  1) + STQj+2 j-l                    otherwise                                  otherwise j+2                                      j+2 SODj + SODj+j + SODj+ .)
Sod. =                            I if j=I J                    3 Sod    *(j + I) + SODj+2 otherwise j+2
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 23 of 42 Through-Wall Stress Distribution for ID Flaws (i.e. ID to OD Stress distribution)
U0 :=0.000                u1 := 0.25            u 2 := 0.50    u3 := 0.75                u 4 = 1.00 Y := stack(u 0 u 1 ,u 2 ,u 3 ,u )
4 SIG 1 = stack(Sid[,Sqt      CSmd,    Stq, sod )                SIG2 = stack(Sid 2 sqt2 9Smd 2 Stq2 Sod2 )
SIG 3 = stack( Sid3, Sqt 3 Smd3 'Stq 3 ' Sod 3)                SIG 4 = stack( Sid 4 9Sqt 4 Smd4 9Stq 4 Sod4)
SIG 5 := stack(Sid 5 Sqt 5 Smd59Stq 5 9Sod5 )                  SIG 6 = stack (Sid 6 9Sqt 6 9Smd 6 9 tq6    od 6 )
SIG 7 := stack(Sid7Sqt7 lSmd 9 Stq ' Sod )                      SIG8 = stack (Sidg SqtsSmd,9StqSod8) 7    7    7 SIGg := stack( Sid' Sqtq9 Smd 9 'Stq9 'sod )                    SIG,    := stack (Sid1 0 sqt1 0 Smd10 Stq        sod10) 9                                                            0 SIG 1, 1 := stack(Sid 1'Sqtl ,Smdl 1Stq11 sSod
: 1)                        (
SIG 12 = stack Sid 2 ' Sqt12 ' Smd12 , Stq12 ' Sod12)
SIG 1 3 := stack(Sid1 Ssqt1 Smd 3        3    13 'Stq1 3 Sod13 )                        (
SIG 14 = stack Sid 4 ' Sqt 14 ' Smd 4 ' Stq 4 ' Sod14)
SIG 1 5 := stack(Sid, 9Sqt 5'Smd                              SIG16 = stack(Sid6Sqt61Smd'6' 5                  Stq15 Sod, 5 )                                      6tq16          '6 od16)
SIG  17  = stack(Sid17 ' Sqt17 ' Smd17 'Stq17' Sod1 )
7
(
SIG 1 8 := stack Sid18' Sqt, 8 ' Smd S'tq I,,od 18                18)
SIGIg := stack(Sid      , Sqt19 Smd 19 Stqj99 Sod19)          SIG 2 0 := stack( Sid20 Sqt20 'Smd2O 'tq2O od20)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 24 of 42 Regression of Through-Wall Stress distribution to Obtain Stress Coefficients Using a Third Order Polynomial IDRG 1    regress(Y,SIG 1 , 3)                                  IDRG 2    regress(Y, SIG 2 ,3)
IDRG 3    regress(Y, SIG3 , 3)                                  IDRG4      regress(YSIG 4 ,3)
IDRG 5    regress( Y, SIG 5 ,3)                                IDRG6      regress(Y, SIG 6 ,3)
IDRG7    regress(YSIG 7 ,3)                                    IDRG8      regress(Y,SIG 8 ,3)
IDRG9 := regress(YSIG 9 ,3)                                    IDRGIO:= regress(Y,SIG 1 0 ,3)
IDRG I I    regress(Y, SIG I 1, 3)                              IDRG 1 2    regress(Y,SIG 1 2 ,3)
IDRG1 3    regress(YSIG13 ,3)                                  IDRG 1 4    regress(YSIG1 4 ,3)
IDRG 1 5    regress(Y,SIG  15  ,3)                            IDRG 1 6    regress(Y,SIG 1 6 ,3)
IDRG1 7    regress(Y,SIG  1 7 ,3)                            IDRG1 8      regress(Y,SIG18 ,3)
IDRG 19    regress( Y, SIG 19 , 3)                            IDRG 2 0    regress(YSIG 2 0 ,3)
Stress Distribution in the tube. Stress influence coefficients obtainedfrom thrid-orderpolynonmal curvefit to the throughwall stress distribution
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 25 of 42 Data Files for Flaw Shape Factors from NASA SC04 Model [Ref. 8]
(NO INPUT Required)
Mettu Raju Newman Sivakumar Forman Solution of ID Part throughwall Flaw in Cyinder Jsb :=  -  .
0          1        2 0        1.000      0.200      0.000 1        1.000      0.200      0.200 2        1.000      0.200      0.500 3        1.000      0.200      0.800 4        1.000      0.200      1.000 5        1.000      0.400      0.000 6        1.000      0.400      0.200 7        1.000      0.400      0.500 8        1.000      0.400      0.800 9        1.000      0.400      1.000 70        1.000      1.000    0.000 11        1.000      1.000    0.200 12        1.000      1.000    0.500 13        1.000      1.000    0.800 14        1.000      1.000    1.000 15        2.000      0.200      0.000 16        2.000      0.200      0.200 17        2.000      0.200      0.500 18        2.000      0.200      0.800 19        2.000      0.200      1.000 20        2.000      0.400      0.000 21        2.000      0.400      0.200 22        2.000      0.400      0.500 23        2.000      0.400      0.800 24        2.000      0.400      1.000 25_        2.000      1.000      0.000 26        2.000      1.000      0.200 22        2.000      1.000    0.500 28        2.000      1.000    0.800 29        2.000      1.000      1.000 30        4.000      0.200      0.000 31        4.000      0.200      0.200 32    31 4.000      0.200      0.500 0.800 33~      4.000      0.200      0.800
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 26 of 42 34    4.000  0.200 1.000 35    4.000  0.400 0.000 36    4.000  0.400 0.200 37    4.000  0.400 0.500 38    4.000  0.400 0.800 39    4.000  0.400 1.000 40_    4.000  1.000 0.000 41    4.000  1.000 0.200 42    4.000  1.000 0.500 42    4.000  1.000 0.800 44    4.000  1.000 1.000 45  10.000    0.200 0.000 46_  10.000    0.200 0.200 47  10.000    0.200 0.500 48  10.000    0.200 0.800 49  10.000    0.200 1.000
.5  10.000    0.400 0.000 51  10.000    0.400 0.200 52  10.000    0.400 0.500 53  10.000    0.400 0.800 541  10.00    0.400 1.00
_5  10.000    1.000 0.
56  10.000    1.000 0.200 57  10.000    1.000 0.500 58  10.000    1.000 0.800 59  10.000    1.000 1.000 60  10300.000      0.000 61  300.000    0.200 0.200 62  300.000    0.200 0.500 63  300.000    0.200 0.800 4  300.000    0.200 1.000 5  300.000    0.400 0.000 66  300.000    0.400 0.200 72 300.000    0.400 0.500 N 300.000    0.400 0.800 9  300.000    0.400 1.000 70  300.000    0.400 0.000 71  300.000    1.000 0.200 72  300.000    1.000 0.500 73  300.000    1.000 0.800 74  300.000    1.000 1.000
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 27 of 42 Sambi :=
0        1      2      3      4        5          6              7 O    1.076  0.693  0.531  0.434    0.608    0.083      0.023          0.009 1    1.056  0.647  0.495  0.408    0.615    0.085      0.027          0.013
        .2    1.395  0.767  0.557  0.446    0.871    0.171      0.069          0.038 3      2.53    1.174  0.772    0.58  1.554    0.363      0.155          0.085 4    3.846    1.615  0.995  0.716    2.277    0.544      0.233          0.127 5    1.051  0.689  0.536  0.444    0.74    0.112      0.035          0.015 6    1.011  0.646  0.504  0.421    0.745    0.119      0.041            0.02 7    1.149  0.694  0.529  0.435    0.916    0.181      0.073            0.04 8        1.6  0.889  0.642    0.51  1.334    0.307      0.132          0.073 9    2.087    1.093  0.761  0.589    1.752    0.421      0.183          0.101 10    0.992  0.704  0.534  0.506    1.044    0.169      0.064          0.032 11    0.987    0.701  0.554  0.491    1.08    0.182      0.067          0.034 12      1.01  0.709  0.577  0.493    1.116      0.2    0.078          0.041 13      1.07    0.73  0.623  0.523    1.132    0.218      0.095          0.051 14    1.128    0.75  0.675  0.556    1.131    0.229        0.11          0.06 15    1.049  0.673  0.519  0.427      0.6  0.078      0.021          0.008 16    1.091  0.661  0.502  0.413    0.614    0.083      0.025          0.012 17    1.384  0.764  0.556  0.446    0.817    0.15      0.058          0.031 18    2.059    1.033  0.708  0.545      1.3  0.291      0.123          0.067 19    2.739    1.301  0.858  0.643    1.783    0.421        0.18          0.099 20    1.075  0.674  0.527  0.436    0.73    0.072      0.044          0.021 1    1.045  0.659  0.511  0.425    0.76    0.122      0.043          0.021 2      1.16    0.71  0.536  0.441    0.919    0.197      0.064          0.034 3      1.51  0.854  0.623  0.498    1.231    0.271      0.114          0.062 4    1.876  0.995    0.71  0.555    1.519    0.317      0.161          0.089 25    1.037  0.732  0.594  0.505    1.132    0.192        0.07          0.035 26    1.003  0.707  0.577  0.493    1.113    0.19      0.071          0.036 27    1.023  0.714    0.58  0.495  1.155    0.207        0.08          0.042 28    1.129  0.774  0.619    0.521  1.286    0.247      0.098          0.052 29    1.242    0.84  0.661    0.549  1.416    0.285      0.115          0.061 30    1.003  0.649  0.511    0.43  0.577    0.07      0.015          0.005 31    1.097  0.666  0.511    0.426  0.606    0.079      0.023            0.01 32    1.405  0.776  0.567    0.46  0.797    0.141      0.054          0.028 33    1.959  0.996  0.692    0.542  1.201    0.262      0.108          0.059 34    2.461    1.197  0.808    0.619  1.586    0.37      0.154          0.085 3      1.024  0.668  0.528    0.451  0.737    0.11      0.033          0.015 6    1.057  0.666    0.52  0.439    0.77    0.123      0.042          0.021 7    1.193  0.715  0.545    0.454  0.924    0.174      0.068          0.036 8    1.443  0.828  0.614    0.509  1.219    0.263      0.109          0.059 39  1.665  0.934    0.681  0.565  1.487    0.339      0.143          0.078 UFl    1flA,    n7)    n r07  n riA    1110l    1l PAAR                  ffMA
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 28 of 42
      .41    1.009  0.713      0.588    0.511    1.128      0.194 0.072        0.037 42      1.041  0.726      0.594    0.515    1.191      0.214 0.082        0.043 43      1.105  0.768      0.623    0.536    1.316      0.248 0.097          0.05 44      1.162  0.81      0.653    0.558    1.428      0.277 0.109        0.055 45      0.973  0.635      0.499    0.446    0.579        0.07 0.016        0.005 46      1.115  0.673      0.514    0.438    0.607      0.079 0.023          0.01 47      1.427  0.783      0.571    0.462    0.791      0.138 0.052        0.027 48      1.872  0.96      0.671    0.529    1.179      0.253 0.104        0.056 49      2.23  1.108      0.757    0.594    1.548      0.356 0.149        0.081 50      0.992  0.656        0.52    0.443    0.733      0.109 0.032        0.014 51      1.072  0.672      0.523    0.441    0.777      0.125 0.043        0.021 52      1.217  0.723      0.549    0.456    0.936      0.176 0.069          0.036 3    1.393  0.806      0.601    0.493    1.219      0.259 0.106        0.056 1.521  0.875      0.647    0.528    1.469      0.328 0.135        0.071
        ;5    0.994  0.715        0.59    0.518    1.114      0.187 0.068        0.035 6    1.015  0.715      0.588    0.512      1.14      0.197 0.074          0.038 57      1.05 0.729      0.596    0.515    1.219      0.221 0.085          0.044 58      1.09  0.76      0.618    0.532    1.348      0.255 0.099          0.051 59    1.118  0.788      0.639    0.55    1.456      0.282 0.109          0.056 30    0.936  0.62      0.486    0.405    0.582      0.068 0.015          0.005 1    1.145  0.681      0.514    0.42    0.613      0.081 0.024          0.011
        ;2    1.459  0.79      0.569    0.454      0.79      0.138 0.051          0.026
        ;3    1.774  0.917      0.641    0.501    1.148      0.239 0.096          0.051 1.974  1.008      0.696    0.537    1.482      0.328 0.134          0.07
        ;5    0.982  0.651      0.512    0.427    0.721      0.103 0.031          0.013 6    1.095  0.677        0.52    0.431    0.782      0.127 0.045          0.022
        ;7    1.244  0.727      0.546    0.446    0.946        0.18 0.071          0.037 1.37 0.791      0.585    0.473    1.201      0.253 0.102          0.054 69    1.438  0.838      0.618    0.496    1.413        0.31 0.126          0.066 A := JsbMO                  X := Jsbi(I)        Y := Jsb(2) au := Sambi(&deg;)              aL := Sambie )      aQ := Sambi(2)      aC := Sambi(3)
CU := Sambi(4)              CL := Sambi(5)      CQ := Sambi(6)      CC := Sambi(7)
 
Attachment 7 to Eng- Report No. M-EP-2003-003, Rev. 0 Page 29 of 42 n:=    3 if Rt< 4.0 2 otherwise "a-Tip" Uniform Term MaU := augment(W,X,Y)        VaU := aU      RaU := regress( MaUtVaUn)
                ~~u~~xY  intrl{aU    aU  VaU{XI faU(4,.4,.8) = 1.7089            Check Calculation Linear Term MaL := augment(W, X, Y)        VaL := aL              RaL := regress( MaL, VaL, n)
W]
faL (W, X,Y) :                        x I faL(4,.4,.8) = 0.93393  Check Calculation Quadratic Term MaQ := augment(W,X,Y)        VaQ := aQ              RaQ := regress(MaQ, VaQ, n)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 30 of 42 faQ (W,XY):=interp[RaQ, MaQ9VaQ{x              I1 faQ(4,.4,.8) = 0.67668        Check Calculation Cubic Term MaC := augment(W, X, Y)          VaC := aC        RaC := regress( MaC, VaC, in)
_nte a  ,    VaC,  (W)I faC (Wx,XY) := interp RaC, MaC, VaC,      X I
_                KY)-
faC(4,.4,.8) = 0.54151        Check Calculation
  'C" Tip Coefficients Uniform Term McU := augment(W,X,Y)                VC=Cu        RcU := regress(McU, VcU, n)
XY):=interp RcU, McuVCU, x I]
fcU(W f~~u~~wXY)y                            )
fCU(4, 4,-8) = 1.31015      Check Calculation Linear Term M& := augment(W, X, Y)            V& :=  CL        RCL := regress(McLVcLn)
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 31 of 42 rcL(WXY)L        W' fcL(W, X, Y) := interp RcL sMcL , VcL, x I
_              'Y)_
fcL(2,.4,.8) = 0.28509          Check Calculation Quadratic Term McQ := augment(W, X, Y)                VCQ .=CQ    RcQ := regress( McQ, VCQ ,n)
_            ~~~W)-
fcQ(W, X, Y) := interp RcQ, McQ, VcQ{X I f    MyD) fCQ (4,.4,.S) = 0. 11797    Check Calculation Cubic Term MCC := augment(W, X, Y)                            R~c := regress(Mcc, VcC, n) fC
(, ,Y):=inter{ RcCC M~CCC,            xI1 fcc(4,4,.8) = 0.06384        Check Calculation Calculations: Recursive calculations to estimate flaw growth
 
Attachment 7 to Eng. Report No. M-EP-2003-003. Rev. 0 Page 32 of 42 Recursive Loop for Calculation of PWSCC Crack Growth CGRsambi:"- j*-0 ao *aO co  *- Co t - t2 NCBo    - Cblk while j < Ilim o-    IDRG 3 if cj < cO IDRG 2      if CO < cj < CO + InCStrs.avg 3
IDRG3      if co + IncStrs.avg < Cj < CO + 2 IncStrs.avg IDRG 4      if co + 2 IflCstrs avg < Cj < CO + 3 IflCstrs avg 43 IDRG5      if CO + 3 InCstrs.avg < Cj < CO + 4 InCStrs.avg IDRG 6      if CO  + 4' Incstrs.avg < cj < co + 5lfnCStrs avg 3
IDRG 7      if Co + 5slCStrs.avg < Cj < C0 + 6I fCStrs.avg IDRG 8 3 if co + 6-InCStrs.avg < Cj < co + 7-InCStrs avg IDRG9        if CO + 7-lncStrs.avg < Cj < CO + 8 InCStrs.avg IDRG1 0 3 if co + 8 InCStrs avg < Cj < CO + 9 IlncStrs.avg 3
IDRG I I      if CO + 9- IncStrs avg < Cj < co + i&deg; IncStrs.avg IDRG 1 2      if co+ If lnCStrs.avg < Cj < CO + I IOlCStrs.avg IDRG 1 33 if cO+ 1Ifl CStrs.avg < Cj < Co+ 12 InCStrs.avg IDRG 143 if Co+ 12iIncStrs.avg < Cj < Co+ 13 InCStrs.avg IDRG 1 5      if co+ 13 InfcStrs avg < C; < CO + 14-lncstrs.avg
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 33 of 42 IDRG 16      if Co+ 14 InCStrs avg < Cj < Co+ 15IflCStrs.avg IDRG 17      if Co+ 15-InCStrs avg < Cj < Co+ l6I lCStrs.avg IDRG 183 if Co+ 16- InCStrs avg < Cj < Co + l7 lncStrs avg IDRG 193 ifCo + 17- Incstrsavg < cj < co + l8-Incstrs.avg IDRG 2 0    otherwise a1*- IDRG 1    if cj < co IDRG 2    if co < Cj < Co + InCStrs.avg IDRG34 if Co + InCStrs.avg < Cj < Co + 2 InCStrs avg IDRG44 if Co + 2-InCStrs.avg < cj < Co + 3IInCstrs.avg IDRG 5    if Co + 3-Incstrs.avg < Cj < Co + 4 InCStrs.avg IDRG64 if Co + 4- InCStrs.avg < Cj < Co + 5-InCStrs avg IDRG 7    if Co + 5-lncstrs.avg < Cj < CO + 6 InCStrs.avg IDRG 8 4 if Co + 6-lfCStrs.avg < Cj < Co + 7IInCStrs.avg IDRG 9 4 if CO + 7flncStrs.avg < Cj < co + 8- lCStrs avg IDRG 1 0    if co + 8-IncStrs.avg < Cj < co +9 fInCStrs.avg IDRGI 14 ifco + 9-InCstrs.avg < Cj < Co + lO lncStrs.avg IDRG 1 24 if co+ 10 IlncStrs avg < Cj < CO+ IIflnCStrs.avg IDRG 1 3 4 if CO+ 11 lnCStrs.avg < Cj < Co+ 12 InCStrS avg IDRG144 if co+ 12- lnCStrs avg < Cj          C0 + 13 IncStrs avg IDRG1 5      if Co + 13- Ilncstrs.avg < Cj < Co + 14 lncStrs.avg IDRG 16 4 if Co+ 14 lncStrs.avg < Cj < Co+ I5 IlncStrs.avg 4    ^
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 34 of 42 II)KUj17    it Co+ 15 ifnCstrs.avg < Cj S Co+ 16d fCStrs.avg IDRG 18 4 if cO+ 16* IncStrs.avg < Cj < Co+ 17 InCStrs.avg IDRG1    4  if Co + 17-lncStrs avg <  Cj  < CO + 18 4ncStrs.avg IDRG 2 0    otherwise 4
Y2*- IDRG 1    if cj < co IDRG 2    if co < Cj < Co + InCStrs.avg IDRG 3    if co + InCStrs.avg < cj < C0 + 2 lCStrs.avg IDRG 4    if CO + 2 InCstrs.avg < Cj < Co + 3Ilncstrs.avg IDRGs 5 if CO + 3IlnCstrs.avg < cj < C0 + 4-InCStrs avg IDRG65 if CO + 4 InCStrs.avg < cj < C0 + 5 InCStrs.avg IDRG 7    if C0 + 5 InCStrs.avg < cj < co + 6 InCStrs.avg IDRG8      if CO + 6-Incstrs.avg <  Cj <  Co + 7-Incstrs.avg IDRG9      if Co + 7-IlncStrs.avg < Cj < Co + 8-fCStrs.avg IDRGIO      if co + 8 Incstrs.avg < cj < co + 9 InCStrs.avg 15 if co+9 1DG                  Strs.avg <    < o+io
                                                  &deg;j        Strs.avg IDRG1 25 if co + If lnCStrs.avg < cj < CO + 1 lncStrs.avg IDRG1 32    if co + 1 If-ncstrs.avg < cj < co + 121fncstrs avg IDRG1 4      if Co+ 11 InCStrs.avg <iCj        &deg; 13-lcStrs.avg co+
IDRG 1 55 if cO+ 13 IlncStrs.avg <cj < CO+ 14-Incstrs.avg IDRG 1 65 if co+ 14 IlnCStrs.avg < Cj < co + i5 IlnCStrs.avg IDRG I75 1      if CO + ls IncStrs.avg < Cj < CO + 16 InlCStrs avg IDRGlI R    if co+ 16 lncStrq  v < cj < CO+ 17 1fncStrc.vq,
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 35 of 42 IDRG19-5 if co + 17-IncStrs avg < cj < co + 18 -1CStrs.avg IDRG 2 0    otherwise 5
T3 - IDRG 1    if cj < co IDRG 2    if cO < cj < co + InCStrs.avg IDRG 3    if co + InCStrs.avg < cj < Co + 2 lnCStrs avg IDRG 4 6 if co + 2 Incstrs.avg < Cj < co + 3 IncStrs avg IDRG 5 6 if cO + 3flncstrs.avg < cj < Co + 4 InCStrs.avg IDRG 6 6 if C0 + 4 lncStrs.avg < cj < Co + 5 IlncStrs avg IDRG 7    if Co + 5-flCStrs.avg < cj < Co + 6- fCStrs.avg IDRG 8    if C0 + 6-Incstrs.avg < cj < Co + 7-lncstrs.avg IDRG 9    if Co + 7-Incstrs.avg < cj < Co + 8-IncStrs.avg IDRG 1 6 if Co + 8IncStrs.avg < Cji        co + 9lflcStrs.avg IDRG 1I      if CO + 9flncstrs.avg < cj < co + lOflncStrs.avg IDRG 12 6 if co+      I lnCStrs.avg < Cj < co + IlI lnCStrs.avg IDRG 13 6 if co + 1 - cstrs.avg < cj _ c o + 12 flCStrs.avg IDRG14 6 if co+ 12 IfnCStrs.avg < cj _ co + 13 -lncStrs.avg IDRG 1 5 6 if co+ 13 lncStrs.avg < cj < co+ 14 IlncStrs.avg IDG6 6 ifco+ 14        Strs.avg <    -j co+ 15 IStrs.avg IDRG 17 6 if CO + l4 lnCStrs.avg < cj < co+ 16lIncStrs.avg IDRG18 6 if co+ 16 IlncStrs.avg < Cj < co+ I7 lncStrs.avg IDRG19 6 if co+ I7TlncStrs.avg < cj < co + 18 lncStrs.avg
 
Attachment 7 to Eng. Report No. M-EP-2003-003. Rev. 0 Page 36 of 42 IIDRG 20      otherwise 40        0C 2 (0.25s aj') 2 + 03. ~0.25.aj)V
    ~~ I      <-(To+s Gy    ~        +    02        - )
2          0.5-aj)'
2 <-- 00 + (3I -                + 02-                + (YY      t )
: 02. 0.75. aj)    2 43-    00+0~    I  75ai-    +                          +3 0.75.aj)V t    )
~44 -        0+r10aj + 02.                        2.O+aC'F3 (.O. aj 'V
    *0<- 0.0 xi - 0.25 x2        0.5 X3        0.75 X  v    stack(x      , x 2 , x 3 , X4 )
ST*- stack(4O          1,42,43't4)
RG*- regress(X, ST, 3)
(000-        RG 3 + Plnt 0o10-        RG4 o2 0 - RG5 030*- RG6 ARj - aj Cj ATJ    v- aj t
G--    <- f . .(R..AR;..AT;\
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 37 of 42
-auj-a        xs              J Gal i    faL(Rt, ARj,ATj)
Gaq < faQ(RtARj, ATj)
Gacj      faC(Rt1,ARjATJ)
GcI < fcL(Rt, ARj, ATj)
Gcq j    fcQ(Rt,ARj ATj)
GCC  v  fcC (Rt, ARj, ATJ)
Qj v-    1+ 1.464-(-)                if cj 2 aj 1+    1.464-K1.65    otherwise 0.5 Kaj    (        )
* 0OOauj + (aI O Gal + CY20-Gaqj + (Y30Gacj)
K*C <                    (O
                          .('I0 0 Gcuj +  10 ,Gcl1 +a 2 0 .Gcqj + 30-Gccj)
*"  <--Kaj 1.099 i        i KYJ - Kci- 1.099 Ka    v    9.0    if Ka < 9.0 Ka        otherwise Ky    -    9.o if Kr < 9.0 Ky, otherwise Da + CO K                  90) n          InT      rr C      . ..    . if K-      nn
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 38 of 42 g      I-    a  ' intirblk
* _
l 4  0 -CFinhr-Cblk otherwise DC *<-co.(Ky          -_ 9.0) 1.16 Dcgj
* lDcj CFinrh.Cblk if K        < 80.0 l4-lo--CFinhr -Cblk otherwise output(j,o)    (- j output~j, I) <- aj OUtpUt(j, 2 ) - Cj - CO output(j , 3)  +  Dagj OUtpUt(j, 4) *- Dcg.
outpUt(j, 5)    (  Kaj OUtpUt(j, 6) -    KC NCBj OUtpUt(j    7)    365.24 outpUt(j, 8)  F  Gau.
output(j, 9) E Gal output(j, 10) v Gaq output(j, II) 4      Gac OUtpUt(j, 12)    + Gcq output~j, 13) <- Gclj outPUt(j, 14)
* Gcq.
a; - aj I1 +
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 39 of 42
                      . v        6~_j_I CjiCji-+Dcg._-
aj  -  It  if aj &#x17d; t aj otherwise NCBj  v-  NCBj.. + Cblk output O.. him The curve below shows the flaw growth through-wall and the operating time (in years) it takes to go through-wall.
Flaw Growth in Depth Direction 0.6                                    6.99
  *~0.5 0.401 3    0.4 0.3 0.2 0.1                    I          I        I        I    I          I 0      2          4          6        8        10  12        14 Operating Time {years}
 
Attachment 7 to Eng Report No. M-EP-2003-003, Rev. 0 Page 40 of 42 The propagation length for the ICI nozzles is defined as the length for which the initial flaw in the blind zone would extend out of the blind zone and grow to a detectable flaw. Reference I I gives the minimum detectable flaw size of 4 mm (0.16) in length; thus, 0.16 inch was considered as this minimum detectable flaw length. This dimension is added to the end of the blind zone.
Prop.Length      BZ=ength - C + 0.16 PropLength = 0.16 This implies that a flaw initially spanning the length of the blindzone must grow 0.16 inch to become detectable via UT.
The curve below shows the flaw growth along the length of the ICI nozzle and the operating time (in years) it takes to reach the Prop Length value defined above.
2 3,,83/
1.5 C
      - 0.5 5                                                                ~~~~~~~~~~~~~~~~~~~~~~~~
0
      -0.5 0          2            4        6          8          10        12          14
                                        - Operating Time {years}
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 41 of 42 Stress Intensity Factors 100 80 rA~~~~~~~~~~~~~~~~~~~~~~~'
.~60 00 20 20 0      2                  4      6          8        10 12 14 Operating Time {years}
        - Depth Point Surface Point
 
Attachment 7 to Eng. Report No. M-EP-2003-003, Rev. 0 Page 42 of 42 Influence Coefficients - Flaw 3
2.5 2
E 1.5 0
_____-          _    -~~~~---------
0 O~~~~~~~~~~                            -________________-- -    -- - --
: 0.      _    11 11                      -a 0                2              4          6              8              10  12          14 Operating time {years}
          -I"a"      - Tip -- Uniforrn
      ----- Ia" - Tip Linear Ia" - *Tip-- Quadratic "a" - Tip Cubic
            -    "c" - T
                ""-      Tip      Uniform
                                -- Quadratic ip --
              -~~~~"c'
                      - Tip -- Linear
      -- - "c" - Tip -- Quadratic "c" -Tip--Cubic
 
ENCLOSURE 3 CNRO-2003-00035 LICENSEE-IDENTIFIED COMMITMENTS
 
LICENSEE-IDENTIFIED COMMITMENTS TYPE (Check one)        SCHEDULED ONE-TIME    CONTINUING    COMPLETION COMMITMENT                        ACTION    COMPLIANCE        DATE
: 1. Entergy will provide in the 60-day report                                  60 days after for ANO-2, as required by the Order,                                      startup from the specific inspection information; i.e., extent                              next refueling of inspections and results of those                                            outage inspections.
: 2. If the NRC staff finds that the crack-growth        1                  Within 30 days after formula In MRP-55 is unacceptable,                                      the NRC informs Entergy shall revise its analysis that                                Entergy of an NRC-justifies relaxation of the Order within 30                              approved crack-days after the NRC informs Entergy of an                                  growth formula.
NRC-approved crack-growth formula.
: 3. If Entergy's revised analysis (#2, above)          I                    Within 72 hours shows that the crack growth acceptance                                from completing the criteria are exceeded prior to the end of                              revised analysis in Operating Cycle 17 (following the                                            #2, above.
upcoming refueling outage), Entergy will, within 72 hours, submit to the NRC written justification for continued operation.
: 4. If the revised analysis (#2, above) shows                              Within 30 days from that the crack growth acceptance criteria                                  completing the are exceeded during the subsequent                                      revised analysis in operating cycle, Entergy shall, within 30                                    #2, above.
days, submit the revised analysis for NRC review.
: 5. If the revised analysis (#2, above) shows            I                Within 30 days from that the crack growth acceptance criteria                                  completing the are not exceeded during either Operating                                revised analysis in Cycle 17 or the subsequent operating                                        #2, above.
cycle, Entergy shall, within 30 days, submit a letter to the NRC confirming that is analysis has been revised.
: 6. Any future crack-growth analyses                                                N/A performed for Operating Cycle 17 and future cycles for RPV head penetrations will be based on an acceptable crack growth rate formula.
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Latest revision as of 07:40, 16 January 2025

Arkansas, Unit 2 - Response to Request for Additional Information Pertaining to Relaxation Request to NRC Order EA-03-009 for In-Core Instrumentation Nozzles
ML032681163
Person / Time
Site: Arkansas Nuclear Entergy icon.png
Issue date: 09/03/2003
From: Krupa M
Entergy Operations
To:
Document Control Desk, Office of Nuclear Reactor Regulation
References
CNRO-2003-00035, EA-03-009
Download: ML032681163 (252)
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