ML091030445

Requests for Relief for Alternate Examination Frequency - Attachments 1 Through 4

ML091030445
Person / Time
Site:	Byron
Issue date:	04/02/2009
From:	Exelon Generation Co, Exelon Nuclear
To:	Office of Nuclear Reactor Regulation
References
N-729-1, RS-09-050
Download: ML091030445 (382)

Text

ATTACHMENT 1 10 CFR 50.55a Relief Request 13R-16

ISI ProgramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 1 of 8)

Request for Relief for Alternate Examination Frequency Under ASME Code Case N-729-1 for Reactor Vessel Head Penetration Welds in accordance with 10 CFR 50.55a(a)(3)(i)

1. ASME CODE COMPONENT(S) AFFECTED Code Class: 1

Reference:

ASME Code Case N-729-1 Item Number: B4.10 and B4.20

Description:

B4.10, Head with UNS N06600 nozzles and UNS N06082 or UNS W86182 partial penetration welds, and UNS N06600 nozzles and B4.20, UNS N06082 or UNS N06082 or UNS W86182 partial-penetration welds in head Drawing Numbers: 185282E Revision 1, 185283E Revision 1, and 185286 Revision 2

2. APPLICABLE CODE EDITION AND ADDENDA The current code of record for the Byron Station Unit 2 Inservice Inspection (ISI)

Third Ten-Year Interval is the ASME Section XI Code, 2001 Edition through the 2003 Addenda, as augmented by ASME Code Case N-729-1, "Alternative Examination Requirements for PWR Reactor Vessel Upper Heads With Nozzles Having Pressure-Retaining Partial-Penetration WeldsSection XI, Division 1," as amended and noticed in the Federal Register (73 FR 52730, September 10, 2008).

Upon implementation, ASME Code Case N-729-1 superseded the First Revised NRC Order EA-03-009 (i.e., Reference 8.1).

3. APPLICABLE CODE REQUIREMENT Note (4) of ASME Code Case N-729-1, Table 1, "Examination Categories," states:

If EDY <8 and no flaws unacceptable for continued service under -3130 or -3140 have been detected, the reexamination frequency may be extended to every third refueling outage or 5 calendar years, whichever is less, provided an IWA-2212 VT-2 visual examination of the head is performed under the insulation through multiple access points in outages that the VE is not completed. This IWA-2212 VT-2 visual examination may be performed with the reactor vessel depressurized.

Note (8) of ASME Code Case N-729-1, Table 1, "Examination Categories," states:

If flaws have previously been detected that were unacceptable for continued service in accordance with -3132.3 or that were corrected by a repair/replacement activity of -3132.2 or -3142.3(b), the reexamination frequency is the more frequent of the normal reexamination frequency (before RIY =2.25) or every second refueling outage, and [Note (9)] does not apply.

ISI ProgramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 2 of 8)

Additionally, repaired areas shall be examined during the next refueling outage following the repair.

However, as identified in a final rule action published in 73 FR 52730, dated September 10, 2008, 10 CFR 50.55a(g)(6)(ii)(D)(5) has added the following condition modifying ASME Code Case 729-1, Note (8):

If flaws attributed to PWSCC have been identified, whether acceptable or not for continued service under Paragraphs -3130 or -3140 of ASME Code Case N-729-1, the re-inspection interval must be each refueling outage instead of the re-inspection intervals required by Table 1, Note (8) of ASME Code Case N-729-1.

4. REASON FOR REQUEST:

As part of the NRC required (Reference 8.1) reactor vessel upper head penetration nozzle weld volumetric examinations conducted using ultrasonic testing (UT) during Byron Unit 2 refueling outage B2R13 (i.e., spring 2007), an indication was detected in Penetration 68 that was suggestive of primary water stress corrosion cracking (PWSCC). Subsequent dye penetrant examination (PT) of the J-groove weld surface revealed a linear indication and a rounded indication as shown in Figure 1 below.

Figure 1: Dye penetrant examination results of Penetration 68 showing the rounded and the linear indications.

In order to determine the source of the detected indications, a specimen (more commonly referred to as a boat sample) of the J-groove weld and underlying penetration tube material was removed for examination. The boat sample contained the linear indication detected by UT and PT as well as a portion of a subsurface defect.

During the B2R13 refueling outage, Exelon Generation Company (EGC) submitted relief request 13R-114 (Reference 8.2) requesting authorization to repair the indication and the boat sample excavation site by an embedded flaw weld overlay process. The NRC subsequently approved this alternate repair request (Reference 8.3). The overlay repair covered the entire J-groove partial penetration weld area and the lower portion of the nozzle with PWSCC-resistant material.

ISI PracramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 3 of 8)

In September 2008, ASME Code Case N-729-1 was incorporated into 10 CFR 50.55a(g)(6)(ii)(D) and superseded Order EA-03-009 as the governing rule for Reactor Pressure Vessel (RPV) upper head penetration nozzle examinations.

10 CFR 50.55a(g)(6)(ii)(D)(5) states that if flaws attributed to PWSCC have been identified, the re-inspection interval must be each refueling outage instead of the re-inspection intervals required by Table 1, Note (8) of ASME Code Case N-729-1.

In addition, with the detection of PWSCC, Item B4.10 now requires a visual examination to be completed each outage.

While the destructive examination of the boat sample confirmed the presence of PWSCC, the final report of the destructive examination concluded that the origin of the PWSCC was attributed to welding defects from the original fabrication and not solely due to exposure to the bulk operating environment.

Therefore, relief is requested from the requirements of 10 CFR 50.55a(g)(6)(ii)(D)(5) with a proposed alternative extent of examination of all nozzles, with the exception of Penetration 68, at a frequency of once every fourth refueling outage or six calendar years, whichever is less, and a bare metal visual examination of the RPV head every third refueling outage, or five calendar years, whichever is less, as allowed by Note (4) of N-729-1. Penetration 68 will be examined each refueling outage by volumetric and /or surface and visually as required by N-729-1.

This request is proposed for the remainder of the Byron Unit 2 Third ISI Inspection Interval beginning with refueling outage B2R15 in spring 2010.

5. PROPOSED ALTERNATIVE AND BASIS FOR USE:

EGC proposes to continue the required volumetric and surface examinations of 10 CFR 50.55a(g)(6)(ii)(D); however, an alternative inspection frequency is proposed based on the uniqueness of the occurrence of PWSCC in Penetration 68. Specifically, EGC is proposing to perform volumetric and/or surface examinations of all penetrations as identified by Table 1 of ASME Code Case N-729-1 at a frequency of once every fourth refueling outage or six calendar years whichever is less, except for Penetration 68, which will be volumetrically and/or surface examined each refueling outage. In addition, bare metal visual examinations of the RPV head will occur every third refueling outage or five calendar years, whichever is less. The proposed alternative examination frequencies provide an acceptable level of quality and safety.

ASME Code Case N-729-1 inservice examination methods and frequency are determined using parameters to characterize the susceptibility for PWSCC crack initiation and the potential for crack propagation. The parameters, effective degradation years (EDY) and reinspection years (RIY), are functions of time and temperature, and are normalized to a reference temperature of 6000 F. EDY indicates the susceptibility to crack initiation, and RIY is an indicator of the potential for crack propagation. At the time of refueling outage B2R13, the EDY value for Unit 2 was 2.2, which is considered to be very low. Based on the low value of EDY, Byron Unit 2 was not expected to have initiated PWSCC by B2R13.

ISI PrQqramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 4 of 8)

EGC had previously completed the volumetric examinations of Byron Unit 1 and Braidwood Unit 1 and 2 prior to the scheduled volumetric examination of Byron Unit 2 in B2R13. These reactor heads are the same vintage and design as the Byron Unit 2 head. During the examinations of the other three units, there were no indications of any PWSCC flaws that would have forecast the results for Byron Unit 2. The Byron Unit 2 RPV head is considered a T-cold head (-553 0 F) due to the reactor coolant system (RCS) cold leg bypass flow into the upper head region. Further, industry experience from Europe predominately pertained to RPV heads with higher temperatures than Byron Unit 2, and therefore, a higher susceptibility to initiation of PWSCC.

Byron Unit 2 Penetration 68 is the only one of over 1400 domestic, cold head RPV nozzles inspected to have found an indication of PWSCC. Statistically, the likelihood of Byron Unit 2, or any low susceptibility head, finding PWSCC-initiated indications at the refueling outage subsequent to the baseline inspection has been shown to be less than 1% and is independent of the indication found in Penetration 68. An extensive review of domestic and international industry operating experience with rounded surface indications on RPV head penetrations was conducted (Reference 8.4). The conclusion reported from the other industry examples stated that the PWSCC associated with the indication had crack growth propagating from the wetted surface toward the interior.

Since the probability of initiating PWSCC in Byron Unit 2 was very low, the decision was made during B2R1 3 to remove the detected indication and perform a destructive examination. A complete destructive metallurgical failure analysis was completed by Exelon PowerLabs to help determine the cause of the indication found, and the results are documented in Reference 8.6. The boat sample contained a portion of the axial indication identified by the UT and PT exams. A post-removal PT exam of the excavation site uncovered an angled, subsurface linear defect that intersected the original axial indication; the subsurface defect was partially captured by the boat sample.

The orientation of the boat sample with respect to the penetration tube and the J-groove weld can be seen in Figure 2.

The crack-growth surface of the weld exhibited characteristics typical of both PWSCC and hot cracking. Lack of fusion between weld passes, which was parallel to the fusion line, could be seen on the crack-growth surface of the weld, and within the weld there were several cracks that were connected to the lack of fusion defect. Based on the general characteristics of the weld defects, interdendritic weld separations, direction of crack branching, and local ductile tearing, it was concluded that the primary direction of propagation within the weld was toward the wetted surface of the boat sample. These characteristics suggest the PWSCC did not initiate from the wetted surface of the boat sample. "Detail A" of Figure 2 illustrates the results of the UT exam and the location of the defect (i.e., weld defects and PWSCC cracking) that was partially captured in the boat sample and partially remained in the penetration tube. The spatial relationship between these features and the rounded indication that was not captured in the boat sample can also be seen in Figure 2.

Although the PWSCC did not initiate from the J-groove weld surface, the ingress of primary water to the subsurface weld defects is attributed to the rounded surface indication identified by the PT surface examination of the J-groove weld. The source of the original rounded indication on the weld wetted surface cannot be determined.

However, based on the presence of welding defects in the boat sample, the most

ISI Prawam Plan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 5 of 8) probable cause is considered a welding imperfection that was not detectable or an indication that was considered acceptable per the fabrication inspection requirements.

The Byron Unit 2 reactor head was fabricated by Babcock & Wilcox in 1977; the applicable code was the 1971 Edition of the ASME Section III, Summer 1973 Addenda.

Per the 1971 edition of ASME Section III, NB-5000, an isolated 3/16" (0.1875") rounded dye penetrant indication would be considered acceptable. At 0.050", the rounded indication on the J-groove weld surface of Penetration 68 was well within this limitation.

The subsurface volume of the rounded indication, as correlated to the size of the dye penetrant bleed area, would have been sufficient to be incident upon the network of interconnected weld defects.

At the time of B2R13, the presence of PWSCC in Byron Unit 2 was unexpected based on the low value of EDY. The conclusion drawn in the boat sample failure analysis report is that the PWSCC was not the result of exposure of the Alloy 600 tube material or the Alloy 182 weld material to the bulk primary water environment; rather, the premature initiation of PWSCC is attributed to a series of weld defects that created a conducive crevice corrosion environment in the high-stress region of the J-groove weld.

To illustrate the uniqueness of the PWSCC event at Byron Unit 2, an assessment of PWSCC in Penetration 68 has been conducted by employing probabilistic and structural reliability tools (Reference 8.4). The results showed that the probability of having the observed 50% through-wall flaw in Penetration 68 after 20 years of service were three orders of magnitude below those expected for flaw initiation and growth due to PWSCC in Byron Unit 2 and that the observed flaw did not occur in the most likely Control Rod Drive Mechanism (CRDM) penetration location in Byron Unit 2. The conclusion of the probabilistic calculations is that the PWSCC observed in Penetration 68 of Byron Unit 2 was not due to normal flaw initiation and growth by PWSCC in the Alloy 600 penetration tube material, and additional conditions, such as the weld defects identified in the boat sample metallurgical analysis, were needed to initiate and grow a PWSCC flaw in Penetration 68.

In accordance with NRC Order EA-03-009, which was the governing document in the fall of 2008, volumetric, bare metal visual, and surface examinations were performed on Byron Unit 2 during refueling outage B2R14 as required due to the discovery of PWSCC during the previous refueling outage (i.e., B2R13). The results showed no indications of PWSCC by volumetric examination, no evidence of boric acid on the RPV head, and no indications on the surface of Penetration 68 by dye penetrant examination.

ISI Program Plan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Revision 0 (Pacqe 6 of 8)

SEE SEE

/

1. SKETCH OF THE ORIGINAL ULTRASONIC INDICATION IDENTIFIED IN THE WESTINGHOUSE UT REPORT. THE INSPECTION IDENTIFIED A 0.520" LONG 0.@326" DEEP AXIAL. EXTERNAL INDICATION IN THE PENETRATION TURF NEAR THE J-GROOVE ELEVATION. THE 0.326" DEPTH CORRESPONDED TO "DETAIL A" APPROXIMATELY 52% OF THE 0.625" TUBE THICKNESS.

2 THIS REGION CONTAINED THE WELD DEFECTS AND THE SUBSURFACE DEFECTS THAT WERE CONTAINED IN THE BOAT SAMPLE, Figure 2: Schematic representation of the removed boat sample illustrating the location of the rounded and linear defects with respect to the rounded surface indication that was not captured by the boat sample.

ISI PrQqramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 7 of 8)

Based on a Weibull analysis of cold head RPV penetrations and low-temperature bottom head penetration inspection and failure data (Reference 8.4), the probability of repair of one or more RPV penetrations at Byron Unit 2 during B2R14 in fall 2008 was approximately 1%. The examinations performed during B2R14 supported this analysis, since no flaws were detected and no repairs were required.

In addition to the destructive examination of the boat sample and the probabilistic and Weibull analyses of RPV penetration inspection results, a fracture mechanics analysis was performed to study the PWSCC crack growth behavior of the flaw in Penetration 68 (Reference 8.5). The analysis was conducted using the available stress distribution data, the industry-approved PWSCC crack growth formulation, and a standard fracture mechanics algorithm.

The results of the analysis showed that a minimum of six eighteen-month fuel cycles would be required to propagate a postulated flaw positioned in the middle of the J-groove weld at the point of the highest tensile stress to the top of the J-groove weld such that a leak path would be established. Therefore, at a minimum, an additional six fuel cycles would be necessary to establish a leak path if an undetected flaw was left in service. Further, the results of the analysis demonstrated that initiation of a flaw would require extenuating circumstances such as the fabrication defect found in Penetration 68, and the likelihood of detection of such a defect in other nozzles would be very high.

In an effort to forestall the initiation of PWSCC, zinc injection was implemented at Byron Unit 2 in Operating Cycle 12 following the spring 2004 refueling outage (B2R1 1). The purpose of zinc addition is to provide some mitigation of PWSCC with an ancillary benefit of radiation field reduction. Since the start of zinc addition in December 2004 through completion of operating Cycle 14 in October 2008, Byron 2 has accumulated 125.4 parts-per-billion-months (ppb-mos). Zinc addition has resumed in the current Operating Cycle 15, and plans call for the injection of zinc in future Byron 2 operating cycles with an average zinc concentration of 5 ppb. However, the decision to resume zinc addition as well as the levels and rates of injection for future cycles is dependent on the results of each cycle's chemistry and core data review.

In conclusion, based on the results of the boat sample examination, the probabilistic fracture mechanics study, and the crack growth analysis, EGC contends that an acceptable alternative is a volumetric examination and/or surface examination frequency of every fourth refueling outage or six calendar years, whichever is less, and a bare metal visual examination of the RPV head every third refueling outage, or five calendar years, whichever is less. Penetration 68 will be examined each refueling outage by volumetric and /or surface and visually as required by N-729-1.

6. DURATION OF THE PROPOSED ALTERNATIVE:

The duration of the proposed alternative is for Byron Station Unit 2 Third Inservice Inspection Interval currently scheduled to end in 2016.

7. PRECEDENT:

None

ISI ProgramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-16 Attachment 1 (Page 8 of 8)

8.

REFERENCES:

8.1 NRC Order EA-03-009, "Issuance Of First Revised NRC Order (EA-03-009)

Establishing Interim Inspection Requirements for Reactor Pressure Vessel Heads at Pressurized Water Reactors," dated February 20, 2004 8.2 Letter from D. M. Benyak (Exelon Generation Company, LLC) to U. S. NRC, "Byron Station Unit 2 Inservice Inspection Relief Request 13R-14: Alternative Requirements for the Repair of a Reactor Vessel Head Penetration," dated April 13, 2007 8.3 Letter from R. Gibbs (U. S. NRC) to C. M. Crane (Exelon Generation Company),

"Byron Station, Unit No. 2 - Relief Request 13R-14 for Evaluation of Proposed Alternatives for Inservice Inspection Examination Requirements (TAC No.

MD5230)," dated May 23, 2007 8.4 Exelon Nuclear Generating Company Nuclear Engineering Department Document AM-2007-1 1, "Byron Unit 2 - Technical Basis For Reactor Pressure Vessel Head Inspection Relaxation," Revision 1, dated September 27, 2007 8.5 Exelon Nuclear Generating Company Nuclear Engineering Department Document AM-2007-006, "Evaluation of Crack Growth of a Postulated Flaw in Byron Unit 2 CRDM Nozzles by Primary Water Stress Corrosion Cracking,"

Revision 0, dated July 4, 2007 8.6 Exelon PowerLabs Project BYR-48053, "Metallurgical Evaluations of a 'Boat' Sample from the #68 CRDM Penetration on Byron Unit 2," dated May 23, 2007

ATTACHMENT 2 10 CFR 50.55a Relief Request 13R-17

ISI ProgramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-17 Attachment 2 (Page 1 of 6)

Request for Relief from Requirements for Limited Examination of Reactor Vessel Head Penetration Welds In Accordance with 10 CFR 50.55a(a)(3)(i)

1. ASME CODE COMPONENT(S) AFFECTED:

Code Class: 1

Reference:

ASME Code Case N-729-1 Item Number: B4.20

Description:

UNS N06082 Nozzles and UNS N06082 or UNS W86182 partial-penetration welds in head (Byron Station Unit 2 has seventy-nine (79) reactor pressure vessel (RPV) head penetration nozzles comprised of fifty-five (55) penetration tubes with thermal sleeves, twenty-three (23) locations without thermal sleeves, and one (1) vent penetration nozzle.)

Drawing Numbers: 185282E Revision 1, 185283E Revision 1, and 185286 Revision 2

2. APPLICABLE CODE EDITION AND ADDENDA:

The current code of record for the Byron Station Unit 2 Inservice Inspection (ISI)

Third Ten-Year Interval is the ASME Section XI Code, 2001 Edition through the 2003 Addenda, as augmented by ASME Code Case N-729-1, "Alternative Examination Requirements for PWR Reactor Vessel Upper Heads With Nozzles Having Pressure-Retaining Partial-Penetration WeldsSection XI, Division 1 ," as amended and noticed in the Federal Register (73 FR 52730, September 10, 2008).

Upon implementation, ASME Code Case N-729-1 superseded the First Revised NRC Order EA-03-009.

3. APPLICABLE CODE REQUIREMENT:

Table 1, "Examination Categories," of ASME Code Case N-729-1 defines the examination requirements using Figure 2, "Examination Volume for Nozzle Base Metal and Examination Area for Weld and Nozzle Base Metal." Note (5) of Table 1 states:

... If the examination area or volume requirements of Fig. 2 cannot be met, the alternative requirements of Appendix I shall be used and the evaluation shall be submitted to the regulatory authority having jurisdiction at the plant site.

ISI Proaram Plan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-17 Attachment 2 (Page 2 of 6) 10 CFR 50.55a(g)(6)(ii)(D)(6) states:

Appendix I of ASME Code Case N-729-1 shall not be implemented without prior NRC approval.

Further, ASME Code Case N-729-1, Figure 2, identifies the examination volume or surfaces as:

a = 1.5 in. (38 mm) for Incidence Angle, 0, < 30 deg and for all nozzles > 4.5 in.

(115 mm) OD or 1 in. (25 mm) for Incidence Angle, 0, > 30 deg; or to the end of the tube, whichever is less where "a" is the length of the penetration nozzle beyond the J-weld.

4. REASON FOR REQUEST:

Due to the physical configuration and limitations of the examination equipment associated with fifteen RPV penetration nozzles, the full examination volume required by ASME Code Case N-729-1 Table 1 cannot be achieved for Item B4.20.

For Byron Station Unit 2, the bottom of each RPV head penetration nozzle includes a threaded region approximately 1.00 inch long on the outside diameter along with a chamfered area at the inside diameter which extends approximately 0.76 inches from the bottom of the penetration tube (see Figure 1). The chamfered surface is machined at a 200 angle.

The distance from the top of the thread relief to the bottom of the fillet of the J-groove weld, identified as "A" in Figure 1, varies based on location of the penetration in the RPV head. These distances are generally longer for penetrations at "inboard" locations and become progressively shorter for penetrations located farther away from the center of the RPV head. At the fifteen subject penetration nozzles (i.e., numbers 33, 34, 39, 42, 44, 45, 51, 52, 53, 55, 56, 58, 63, 69 and 71) the configuration is such that the distance "a" (as defined in ASME Code Case N-729-1, Figure 2) below the lowest point of the J-groove weld toe cannot be fully interrogated.

Table 1 contains information specific to the fifteen penetrations for which relief is being requested. The values for CRDM penetration hoop stress distributions at a point where the operating stress levels are less than 20 ksi tension (i.e., 20 ksi Line) were extrapolated from the associated graphs contained in Appendix A of Topical Report WCAP-1 6394-P, Revision 0, "Structural Integrity Evaluation of Reactor Vessel Upper Head Penetrations to Support Continued Operation: Byron and Braidwood Units 1 and 2," (Reference 8.1) dated February 2005. Reference 8.1 was submitted to the NRC as part of Reference 8.2.

ISI ProgramPlan Unit 2, 2, Third Interval IS! Program Plan Unit Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-17 Attachment 2 (Page 3 of 6)

Carbon Steel Buttering Thermal Sleeve "A

Stainless Steel 1,18" 1.00" 0.76" Figure 1 Illustration of Volumetric Examination Coverage on Byron Station Unit 2 Penetration Geometry (Including General Dimensions) at 0 Degrees

ISI Procyam Plan Unit 2, Third Interval ni ,TidItra ISr rmPa 10 CFR 50.55a RELIEF REQUEST 13R-17 Attachment 2 (Page 4 of 6)

Table 1 Penetrations with Limited Examination Volume (Shaded Areas Do Not Meet N-729-1 Requirements)

B2R13 20 Ksi Line Inspection (Inches below J-Groove Weld)

Penetration Angle )

Number (Degrees) Coverage Uphill Side Downhill Side (Inches Below Weld) ID OD ID OD 33 29.3 1.85 .61 .45 .92 34 29.3 1.85 .61 .45 .92 39 32.9 1.85 .61 .45 .92 42 34.1 2.9 .62 .62 .46 44 34.1 2.9 .62 .62 .46 45 34.1 2.9 .62 .62 .46 51 35.2 2.9 .62 .62 .46 52 35.2 2.9 .62 .62 .46 53 35.2 2.9 .62 .62 .46 55 37.4 2.9 .62 .62 .46 56 37.4 2.9 .62 .62 .46 58 37.4 2.9 .62 .62 .46 63 42.8 2.9 .62 .62 .46 69 43.8 3.0 .60 .60 .46 71 43.8 3.0 .60 .60 .46

ISI Program Plan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-17 Attachment 2 (Page 5 of 6)

5. PROPOSED ALTERNATIVE AND BASIS FOR USE Exelon Generation Company, LLC, (EGC) proposes to define the lower boundary of the inspection volume for the effected RPV head penetration nozzles as: "the volume of the penetration tube extending from a distance "a" (as defined in ASME Code Case N-729-1, Figure 2) above the J-groove weld down to the lowest elevation that can be practically inspected." EGC proposes to use Appendix I of ASME Code Case N-729-1 to validate the alternative inspection volume. As originally submitted as Reference 8.2, the basis for establishing the frequency of examination and required coverage requirements used a similar methodology that is consistent with Appendix I of ASME Code Case N-729-1.

Testing of portions of the nozzle significantly below the J-groove weld is not significant to the phenomena of concern. The phenomena that are of concern are leakage through the J-groove weld and circumferential cracking in the nozzle above the J-groove weld.

In all cases, the measured coverage is adequate to allow Byron Station Unit 2 to continue to operate prior to the hypothetical flaws reaching the J-groove weld. In accordance with 10 CFR 50.55a(g)(6)(ii)(D)(5) requirements, the next examination required for the Byron Station Unit 2 RPV penetrations would be completed prior to flaw propagation into J-groove welds. In addition, the flaw propagation studies are aligned with the examination interval proposed in Relief Request 13R-16 contained in Attachment 1 of this submittal.

Control Rod Drive Mechanism (CRDM) Penetration 68 was previously included in the population of nozzles addressed in Reference 8.2; however, EGC proposes to perform volumetric and/or surface examinations of Penetration 68 every refueling outage as the result of the occurrence of PWSCC in this penetration. During B2R1 3 in spring 2007, an embedded flaw repair was made to Penetration 68 after the removal of a boat sample.

A weld overlay of a PWSCC-resistant material (i.e., Alloy 52/152) was applied to the outer surface of the penetration tube, the J-groove weld, and an area of the RPV head extending one-half inch past the J-groove weld.

In conclusion, based on the probabilistic fracture mechanics study and the crack growth analysis, a volumetric examination frequency of every fourth refueling outage or six calendar years, whichever is less, provides an acceptable level of quality and safety for all penetrations, except Penetration 68, which will continue to be inspected at every refueling outage. Examination frequency and inspection requirements for Penetration 68 are discussed in detail in Attachment 1 of this submittal.

6. DURATION OF PROPOSED ALTERNATIVE:

The duration of the proposed alternative is for the remainder of the Byron Station Unit 2 Third Ten-Year ISI Interval currently scheduled to end in 2016.

ISI ProgramPlan Unit 2, Third Interval 10 CFR 50.55a RELIEF REQUEST 13R-17 Attachment 2 (Page 6 of 6)

7. PRECEDENT:

Letter from R. Gibbs (U. S. NRC) to C. Pardee (Exelon Generation Company), "Byron Station, Unit No. 2 - Relaxation of the First Revised Order EA-03-009 (TAC No.

MD6638)," dated February 7, 2008

8.

REFERENCES:

8.1 WCAP-16394-P, Revision 0, "Structural Integrity Evaluation of Reactor Vessel Upper Head Penetrations to Support Continued Operation: Byron and Braidwood Units 1 and 2," February 2005 8.2 Letter from J. A. Bauer (Exelon Generation Company, LLC) to U. S. NRC, "Relaxation Request for First Revised Order EA-03-009 Establishing Interim Inspection Requirements for Reactor Pressure Vessel Heads at Pressurized Water Reactors," dated March 31, 2006 8.3 Letter from R. Gibbs (U. S. NRC) to C. Pardee (Exelon Generation Company),

"Byron Station, Unit No. 2 - Relaxation of the First Revised Order EA-03-009 (TAC No. MD6638)," dated February 7, 2008

ATTACHMENT 3 Byron Unit 2 - Technical Basis for Reactor Pressure Vessel Head Inspection Relaxation

BYRON UNIT 2 - TECHNICAL BASIS FOR REACTOR PRESSURE VESSEL HEAD INSPECTION RELAXATION DocumentNumber AM-2007-011 Revision 1 September27, 2007 Corporate Engineering Department Exelon Nuclear PREPARED BY: QVM&44 ,I MX4lJ V' E~iAN L 'SuTH4 DATE:

REVIEWED BY. GUY H. DEBOO DATE: 9/2... ,T DATE: 24)

DATE DATE: _______

(DATE ISSUED)

AM-2007-011 Revision 1 Executive Summary The U.S. Nuclear Regulatory Commission (NRC) issued Order EA-03-009 in February 2004 to all U.S. pressurized water reactor (PWR) licensees to address the potential for primary water stress corrosion cracking (PWSCC) in the penetration nozzles and related welds of the reactor pressure vessel (RPV) head. During B2R13 in April 2007, Byron Unit 2 conducted an inspection of the penetration nozzles in compliance with the Order.

The inspections revealed an indication in penetration Nozzle 68. A metallurgical examination of a boat sample removed from Nozzle 68 concluded that a lack-of-fusion weld defect created during the manufacturing of the head had caused the initiation of PWSCC. The NRC Order requires any head that has observed PWSCC to follow the inspection interval for a high susceptibility head for subsequent outages; the Order does not specifically address the inspection frequency when the source of crack initiation is not PWSCC, Therefore, a series of evaluations were completed to determine a technically justified frequency for future examinations.

A detailed probabilistic evaluation was carried out to determine the probability of developing a PWSCC crack of the size found in Nozzle 68. The evaluation showed that the probability of having a PWSCC flaw of this size would be about three orders of magnitude less than the probability corresponding to cracking which has been observed in plants. This finding further supportsthe conclusions of the metallurgical failure analysis report which states that the crack initiation was due to an extenuating circumstance, namely the lack-of-fusion weld defect.

The probabilistic evaluation was also used to determine the effect of inspection frequency on the probability of leakage due to PWSCC initiation and growth. It was found that an inspection frequency of six years, which is consistent with the frequency required for low susceptibility plants, led to a very low probability of leakage.

A statistical treatment of all the available inspection results for head penetrations was completed to estimate the probability that flaws would be found in the future as a function of inspection frequency. For the base case chosen, the results show there is approximately a one percent chance of cracking in the next cycle and about a five percent chance in the next six years.

Although the likelihood of a crack existing is low, a deterministic analysis of crack growth rates was completed. In the study, a flaw, which had not been found by the inspection methods used, was postulated to exist and was allowed to grow according to the accepted industry model. Flaws in a range of shapes and orientations were considered, and the results showed that each flaw would remain within the Code acceptance limits for at least six years.

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AM-2007-011 Revision 1 In summary, it was demonstrated that the flaw found in Byron Unit 2 Nozzle 68 did not originate from PWSCC. Two complementary approaches have shown that a six year inspection frequency results in a very low probability of the development of cracks in the future. Even if a flaw had been below the threshold of detection at B2R13, calculations show that it would remain acceptable to the ASME Code criteria for at least six years.

Based on these analyses, an inspection frequency for Byron Unit 2 that is consistent with a low susceptibility head would not significantly increase the probability of a through-wall crack and subsequent leakage on top of the RPV head; therefore, the low susceptibility inspection frequency is acceptable.

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AM-2007-011 Revision 1 TABLE OF CONTENTS I INTRODUCTION 5 2 REACTOR PRESSURE VESSEL HEAD INSPECTIONS 6 2.1 BYRON AND BRAIDWOOD INSPECTION RESULTS 6 2.2 BYRON UNIT 2 INSPECTION RESULTS 6 2.3 INDUSTRY INSPECTION RESULTS 11 2.4 RELIABILITY OF INSPECTION TECHNIQUES 13 3 METALLURGICAL EXAMINATION OF BYRON UNIT 2 NOZZLE 68 15 3.1 METALLURGICAL EXAMINATION RESULTS 15 3.2 PWSCC REQUIREMENTS 22 3.3 PWSCC INBYRON UNIT 2 23 3.4 PWSCC INITIATION AND CHROMIUM DEPLETION 24 3.5 OTHER INDUSTRY PWSCC EXPERIENCES 25 4 PROBABILISTIC ASSESSMENT OF PWSCC IN BYRON UNIT 2 27 4.1 PROBABILISTIC MODELS FOR PWSCC ASSESSMENT 28 4.2 PWSCC ASSESSMENT RESULTS 41 4.3 EFFECTS OF IN-SERVICE INSPECTIONS 42 4.4 PROBABILISTIC ASSESSMENT

SUMMARY

AND CONCLUSIONS 43 4.5 WEIBULL ANALYSIS OF COLD HEAD RVHP INSPECTION RESULTS 44 5 BYRON UNIT 2 PWSCC GROWTH PROJECTIONS AND FLAW TOLERANCE 49 5.1 PWSCC CRACK GROWTH RATES 50 5.2 BYRON UNIT 2 PWSCC GROWTH PROJECTIONS 53 5.3 REACTOR VESSEL HEAD INSPECTION INTERVALS 60 6

SUMMARY

AND CONCLUSIONS 60 7 REFERENCES 63 4 of 66

AM-2007-011 Revision 1 1 Introduction The U.S. Nuclear Regulatory Commission (NRC) issued Order EA-03-009 1 in February 2004 to all U.S. pressurized water reactor (PWR) licensees to address the potential for primary water stress corrosion cracking (PWSCC) in the penetration nozzles and related welds of the reactor pressure vessel (RPV) head. The Order recognizes that the susceptibility of RPV head penetrations to PWSCC appears to be strongly linked to the operating time and temperature of the RPV head. Accordingly, the necessary RPV head inspections required by the Order are dependent on the value of effective degradation years (EDY), which are calculated using an equation defined in the Order.

The equation for EDY is a function of time at temperature and is normalized to a reference temperature of 600 0 F. At the time of Byron Unit 2 Refueling Outage 13 (B2R13) in April 2007, the value for Unit 2 was 2.2 EDY, which is considered by the Order to be in the low susceptibility category. Based on the low value of EDY, Byron Unit 2 was not expected to have initiated PWSCC by B2R 13.

The following report describes the inspections performed in accordance with the NRC Order at Byron Unit 2 during B2R13, and it discusses the indications that were detected during the inspections. The report highlights the outlier nature of this finding relative to the numerous inspections that have been performed in the industry according to the Order.

A summary of the metallurgical failure analysis that was performed on a boat sample removed from Byron Unit 2 describes the discovery of an original fabrication weld defect, which created the environment necessary for PWSCC. A discussion of the requirements for the initiation of PWSCC is included to illustrate the uniqueness of the conditions at Byron Unit 2 and their effect on the detected flaw.

A probabilistic analysis of the occurrence of PWSCC in Byron Unit 2 after 20 years of service is presented along with a probabilistic evaluation to determine the effect of inspection frequency on the probability of leakage. The analysis provides further evidence that PWSCC would have been highly unlikely without the existence of an extenuating factor such as the original fabrication weld defect. A statistical treatment of all the available inspection results is used to estimate the probability as a function of inspection frequency that flaws would be found in the future.

Based on an initial flaw size at the threshold of detection by current inspection techniques, a crack growth study is presented that indicates the inspection frequency prescribed by the Order for a low susceptibility head is appropriate for Byron Unit 2 despite the discovery of PWSCC.

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AM-2007-011 Revision 1 2 Reactor Pressure Vessel Head Inspections This section reports the results of the inspections conducted by Byron Unit 2 and the industry in accordance with NRC Order EA-03-009. A discussion of the inspection techniques and their reliability is included.

2.1 Byron and Braidwood Inspection Results Byron and Braidwood first implemented bare metal visual (BMV) examinations of the reactor pressure vessel head starting in 2002 to meet the requirements of NRC Bulletin 2002-022. The following dates are for completion of the first BMV exams:

, Braidwood 1 - Spring 2003

• Braidwood 2 - Spring 2002

• Byron 1 - Fall 2003

• Byron 2 -Fall 2002 The initial BMV and all subsequent exams (both Byron and Braidwood) have not detected any evidence of boric acid in the annulus region of the CRDM nozzle-to-head interface. With the issuance of NRC Order EA-03-009 in February 2004, specific criteria were established for frequency of BMV and the requirement for a volumetric examination was added. Both Byron and Braidwood established a three-year frequency of examination for the BMV starting with the initial BMVs performed to meet Bulletin 2002-02.

In accordance with NRC Order EA-03-009, each reactor vessel head (CRDM nozzles) must be examined per the order by February 2008. Byron and Braidwood have used volumetric examination of the CRDM nozzle tube by use of a blade probe for the CRDM nozzles with thermal sleeves installed and an open probe for nozzles without thermal sleeves. Each of the two exam methods has both ultrasonic exam (UT) and eddy current exam (ET) capabilities. The main exam is completed using the UT probe with supplementary EC probes also taking data. The exam of the CRDM nozzles is completed from the ID of the tube for the full wall thickness and approximately 10% of the J-Groove weld being examined.

Both Byron 'and Braidwood have completed these exams on all four units, and the total population inspected to date is 312 CRDM nozzles and four 1" vent line connections.

Of these four units only Byron Unit 2 has found an unacceptable condition in one nozzle.

2.2 Byron Unit 2 Inspection Results During Refueling Outage B2R13 in Spring 2007, Byron Unit 2 was required to meet the requirements of NRC Order EA-03-009. As a low susceptibility head plant, Byron was 6 of 66

AM-2007-011 Revision I required to complete a volumetric exam of all 78 CRDM nozzles and the one 1" vent line connection. All 78 CRDM nozzles and the vent connection were examined. During this examination CRDM Nozzle 68 had an indication detected. This indication was reflective of PWSCC, and the decision was made to obtain a confirmatory boat sample.

Subsequent metallurgical analysis identified a lack-of-fusion weld defect, which was responsible for the initiation of the observed PWSCC. The examination also identified 39 Parent Tube Indications (PTI). Each one of the PTIs was evaluated in accordance with WesDyne procedure WDI-UT-01 33 and was dispositioned as No Detectable Defect (NDD), which equates to no evidence of PWSCC.

2.2.1 Penetration 68 After identification of the indication on Penetration 68, additional examinations were undertaken to determine the exact nature of the indication. The first exam completed was the Dye Penetrant (PT) examination of the exterior surface of the4 J-Groove weld.

The PT exam identified two indications, one rounded and one linear.

After retrieval of the boat sample, a PT of the excavation was completed; Reference 5 contains the details of the inspection. 5 Following the PT exam, the excavated area was repaired, and an overlay of the CRDM nozzle and J-groove weld was completed. The overlay was then inspected using a PT exam to ensure no surface defects existed.5' 7 With the identification of PWSCC on Penetration 68, Byron Unit 2 was categorized as a "High Susceptibility' head in accordance with the NRC Order. Byron initiated and completed a 100% Bare Metal Visual Examination during the outage as required by the NRC Order. No evidence of any leakage was found.

2.2.2 Other Tube Indications The RPVH CRDM inspection was analyzed using WesDyne procedure WDI-UT-013 Rev. 12. The inspection probe employed was the Trinity design, which contains an axial shooting time-of-flight diffraction (TOFD) pair optimized for OD initiated flaws, a 0 degree probe for leak path detection, and an eddy current probe. The UT TOFD method was demonstrated through the MRP/EPRI protocol, as documented in MRP-89.8`

The UT TOFD method is inherently very sensitive to crack tip diffraction signals.

However, it is also equally sensitive to a myriad of other signal sources, most of which are associated with the machining and welding fabrication processes associated with the J-groove weld. The technique is sufficiently sensitive to respond to the grain structure change going from the nozzle base metal into the weld metal. These signals are broadly characterized as weld interface indications (WlI). Because of local grinding and weld repairs, this interface often is not a straight line and the signals can take on some characteristics of a crack tip diffraction response. The vast majority of signals detected have not been associated with PWSCC.

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AM-2007-011 Revision 1 The analysis procedure has detailed flow charts (Figures 2-1, 2-2, and 2-3) which specify a step-by-step process for distinguishing actual PWSCC response from manufacturing artifacts. Initially, any suspect response is categorized as a parent tube indication (PTI). Then the overall shape of the response is evaluated to determine if the response is a linear crack-like response or more like a diffuse surface response associated with metallurgical changes. Linear responses are categorized as special interest (SI) while surface-type responses are dispositioned as no detectable degradation (NDD). This analysis process differs slightly for indications that are entirely within the elevation of the weld (Figure 2-2) or outboard of the weld (Figure 2-3)

.because additional inferences can be drawn for the OD back wall that are not possible at the weld location.

Penetration 68 had a PTI indication within the weld zone that was analyzed as linear and given a 'special interest' designation. The SI designation then allows for additional confirmatory testing be eliminate potential false positives by determining if the indication is connected to a wetted surface, which is a requisite condition for initiation of PWSCC.

In this case PT was performed on the J-groove weld surface and both a rounded and linear indication were detected coincident with the SI location.

The same process was followed for each of the 78 nozzles. There were 39 PTI designations initially. Other than Nozzle 68, all the other indications were evaluated as surface type responses and were dispositioned as NDD.

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AM-2007-011 Revision 1 ET/UT: ID INDICATION SCREENING Figure 2-1: ET/UT: ID Indication Screening Flowchart (Ref. 3) 9 of 66

AM-2007-011 Revision 1 UT: OD INDICAT1ON SCREENING WITHIN WELD ZONE Figure 2-2: UT: OD Indication Screening Within Weld Zone Flowchart (Ref. 3) 10 of 66

AM-2007-011 Revision I UT: OD INDICATION SCREENING ABOVEIBELOW WELD ZONE Figure 2-3: UT: OD Indication Screening Above/Below Weld Zone Flowchart (Ref. 3) 2.3 Industry Inspection Results As of the end of the Spring 2007 outage season, only three plants categorized as low susceptibility by the NRC Order had yet to be inspected. Over the period of 2004 through 2007, approximately 1404 upper head penetrations have been inspected, and with the exception of Byron Unit 2 CRDM Nozzle 68, no detectable defects have been observed. The plants that have been inspected are listed in Table 2-1, and the table includes only plants with reported head temperatures of 561 *F or less. Approximately ten additional plants at slightly higher head temperatures could be added to the table; however, the represented group was selected to ensure conservatism. The listed units are all of the Westinghouse cold head design, and all have 78 penetrations per head.

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AM-2007-011 Revision 1 Another large database of low temperature head penetrations is the bottom head penetrations. The U.S. inspection results are shown in Table 2-2. A total of 15 plants have been inspected representing approximately 804 penetrations. The number of penetrations is not the same for every plant, and in some cases, the inspected penetration population was affected by other outage related considerations. In addition, these results do not include South Texas 2, which was found to have two leaking bottom penetrations in April 2003. Foreign results are also not included in the table; although, results to date indicate more than 1600 bottom mounted nozzles have been inspected in France, Sweden, Belgium, and Japan with no indications found.

Table 2-1 Inspections Completed on Cold Head Plants to Date Number of Penetrations Spring 2005 Byron 1 78 Braidwood 2 78 Comanche Peak 2 78 Spring 2006 Shearon Harris 78 Braidwood 1 78 Fall 2006 Vogtle 1 78 Seabrook 78 Wolf Creek 78 McGuire 2 78 Catawba 1 78, V. C. Summer 78 South Texas 1 78 Sequoyah 2 78 Spring 2007 Byron 2 78 Vogtle 2 78 McGuire 1 78 Callaway 78 Millstone 3 78 12 of 66

AM-2007-011 Revision I ITable 2-2 Bottom Head Penetrations Inspected to Date Findings 2004 Callaway NDD Catawba 2 NDD Surry 1 NDD Turkey Point 3 NDD 2005 McGuire 2 NDD Byron 1 NDD Surry 2 NDD Catawba 1 NDD Wolf Creek NDD Diablo Canyon 1 NDD Turkey Point 4 NDD 2006 Diablo Canyon 2 NDD Indian Point 2 NDD Vogtle 1 NDD 2007 Vogtie 2 NDD 2.4 Reliability of Inspection Techniques The volumetric examination equipment has completed a detailed demonstration as described in MRP-89, "Demonstrations of Vendor Ecuipment and Procedures for Inspection of Control Rod Drive Head Mechanisms".

The second phase of demonstration, which began in August 2002, employs mockups containing manufactured flaws of accurately known size and location. The MRP Inspection and Assessment Committees conducted joint meetings to identify the scope of the demonstrations and to design the demonstration mockups. The demonstration protocol is listed in MRP document MRP-89 Section 8.

The scope of the demonstration was to:

e Quantify detection limits of ID and OD connected flaws from the ID of the penetration tube

• Document sizing capabilities of the ID and OD connected flaws from the ID of the penetration tube 13 of 66

AM-2007-011 Revislon 1

• Evaluate capabilities to detect defects on the wetted surface of the RVHP attachment weld

• Investigate the capability to detect flaws approaching the weld-to-tube interface (triple point) using UT inspection from the ID surface of the penetration tube.

Based on the mockup design criteria, flaw manufacturing processes were selected as appropriate for the NDE methods employed by inspection vendors. The NDE methods employed are pulse-echo ultrasonic (UT), forward scatter time-of-flight diffraction (TOFD) UT, and eddy current techniques (ET) for the tube inside surface.

The morphology of the manufactured flaws in the MRP-89 Phase II demonstrations is based on the metallurgical investigations of tube and weld flaws removed from Oconee Nuclear Plant Units 1 and 3. The UT and ET responses of the manufactured flaws used in the demonstrations have been shown to be comparable to responses from service-induced PWSCC. A wide range of flaw sizes and locations were included in the mockups to quantify the performance of the demonstrated inspection techniques throughout the inspection volume.

WesDyne displayed a very high confidence of detection and sizing in their demonstration activities. Mockup (J) was the OD-flawed mockup used in the demonstration. Of the numerous flaws in this mockup, only one flaw (8% of the wall thickness) was missed during one inspection, and the flaw size was under the size used for the crack growth analysis in this report, i.e. 0.075" deep by 0.15" in length.

WesDyne also has examined approximately 5,000 nozzles during 62 outage campaigns and to date all nozzles returned to service as NDD have not leaked. There has been only one case where an indication resolved as NDD subsequently grew during the next cycle.

WesDyne's procedure also provides additional confidence with redundant analysis of any parent tube indication (PTI). The inspection procedure requires that any indication greater than 10% be identified as a PTI. The 10% limit is based on the manufacturing process whereby in process "modifications" do not exceed 10% wall removal into the nozzle. Since there is progressive PT during welding, some grinding and repair welding may be performed. A manufacturing repair is only documented if it occurs after the final PT, so everything prior to that is not considered a repair. Therefore, based on this cutoff, the demonstrated detection was 100%.

The inspection data analysis process uses two production analysts who report indications greater than 10%, and afterward a resolution analyst resolves the reported indication as having flaw/non-flaw characteristics. For example, if each analyst had a POD of 80%, their combined POD is 96%. With the third analyst, also with a POD of 80%, the combined POD would then be 99%. Therefore, with three looks at the data and 100% detection, the POD for the process should be extremely high.

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AM-2007-011 Revision 1 3 Metallurgical Examination of Byron Unit 2 Nozzle 68 After the indication was detected in Nozzle 68, the decision was made to collect a boat sample to gain a better understanding of the nature of the indication. This section presents the results of the metallurgical examination of the boat sample, discusses the factors involved in the initiation of PWSCC, and compares the occurrence of PWSCC in Byron Unit 2 to other reported cases of PWSCC in RPV head penetrations.

3.1 Metallurgical Examination Results In order to evaluate the indications that were found during the UT and PT examinations, a "boat" sample was removed from the Nozzle 68 tube and J-groove weld by electrode discharge machining (EDM). The laboratory analysis of the boat sample was conducted at BWXT in Lynchburg, VA, and the metallurgical failure analysis report9 was prepared by Exelon PowerLabs. Figure 3-1 illustrates the two dye penetrant indications (denoted by arrows) on the surface of the J-groove weld on Nozzle 68. The axial indication corresponded to the approximate location of the axial ultrasonic reflector, and the J-groove-weld toe extended beyond the axial indication. A rounded indication approximately 0.050" diameter was also detected.

After the boat sample was removed, a PT exam was conducted on the excavation site.

The PT exam uncovered an angled, subsurface linear defect that intersected the original axial indication; the subsurface defect was partially captured by the boat sample. The PT exam also showed that the deepest portion of the original surface axial indication was not captured by the boat sample nor was the original rounded surface PT indication. The post-excavation PT exam results are shown in Figure 3-2.

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AM-2007-011 Revision I Figure 3-1: A photograph of the two dye penetrant indications on the surface of the J-groove weld on CRDM 68.

Figure 3-2: A photograph of the field dye penetrant results of the excavation site after the boat sample was removed. The excavation uncovered an angled, subsurface linear defect (#3) that intersected the subsurface portion of the original axial linear defect (#2). The original rounded indication (#1) remained in the penetration.

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AM-2007-011 Revision 1 The boat sample measured approximately 1.5" long by 0.75" wide and had a maximum thickness of 0.375". The boat sample can be seen in Figure 3-3. The front surface is the wetted J-groove weld; the back surface is the EDM cut surface. Heavy grinding marks can easily be seen on the weld surface.

The horizontal cut between Sections A and B was below the axial indication on the wetted surface of the boat sample; however, it intersected the axial indication on the EDM surface. A metallurgical mount was prepared of this surface on Section B. The tube base metal contained branched, intergranular cracking typical of PWSCC. The crack branches had sharp tips and contained little oxidation. There was limited interdendritic cracking into the weld as shown in Figure 3-4. Within the Section B mount, none of the cracking in the tube extended to the wetted surface of the boat sample.

The horizontal cut face in Section B was also used to determine the hardness properties. The results of the hardness tests were considered typical for mill annealed Alloy 600 tubing and Inconel 182 weld metal; although, an area of relatively high hardness was present on the heavily ground (cold worked) surface layer of the weld.

Section C, shown in Figure 3-3, was used to determine the weld metal and tube metal chemistries, which were found to be consistent with Inconel 182 filler metal and the original heat fabrication records, respectively.

In the laboratory, Section A was subjected to bending along the axial indication to reveal the crack growth surface. The exposed crack surface of the tube material was reflective with an intergranular appearance (Figure 3-5). There were no clear indications of crack age in the tube material; however, a thumbnail-shaped region emanating from the EDM cut surface appeared to be more oxidized than the remainder of the sample.

The exposed surface of the weld exhibited characteristics typical of both PWSCC and hot cracking. Lack of fusion between weld passes, which was parallel to the fusion-line, could be seen on the exposed weld surface (Figure 3-6), and within the weld there were several cracks that were connected to the lack of fusion defect. Dimpled voids, which are indicative of ductile tearing, were present at various locations in the weld. It is likely that the ductile tearing regions were small intact ligaments that failed when the crack surface was broken open in the lab. In general, there were more ductile tearing regions adjacent to the wetted surface of the sample (also seen in Figure 3-6).

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AM-2007-011 Revision 1 Figure 3-3: A photograph of the boat sample after initial sectioning in the laboratory. The front surface is the wetted surface of the J-groove weld; the back surface is the EDM cut surface.

Figure 3-4: Photomicrograph of the metallurgical mount prepared from the horizontal cut face in Section B. The direction of crack growth is from the tube material into the weld. (Original magnification 375X; electrolytic phosphoric-nital dual etch) 18 of 66

AM-2007-011 Revision 1 Figure 3-5: A stereoscope view of the exposed surface of the axial indication from Section A. The weld is toward the left side of the sample.

Figure 3-6: A scanning electron micrograph of the exposed surface of the axial indication from Section A. The arrow points to the lack of fusion between the weld passes. A ductile region can be seen in the upper left corner of the sample.

(Original magnification 50X) 19 of 66

AM-2007-011 Revision 1 Based on the general characteristics of the weld defects, interdendritic weld separations, direction of crack branching, and local ductile tearing, it was concluded that the primary direction of propagation within the weld was toward the wetted surface of the boat sample. These characteristics suggest the PWSCC did not initiate from the wetted surface of the boat sample.

A portion of the subsurface angled defect was captured in the boat sample; the defect had the appearance of a rounded defect and was visible on the EDM cut surface of Section A. A metallurgical mount was prepared on a cross-sectional plane adjacent to the indication. After a series of grind-polish-examine steps, the indication was identified as a weld lack-of-fusion defect between the outer surface of the tube and the weld.

(Figure 3-7)

After repolishing the sample in preparation for an SEM exam, a porous inclusion near the edge of the lack-of-fusion crevice was uncovered as seen in Figure 3-8. Several incipient interdendritic cracks had initiated from the edge of the inclusion and the lack-of-fusion crevice. Most of the cracks appeared to be hot cracks; however, the angular appearance of two cracks appeared similar to incipient PWSCC.

The large inclusion and most of the smaller inclusions contained titanium, nitrogen, and oxygen. The lack-of-fusion crevice contained oxidized metallic particles from the EDM cutting tool and base metal debris. No measurable fluorine or other potentially corrosive elements were identified in the incipient cracks or the lack-of-fusion crevice.

The laboratory evaluations identified the axial indication as a combination of PWSCC and welding defects including lack of fusion and hot cracking. The subsurface defect was identified as lack of fusion between the outer diameter of the tube and the J-groove weld. Within the boat sample, the cracking characteristics indicated the PWSCC initiated at a subsurface location on the tube OD, propagated in an axial/radial direction into the tube, and propagated toward the wetted surface of the J-groove weld fillet leg.

The source of the original rounded indication on the weld wetted surface, which was not captured by the boat sample, cannot be determined. However, based on the presence of welding defects in the boat sample, the most probable cause is considered a welding imperfection that was not detectable or an indication that was considered acceptable per the fabrication inspection requirements. The Byron Unit 2 reactor head was fabricated by Babcock & Wilcox in 1977; the applicable code was the 1971 Edition of the ASME Section III, Summer 1973 Addenda. Per the 1971 edition of ASME Section Ill, NB-5000, an isolated 3/16" rounded dye penetrant indication would be considered acceptable. At 0.050", the rounded indication on the J-groove weld surface of CRDM

1. 68 was well within this limitation.

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AM-2007-011 Revision 1 Figure 3-7: An etched view of the lack-of-fusion defect contained in Section A.

Also note the flat interface at the fusion line, which indicates there was little penetration at this location. (Original magnification 190X, electrolytic phosphoric-nital dual etch)

Figure 3-8: A scanning electron micrograph of the lack-of-fusion defect after repolishing, which revealed the large inclusion. (Original magnification 200X) 21 of 66

AM-2007-011 Revision 1 The CRDM J-groove welds were fabricated with multiple weld passes. For Nozzle 68, grinding was performed throughout the weld to remove indications, and no weld repairs were reported for this penetration. A final fabrication dye penetrant examination was performed, and it is possible that the rounded indication was less than the minimum relevant size.

At the time of B2R1 4, the presence of PWSCC in Byron Unit 2 was unexpected based on the categorization of Unit 2 as a low susceptibility plant per the methodology of NRC Order EA-03-009. The conclusion drawn in the boat'sample failure analysis report is that the PWSCC was not the result of exposure of the Alloy 600 tube material to the bulk primary water environment; rather, the premature initiation of PWSCC is attributed to a series of weld defects, which created a conducive crevice corrosion environment in the high stress region of the J-groove weld.

3.2 PWSCC Requirements Stress corrosion cracking (SCC) is the term given to crack formation of susceptible alloys under the influence of a tensile stress of sufficient magnitude exposed to a system-specific corrosive environment. Most alloys are susceptible to SCC in at least one environment; although, pure metals are generally resistant to SCC. The three key elements that must be present simultaneously for SCC to occur are a susceptible metallurgical condition, a tensile stress, and a critical corrosive environment. The elimination of any one of these three elements or the reduction of one of these three elements below some "threshold" level can mitigate SCC.

3.2.1 Metallurgy SCC may be either transgranular or intergranular; however, the crack follows a macroscopic path that is generally normal to the tensile component of stress. The intergranular failure mode (IGSCC) suggests an inhomogeneity at the grain boundaries.

Primary water stress corrosion cracking (PWSCC) refers to IGSCC in the primary water environment of PWRs. Alloy 600 is a high nickel austenitic alloy containing approximately 72 weight percent nickel that is prone to PWSCC. In Alloy 600, the susceptibility to PWSCC is increased by a lack of contiguous coverage of chromium carbides at the grain boundary. Grain boundary coverage is dependent on the heat treating history and carbon content of the material.

3.2.2 Stress The reactor pressure vessel (RPV) head in a PWR has numerous penetrations for instrumentation and control rod drive mechanisms (CRDMs). The penetrations are held in place by a J-groove weld. Due to residual weld stresses and operational pressures, a number of high tensile stress regions exist in both the J-groove weld and the outer 22 of 66

AM-2007-011 Revision 1 diameter of the penetration tube. These tensile stresses can be above the threshold required to initiate and propagate PWSCC provided the material is susceptible and the environment is conducive to PWSCC.

3.2.3 Environment PWSCC of Alloy 600 and its weld metals (e.g., Alloys 182 and 82) is primarily affected by material properties and loading parameters; however, the fact that IGSCC of Alloy 600 occurs in an apparently innocuous environment such as deaerated high-purity water indicates a secondary effect by environmental factors on both PWSCC initiation and propagation. The environmental parameters that can affect PWSCC include lithium, boron, and zinc concentrations; pH at temperature; temperature; and dissolved hydrogen concentration10 with the largest impact being made by temperature and dissolved hydrogen.

Temperature is an environmental variable that strongly affects PWSCC crack initiation and propagation in Alloy 600. Temperature dependence has been represented according to an Arrhenius plot with an apparent activation energy. The propensity of PWSCC initiation and subsequent crack propagation increases with increasing temperature; however, at temperatures below 570°F (3000C) as is the case at Byron Unit 2, the high-value of the apparent activation energy indicates that both crack initiation and propagation become very slow processes.11 The main effect produced by an increase in partial pressure of hydrogen is the lowering of the corrosion potential to a more anodic value where SCC susceptibility is higher.

While this effect may be significant, a statistical evaluation of PWSCC initiation data indicates that the effect of hydrogen on PWSCC is not especially strong in the normal operating range of 25 to 50 cc/kg (2.2 to 4.5 ppm) dissolved hydrogen.

3.3 PWSCC In Byron Unit 2 This section considers the three key elements of PWSCC as applied to Nozzle 68. The mill annealed Alloy 600 material is known to be susceptible to PWSCC, and susceptibility is related to grain boundary carbide coverage. The Alloy 600 material from B&W Heat 80054 contained in the boat sample had grain boundary carbide coverage in excess of 50%12, which is considered to be a significant level of coverage.

The downhill side of the J-groove weld is a high tensile hoop stress region due to residual welding stresses and operating pressure; 13 although, it will be shown in Section 4 that Nozzle 68 does not represent the location with the highest probability for initiating PWSCC.

The low operating temperatures in the upper RPV head at Byron Unit 2 do not constitute an environment that is conducive to PWSCC during a life cycle of 2.2 EDY.

At this temperature, an extenuating factor must be involved for the pdmary water 23 of 66

AM-2007-011 Revision 1 environment to become a key element of SCC. In Nozzle 68, the extenuating factor was the crevice created by the lack-of-fusion defect. The local changes in the environment caused by the presence of a crevice are known to facilitate PWSCC initiation.

For PWSCC to initiate at a subsurface location and to propagate towards the wetted surface, the initiation site (i.e., the lack-of-fusion weld defect) would need to be wetted by the primary water. In Nozzle 68, the wetted path from the bulk primary water environment to the subsurface initiation site is believed to have consisted of a series of weld defects starting with the rounded surface indication and including lack of fusion between weld passes and between the tube and hot cracks within the weld. This conclusion is supported by the incipient cracks seen adjacent to the lack-of-fusion defects that were present between weld passes and between the weld and tube materials.

3.4 PWSCC Initiation and Chromium Depletion In an effort to understand the mechanisms of degradation affecting materials in light water reactors, EPRI has prepared the report Status Review of Initiationof EnvironmentallyAssisted Crackingand Short Crack Growth14 to provide a status review of current knowledge of SCC initiation and short crack growth in nickel base alloys, austenitic stainless steels, and carbon and low alloy steels exposed to typical PWR and BWR aqueous environments. The report illustrates that in deaerated high temperature water, the oxidation of Ni-Fe-Cr alloys leads to the formation of a multilayered oxide that is well crystallized and that may contain some nickel hydroxides. The inner, Cr-rich oxide layer is assumed to be protective. The external layer consists of relatively large crystallites spread over the surface and is much lower in chromium or even chromium-free. The overall thickness of this oxide is much greater than the passive layers formed near room temperature. It is not well established if only part of the inner oxide layer is truly protective, and the thickness of the inner layer is not known. Relatively recently, it has been demonstrated that the metal substrate can also undergo two types of damage during oxidation in high temperature water: 1) penetration of oxygen at the grain boundaries, and 2) selective oxidation of chromium resulting in a Cr-depleted layer.

This damage has been observed on Ni-base alloys such as Alloy 600.

The presence of a Cr-depleted layer on the surface and possibly at the grain boundaries may increase susceptibility to PWSCC. As stated by EPRI, this degradation mechanism warrants further investigation. Projecting the potential effects of chromium depletion to Byron Unit 2 does not reconcile the occurrence of PWSCC in Nozzle 68.

Chromium depletion on the wetted metal surface would presumably facilitate crack initiation on the wetted surface with crack propagation proceeding towards the interior of the weld or tube material. In the case of Nozzle 68, the direction of crack propagation was from a subsurface location towards the wetted surface of the J-groove weld.

24 of 66

AM-2007-011 Revision 1 3.5 Other Industry PWSCC Experiences 3.5.1 Palisades

Background

Palisades is a Combustion Engineering (CE) unit that began commercial operation in December 1971. During refueling outage (RFO) 17 in October 2004, Palisades conducted full volumetric UT examinations of the RPV head penetrations per NRC Order EA-03-009. At that time, Palisades was a moderate susceptibility head with an EDY -9. The ultrasonic inspections revealed leak path indications in CRDM Penetrations 29 and 30. A bare metal visual examination was performed on the exterior of the RPV head, and no evidence of leakage was visible. Dye penetrant testing on the two penetrations showed minor surface indications that required further evaluation.

Grinding operations on Penetration 29 revealed a 14" axial indication perpendicular to the fusion line of the J-weld and butter and on Penetration 30 revealed a circumferential crack approximately 1" long adjacent to the fusion line of the J-weld and the butter. The cracks were small and tight with no visible evidence of leakage. Although, a boat sample was not removed from either penetration, the bottom portion of each nozzle was cut and removed. New half nozzles were inserted and welded to the upper portion of the existing nozzles and to the RPV head. The unit was placed back into service.

Without a metallurgical analysis, Palisades did not have the basis to seek relaxation or relief from the inspection requirements of the Order. As such, Palisades is now classified as a high susceptibility head per the Order. Full volumetric UT and BMV examinations were conducted at the subsequent refueling outage (RFO 18 in Spring 2005), and no indications were found.

Comparison to Byron Unit 2 The initiation point for PWSCC at Palisades was not determined; however, observations made during the in-situ exploratory grinding operations performed on the surface suggest that the direction of crack propagation was from the external wetted surface towards the interior. In contrast, the PWSCC in Byron Unit 2 originated at a subsurface location and progress towards the external wetted surface. Palisades also had a higher value of EDY than Byron Unit 2, so the effect of time at temperature was greater at Palisades.

3.5.2 Oconee Unit 1

Background

Oconee Unit 1 is a Babcock & Wilcox (B&W) unit that began commercial operation in July 1973. As of February 2001, the estimated EDY for Oconee Unit 1 was 22.1, which is in the high susceptibility category. During refueling outage 19 in November 2000, a visual inspection on the top surface of the RPV head was performed as part of the 25 of 66

AM-2007-011 Revision 1 normal shutdown surveillance. The visual inspection and subsequent video inspections showed evidence of boric acid crystals on the vessel head surface around five thermocouple nozzles and CRDM Nozzle 21. An eddy current inspection of CRDM Nozzle 21 performed by Framatome ANP did not identify any indications that suggested a through-wall leak path. An ultrasonic examination of Nozzle 21 was performed'ih an attempt to locate evidence of OD surface cracking or lack of bond condition. The initial 01 weld profile scan showed evidence of a region of lack of bond between the tube OD surface and the J-groove weld; however, a rescan of the nozzle indicated no lack of bond condition existed.

The thermocouple nozzles were each found to contain large axial, crack-like indications originating on the inside of the nozzles above the weld. These cracks were determined to be the leakage pathway for the thermocouples. A boat sample was removed from CRDM Nozzle 21 to determine the cause of the observed radial cracking and to reconcile the UT signal reflection anomalies detected between the nozzle wall and the attachment weld. PWSCC was determined to be the primary mechanism of crack propagation in the weld and CRDM housing base metal. There was some evidence of hot cracking; however, this crack morphology appears to be secondary to the PWSCC.

The destructive examination did not reveal any cracks or other discontinuities at the interface between the weld and the tube material that would explain the anomalous UT signal from this region.

Comparison to Byron Unit 2 Based on EDY, Oconee Unit 1 was a high susceptibility unit at the time of the inspection. The PWSCC observed in CRDM Nozzle 21, and presumably the thermocouple nozzles, was due to exposure of the susceptible material to the corrosive environment in a region of high tensile stress. The occurrence of PWSCC in this unit was not unforeseen based on time at temperature and was not initiated by any identified anomaly.

3.5.3 Ohl Power Station Unit 3 - Kansal Electric Power Company

Background

Ohi Power Station Unit 3 is a Mitsubishi Heavy Industries unit, which began commercial service in 1991. During the 10 th periodical inspection in April 2004 boric acid was detected near the root of CRDM Penetration 47. Leakage from this nozzle was found, and subsequent visual inspections of the remaining 69 locations revealed boric acid deposits on Penetration 67, a thermocouple penetration. At the time of the inspection, the value of effective degradation years (EDY) for this unit was 4.8, which is considered low susceptibility.

Penetration 67 was examined using eddy current testing, UT, and a helium leak test, and no significant signal indications were found. A review of the records of previous inspections showed leakage of primary coolant from the conoseal cover around the 26 of 66

AM-2007-011 Revision 1 upper part of Penetration 67 during trial operation. Previous reports suggested that the leaked boric acid was not properly removed from the nozzle at the time of commissioning, and it has remained in place since that time.

Penetration 47 was examined using eddy current testing, and no significant indications of flaws were observed in the interior of the nozzle. Using the advanced Grooveman with low frequency, two signal indications of cracking were identified in the J-groove weld. Ultrasonic testing revealed no significant signal indications in either the base metal of the nozzle or in the vicinity of the nozzle. Dye penetrant test indications were found on the J-groove weld in the same region as detected using eddy current testing.

No helium gas was detected during a leakage test of the interior of the nozzle; however, helium gas was detected during a test of the J-groove weld and vicinity.

A boat sample was not removed; however, in-situ metallurgical replicas were prepared.

Linear cracks were identified on the J-groove weld surface in the same region as the ET and PT indications. The cracks were observed mainly along the dendrite boundary of the weld metal in the area where PT found indications. Subsequent surface grinding and replication revealed longer, branched cracks along the grain boundaries of the weld metal. After the exam, the J-weld portion of Penetration No. 47 was repaired by weld overlay using Alloy 690. Circumferential abrasions, which were presumed to be grinder marks, were observed in the vicinity of the indications, but marks indicative of buffing, which was required under the normal manufacturing procedures, were not observed.

Mock-up experiments suggest that the lack of buffing on the J-groove weld left the surface under residual tensile stress. The findings indicate that the combination of residual tensile stress, material, and environmental conditions led to the initiation of stress corrosion cracking and the propagation of a through-wall crack.

Comparison to Byron Unit 2 Like Byron Unit 2, Ohi Unit 3 was a low susceptibility head based on EDY. The conclusion drawn by the owner, Kansai Electric Power Company, was that the PWSCC was precipitated by a high level of tensile residual stress attributed to the failure to perform a buffing step during the welding procedure. While a boat sample was not taken, in-situ metallurgical replicas characterized the cracking as typical of PWSCC and laboratory mock-up testing verified that high residual tensile stresses could result from the lack of buffing. The cause of the PWSCC at Ohi Unit 3 is not the same as Byron Unit 2; however, both were isolated occurrences. In both cases, a situation existed in the effected nozzle that made the circumstances unique and increased the susceptibility to PWSCC. Byron Unit 2 and Ohi Unit 3 illustrate that widespread PWSCC is not likely in a low susceptibility head without a unique set of extenuating conditions.

4 Probabilistic Assessment of PWSCC In Byron Unit 2 As reported above, the occurrence of PWSCC in Byron Unit 2 after only 2.2 effective degradation years was not expected, and the three factors necessary to initiate PWSCC 27 of 66

AM-2007-011 Revision 1 would not have been met without the presence of the identified weld defects. To illustrate the uniqueness of the PWSCC event, an assessment of primary water stress corrosion cracking in head penetration Nozzle 68 was conducted by employing probabilistic and structural reliability tools. Included in the assessment as a comparison was Nozzle 72, which, at a 470 angle to the reactor head, represents a location more prone to PWSCC. To calculate the probability of failure of an Alloy 600 vessel head penetration as a function of operating time (t), structural reliability models were used with Monte Carlo simulation methods. This section describes these structural reliability models and their basis for the primary failure mode of crack initiation and growth due to PWSCC, the assessment results, and the conclusions.

4.1 Probabilistic Models for PWSCC Assessment The models used for the probabilistic evaluation of head penetration nozzles1 5 were developed in 1997 and applied to the vessel head penetrations in 41 Westinghouse plants for their response to NRC Generic Letter 97-01. At that time, these probabilistic models had already been verified in the following ways:

1. Calculated stresses compare well with measured stresses (see Figure 4-1).

2. Crack growth rates agree with measured field data (see Figure 4-2).

3. All models have been independently reviewed by APTECH Engineering 16, and an improved model was developed for the effect of monotonic yield strength on time to initiation.

4. A wide range (both high and low values) of calculated probabilities is consistent with actual plant observations that were available in 1997 (Table 4-1).

28 of 66

AM-2007-011 Revision 1 Table 4-1 1997 Comparison of VHPNPROF Calculated Probabilities with Plant Observations Parameters Almaraz 1 D. C. Cook 2 Ringhals 2 North Anna 1 Hours of Operation 85,400 87,000 108,400 91,000 Setup Angle (0) 42.6 50.5 38.6

• Temperature (°F) 604.3 598.5 605.6 600.0 Yield Strength (ksi) 37.5 58 51.2 51.2 Percent GBC 57.0 44.3 3.0 2.0 Flaw Depth/Wall 0.10 0.43 0.25 0.10 Initiation Probability 1.1% 41.4% 37.6% 15.3%

Failure Probability** 1.1% 38.1% 34.6% 15.3%

Penetrations with Reported 0 1 3 0 ISI Indications (2 with scratches)

Notes:

• Calculations performedat an equivalent setup angle for the second-highest stress location since it could be inspected.

• • Defined here as the probability of reaching the specified flaw depth for the individual penetration, 29 of 66

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AM-2007-011 Revision 1 As results of further nozzle inspections became available in 2003, the 1997 probability calculations were reevaluated and still found to be consistent with these observations (Table 4-2). In the models for PWSCC assessment, the most important parameter for estimating the failure probability is the time to failure, tf in hours. It is defined as follows:

tf = tj + (af - ao) / (daldt) (4-1) where:

ti = time to initiation in hours af = failure crack depth in inches ao = crack depth at initiation in inches*

da/dt = crack growth rate in inch/hour Table 4-2 2003 Comparison of VHPNPROF Calculated Probabilities with Plant Observations Parameters Beaver Valley 1 Farley 2 1997 WCAP Report 14913 (Ref. 31) 14906 (Ref. 32)

Years of Operation 27 22 Setup Angle (0) 38.6 42.6 Temperature (OF) 607.0 596.9 Yield Strength (ksi) 48.5 48.5 Percent GBC 23.0 23.0 Flaw Depth/Wall 0.75 0.75 Probability of Flaw of This Depth 43.9% 27.6%**

Penetrations with Reported ISI 4 0 Indications in 2002 (-50% through wall)

• • Note: Probabilities do not reflect any reduction due to several years of operation with Zinc Addition

• a., the crack depth at initiation is 1.5 mm or 0.059 inches for consistency with previous assessments.

32 of 66

AM-2007-011 Revision 1 In Equation (4-1), both the crack depths at failure and initiation may be specified as a fraction of the penetration wall thickness (w). The failure depth af depends upon the failure mode being calculated. Since the failure mode of concern is axial cracks in the penetration that are deeper than the structural limit of 75 percent of the penetration wall thickness (w),.it would be specified as:

af = 0.75 w (4-2)

The constant 0.75 in equation (4-2) can be replaced with other values for different failure modes, such as 0.10 for crack initiation, 0.50 for an observed flaw half-way through the wall or 0.995 for a through-wall flaw that could result in a small leak.

The time to PWSCC crack initiation, tj in hours, is consistent with that developed for PWSCC susceptibility by Rao 17 as updated by Begley and Woodman of APTECH16:

_C,(I+ C2PGBc) ( Q1_"*

ti (T)' exp- (4-3)

C1 the initiation coefficient, which was based upon the data of Hall and others1 8 for forged Alloy 600 pressurizer nozzles, with only the uncertainty in a log-normal distribution based upon the data of Gold and others 19 ,

C2 = coefficient for the effect of grain boundary carbide coverage, which is based upon the data of Norring and others2°,

PGBC = percentage grain boundary carbide coverage in the penetration material, a = the maximum residual and operating stress level derived from the detailed 21 elastic-plastic finite-element analysis from the WOG study of Ball and others as shown in Figure 4-1, with its normally distributed uncertainty being derived from the variation in ovality from Duran and others 22 as shown in Figure 4-3, which is a trigonometric function of the penetration diameter and setup angle (local angle between the head and longitudinal axis of penetration),

Sy yield strength of the penetration material, n1,n2 = exponents on stress and yield strength, respectively (n, = 4, n2 = 2.5),

Q,= the activation energy for crack initiation, which is normally distributed, R = universal gas constant and T = the penetration absolute temperature, which is uniformly distributed based upon the calculated variation of the nominal head operating temperature.

33 of 66

AM-2007-011 Revision 1 Either data from field replication, as was done for Beznau Unit 223 or the correlation model by Rao24 can be used to determine the percent grain boundary carbide coverage, PGBC in Equation (4-3). The model developed by Rao is a statistical correlation of measured values with the certification parameters for 39 commercial heats of Alloy 600 head penetration nozzle materials. For Byron Unit 2, this model was used to calculate the percentage grain boundary carbide coverage in B&W Heat 80054 for Nozzle 68 and B&W Heat 90704 for penetration Nozzle 72 in the same row (highest initiation probability of all nozzles) for the PWSCC assessments. Table 4-3 compares the tensile and chemistry values for these material heats with the range of values that were used to develop the correlation model (Ref. 24). For Heat 80054 in cracked Nozzle 68, chemistry values were available from both the heat certification 25 as well as the metallurgical evaluations of the boat sample by Exelon (Ref. 9).

Table 4-3 Comparison of Material Properties for Byron Unit 2 Head Penetrations and Model Correlation for PGBCC*

Heat No. Data YS* UTS* Carbon Manganese Nickel (Nozzle) Source (Ref.) (Ksi) (Ksi) (%) (%) (%)

80054 (68) CMTR* (25) 36.5 94.6 0.029 0.27 76.23 80054 (68) Boat Sample (9) N/A N/A 0.023 0.14 76.00 90704(72) CMTR* (25) 40.3 90.4 0.024 0.24 75.34 Minimum Model (24) 30.5 83.5 0.028 0.16 73.66 Maximum Model (24) 54.5 104.3 0.100 0.88 85.20

• Abbreviations: PGBCC = percent grain boundary carbide coverage YS = 0.2% offset yield strength UTS = ultimate tensile strength CMTR = certified material testing report N/A = not available 34 of 66

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AM-2007-011 Revision 1 The hours at temperature per operating cycle (one year), which are normally distributed, are used to check if crack initiation has occurred. Even though the operating cycle for Byron Unit 2 is 18 months or 1.5 years, a one-year cycle is used for the PFM calculations, because this value was previously requested by the regulatory reviewers.

Once the crack has initiated, it is assumed to have a depth of a( and its growth rate, da/dt, is calculated by the Peter Scott model, which matches the latest Westinghouse and French data and the previous data given in the WOG report on the industry Alloy 600 PWSCC growth rate testing results26. The crack growth rate is given by:

-- =C3(K,-KT) 1expF--"-1 (4-4) dt '~RT}

C3 = a log-normally distributed crack growth rate coefficient (see Figure 4-2)

K, = the stress intensity factor conservatively calculated assuming a constant stress through the penetration wall for an axial flaw at the inside surface with a length six times its depth using the following form of the Raju and Newman equations27:

K,=0.982+ 1.006(a / w) 2 r(rra) 5 (4-5) 2= activation energy for PWSCC crack growth, which is also normally distributed, and KTH= threshold stress intensity factor for crack growth.

The probability of failure of the Alloy 600 vessel head penetration as a function of operating time t, is calculated directly for each set of input values using Monte Carlo simulation. Monte Carlo simulation is an analytical method that provides a histogram of failures with time in a given number of trials (simulated life tests). The area under the simulated histogram increases with time due to PWSCC. The ratio of this area to the total number of trials is approximately equal to the probability of failure at any given time. In each trial, the values of the specified set of random variables are selected according to the specified distribution. A mechanistic analysis is performed using these values to calculate if the penetration will fail at any time during its lifetime (e.g., 20, 40 or 60 years). This process is repeated many times (e.g., 60,000) until a sufficient number of failures is achieved (e.g., ten per year) to define a meaningful histogram, which is an approximation of the lower tail of the true statistical distribution in time to failure (see Figure 4-4). The shape of the distribution depends upon the input median values and specified distributions of the random variables. For the worst penetration in one plant, the mean time to failure was greater than 160 years but its uncertainty was so large that the normalized area under the histogram (estimated probability) at 60 years was 8 percent.

36 of 66

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AM-2007-011 Revision 1 To apply the Monte Carlo simulation method for vessel head penetration nozzle (VHPN) failure, the existing PROF (probability of failure) object library in the Westinghouse Structural Reliability and Risk Assessment (SRRA) software system was combined with the PWSCC structural reliability models. This system provides standard input and output, including plotting and probabilistic analysis capabilities (e.g., random number generation, importance sampling). The result was program VHPNPROF for calculation of head penetration failure probability with time. Descriptions of the 21 VHPNPROF input variables are given in Table 4-4. This table also indicates the type of statistical

• distribution that was used to simulate the uncertainty in each random variable. The uncertainty in those variables with a constant distribution was not simulated in the current PWSCC assessment.

The Westinghouse SRRA Software System has been verified by hand calculation for simple models and alternative methods for more complex models 28 . Also, the application of this same Westinghouse SRRA methodology to the WOG-sponsored pilot program for piping risk-based inspection has been extensively reviewed and verified by the American Society of Mechanical Engineers (ASME) Research Task Force on Risk-Based Inspection (RBI) Guidelines 29 and other independent NRC contractors. Table 4-5 provides a summary of the wide range of parameters that were considered in this comprehensive benchmarking study that compared the Westinghouse-calculated probabilities from the analysis (labeled SRRA) with those from the pc-PRAISE program 30 . As shown in Figure 4-5, the comparison of calculated probabilities after 40 years of operation is excellent for both small and large leaks and full breaks, including those reduced due to taking credit for leak detection.

As indicated previously, the VHPNPROF Program calculated probabilities of getting a given crack depth due to PWSCC were compared for four plants where sufficient head penetration information and inspection results were available in 1997. The four plants are identified in Table 4-1 along with the values of the key input parameters and calculated failure probabilities. This table also shows the agreement between the inspection results available in 1997 and the VHPNPROF predicted failure trends due to PWSCC.

Almost five years later, the 1997 VHPNPROF results were found to predict the latest Beaver Valley and Farley inspection results. As shown in Table 4-2, the four head penetration nozzles (50 to 53) with deep cracks at Beaver Valley Unit 131 were predicted to have very high probability of a flaw 75% through the wall after 27 years of operation.

For Farley Unit 22, the same material that cracked at Beaver Valley was in almost all the head penetrations but no cracking was observed after 22 years of operation. In both cases, the percent grain boundary carbide coverage was not a predicted value, but a measured value from field replication. The lack of cracking was predicted at Farley Unit 2 because it had operated about five years less that Beaver Valley Unit 1 at a head temperature about 10OF lower. It also operated for several years with Zinc Addition, which is a PWSCC mitigation measure whose effects were not reflected in the probabilities of Table 4-2. Large cracks were never observed at Farley Unit 2 because the vessel closure head and its penetration nozzles were replaced before they could 38 of 66

AM-2007-011 Revision 1 occur. Therefore, it can be concluded that the probability ranges are 34% to 44% for expected failure and 0% to 33% for unexpected failure.

Table 4-4 Variables for Structural Reliability Model of Reactor Vessel Head Penetration Nozzle (VNPNPROF)

No6 Name Description of Input Variable Distribution I ANGLE-P Penetration setup angle (degrees) Constant 2 C0-SIGR Peak hoop stress at 0 degrees (ksi) Normal 3 C1-SIGR Change in stress with angle (ksi) Constant 4 PTEMP-F Penetration material temperature (F) Uniform 5 S-YIELD Material monotonic yield strength (ksi) Normal 6 NCY-ISI Cycles between inservice inspections Constant 7 D05-ISI Depth at 5% detection probability (in.) Constant 8 D50-ISI Depth at 50% detection probability (in.) Constant 9 HRS@T/CY Hours at temperature per operating cycle Normal 10 CO-TINIT Initiation coefficient at 0 PGBCC (hr) Log-Normal 11 PGBCC-TI Percent grain boundary carbide coverage Normal 12 Q-TINIT Initiation activation energy (cal/mole) Normal 13 SEXP-TI Stress exponent for initiation time Constant 14 CI-TINIT Initiation time change with PGBCC (hr) Constant 15 C-GRATE Crack growth rate coefficient (in./hr) Log-Normal 16 KITH-GR Threshold stress intensity (ksi-in.A.5) Constant 17 Q-GRATE Growth rate activation energy (cal/mole) Normal 18 KEXP-GR Growth rate stress intensity exponent Constant 19 DEPTH-L Crack depth at Initiation (in.) Normal 20 DEPTH-L Limit on crack depth (fraction of wall) Constant 21 TH-WALL Penetration wall thickness (in.) Normal 39 of 66

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Perfect Small Large Full Fit Leak Leak Break

............... 0 0 A 0

AM-2007-011 Revision 1 Table 4-5 Parameters Used for the Dc-Praise Benchmarkina Studv Type of Parameter First Value Second Value Pipe Material Ferritic Stainless steel Pipe Geometry 6.625" OD 29.0" OD 0.562" Wall 2.5" wall Failure Modes Small leak Full break (through-wall crack) (unstable fracture)

Last-Pass Weld Inspection No 4-ray Radiographic Pressure Loading 1000 psi 2235 psi Low-Cycle 25 ksi range 50 ksi range Loading 10 cycles/year 20 cycles/year High-Cycle* 1 ksi range 20 ksi range Loading 0.1 cycles/r in. 1.0 cycles/sec.

Design Limiting Stress 15 ksi 30 ksi Disabling Leak Rate 50 gpm 500 gpm Detectable Leak Rate None 3 gpm

• Note: Mechanical vibration (1st value of stress range and 2nd value of frequency) for small pipe, thermal fatigue (2nd value of stress range and 1st value of frequency) for large pipe.

4.2 PWSCC Assessment Results The probabilistic PWSCC assessment results of the vessel head penetrations nozzle (VHPN) numbers 68 and 72 in Byron Unit 2 are summarized in Table 4-6. This table provides the probability of initiating a flaw due to PWSCC as well as propagating it 50 percent (observed in Nozzle 68) and 100 percent through the wall at the end of 20 years (1987 through 2007) of operation at a head temperature of 551* F. The small differences in the minimum and maximum values of probability for head penetration Nozzle 68 are due to the difference in the predicted value of grain boundary carbide coverage for the two sets of chemistry values for the VHPN material heat 80054 that are reported in Table 4-3.

The probabilities based on the occurrence of 50% through-wall crack in VHPN number 68 that was observed after 20 years in Table 4-6, are significantly lower (approximately three orders of magnitude) than the values predicted for observed cracking due to PWSCC initiation and growth in Tables 4-1 and 4-2. The 20-year probabilities reported in Table 4-6 also indicate that crack initiation and growth due to PWSCC is four to six times more likely to occur in VHPN Number 72 than VHPN Number 68, where it was 41 of 66

AM-2007-011 Revision 1 observed in Byron Unit 2. This probability further indicates that another factor (namely, lack of fusion in the weld) facilitated the initiation of PWSCC in Nozzle 68.

Table 4-6 Summary of Byron Unit 2 RVHP Probabilities at 20 Years Penetration No. Failure Mode Probability 68 Initiation 1.90 E-04 (Minimum) 50% Through Wall 4.49 E-05 100% Through Wall 2.06 E-05 68 Initiation 1.97 E-04 (Maximum) 50% Through Wall 4.66 E-05 100% Through Wall 2.15 E-05 72 Initiation 1.20 E-03 100% Through Wall 8.03 E-05 4.3 Effects of In-Service Inspections The beneficial effects of in-service inspection (ISI) were modeled and calculated in the same way as was done in the PFM models for piping RI-ISI (Ref. 28) and in the NRC sponsored pc-PRAISE Code (Ref. 30) for PFM analysis of piping welds. Specifically, only the flaws remaining after an ISI exam are left to cause failures (larger flaw depth of concern) later in life, because flaws that are detected are assumed to be repaired or removed. Existing fabrication or initiated flaws that were not detected in the initial examination would remain in the nozzle and be subject to potential crack growth due to PWSCC. If the undetected crack grows, then the chance of its being detected during a subsequent inspection will increase. The input to these PFM models for the effects of ISI should be selected to represent the inspection accuracy and frequency for the inspection that have been, or will be, performed in accordance with the requirements for reactor vessel head penetration nozzles.

For Byron Unit 2, penetration Nozzle 68 was inspected after 20 years of operation and the fabrication-induced flaw from which PWSCC initiated and slowly propagated at the relatively low head temperatures was detected and subsequently repaired. As noted previously, during this same inspection no flaws were detected in Nozzle 72, which had a higher probability of flaw initiation and growth than for Nozzle 68. This was as expected since Table 4-6 shows that the probability of initiating a flaw due to PWSCC after 20 years of operation is only 0.12%. Since this probability and the probability of having a through wall flaw, which is the primary concern because it could result in a small leak of boric acid, both increase with operating time, Nozzle 72 was selected for 42 of 66

AM-2007-011 Revision 1 evaluation of the effects of ISI after the initial inspection after 20 years. ISI frequencies of 3, 6 and 9 years (2, 4 and 6 operating cycles) were evaluated to determine an acceptable frequency based upon the probability of a through-wall flaw after 60 years of operation.

The probability of detection (POD) that was used in the evaluation of ISI effects was linearly proportional to (a/t), where a is flaw depth and t is the penetration nozzle wall thickness. For this POD of flaws due to PWSCC, there would only be a 10% probability of detecting a flaw depth 10% through the wall and a 50% probability of detecting a flaw depth half way through the wall. This is very conservative because it minimizes the benefit of ISI. In addition, the PWR Materials Reliability Program (MRP) inspection demonstration for Alloy-600 head penetration nozzles (Ref. 8) showed a very high POD for flaw depths equal to or greater than 10% of the wall thickness.

The effects of IS frequency for Byron Unit 2 head penetration Nozzle 72 for inspections after 20 years of operation are shown in Table 4-7. As can be seen in this table, the effect of subsequent ISI is to decrease the probability of a through-wall flaw after 60 years of operation from 2.4% with no ISI to 0.065% with ISI every 6 years (a factor of

-37 reduction). Any of the ISI frequencies that were evaluated, 3, 6, or 9 years (2, 4, or 6 cycles), would be acceptable. These ISI frequencies provide significant improvement over the no ISI case, and the difference between inspection intervals is a factor of three or less.

Table 4-7 Effect of ISI on Cumulative Probability of Through Wall Flaw In Byron Unit 2 Nozzle 72 for First ISI at 20 Years End of Without ISI Every ISI Every ISI Every Year Any ISI 3 Years 6 Years 9 Years 20 8.03E-05 8.03E-05 8.03E-05 8.03E-05 25 4.42E-04 1.66E-04 2.28E-04 2.28E-04 30 1.33E-03 2.OOE-04 3.92E-04 5.24E-04 35 3.33E-03 2.12E-04 5.42E-04 7.89E-04 40 5.86E-03 2.13E-04 6.12E-04 1.02E-03 45 8.95E-03 2.13E-04 6.34E-04 1.12E-03 50 1.29E-02 2.13E-04 6.43E-04 1 .18E-03 55 1.84E-02 2.13E-04 6.46E-04 1.22E-03 60 2.41 E-02 2.13E-04 6.47E-04 1.24E-03 4.4 Probabilistic Assessment Summary and Conclusions

1. PWSCC probabilistic failure assessments were made by employing Westinghouse crack initiation and growth models that were benchmarked in 1997 with cracking 43 of 66

AM-2007-011 Revision I observations in four plants and confirmed six years later with cracking observations in two additional plants.

2. The results of the probabilistic assessments showed that the probability of having the observed 50% through-wall flaw in Nozzle 68 after 20 years of service were three orders of magnitude below those expected (34% to 44%) for flaw initiation and growth due to PWSCC in Byron Unit 2.

3. The results of the PWSCC probabilistic assessments also showed that the observed 50% through-wall flaw did not occur in the most likely nozzle location in Byron Unit 2.

4. The conclusion of these probabilistic calculations is that the 50% through-wall flaw depth observed in vessel head penetration Nozzle 68 of Byron Unit 2 is not due to normal flaw initiation and growth by PWSCC in the Alloy 600 base metal. Additional conditions, such as those identified in the boat sample metallurgical analysis, are needed to initiate and grow a PWSCC flaw in Nozzle 68.

5. This conclusion is further supported by inspection results from cold head plant upper head penetrations and bottom mounted penetration nozzles, as described in Section 2.3.

6. The effect of in-service inspection after 20 years of operation is to reduce the probability of a through-wall flaw due to initiation and growth by PWSCC after 60 years of operation by a factor of about 37 for an inspection interval of six years.

7. Based on these analyses, an inspection frequency for Byron Unit 2 that is consistent with a low susceptibility head would not significantly increase the probability of a through-wall crack and subsequent leakage on top of the RPV head; therefore, the low susceptibility inspection frequency is acceptable.

4.5 Welbull Analysis of Cold Head RVHP Inspection Results In order to determine the probability of developing repairable indications for future outage intervals, a statistical analysis of available industry experience for Alloy 600 reactor vessel head penetrations (RPVH) was conducted for reactor heads with a temperature similar to Byron Unit 2. The goal of this work is to determine the probability of occurrence of repairable indications for future inspection outages. RVHP inspection data available for 18 four-loop cold head plants is summarized in Section 2.3. The effective degradation years (EDY) at the time of inspection for these plants range from about 1.9 to 2.5. An effective degradation year is equivalent to one effective full power year at 600°F. The Byron 2 inspection occurred at 2.2 EDY.

The statistical model is designed to provide probabilistic predictions of the number of RVHP nozzle surfaces that will develop a recordable flaw similar to that discovered at Byron Unit 2 in the interval between the B2R13 and B2R14 inspection outages. The results of the base case are summarized in Table 4-8. The predicted probability of 44 of 66

AM-2007-011 Revision 1 flaws requiring repair developing in one or more penetrations during that interval is 1%.

Restated, if a thousand heads were observed over the interval of interest, 99% of these heads are expected have head penetrations without flaws; equivalently, 1% of the heads would have one or more flawed RVHP.

One assumption of this analysis is that, within the population of cold head plants, the occurrence of a flaw on one penetration at a point in time is independent of (uncorrelated with) the occurrence or non-occurrence of a flaw on another penetration.

This assumption is supported by the unique set of factors that caused the flaw found in Nozzle 68 at Byron Unit 2 (refer to Section 3).

4.5.1 Description of Steps Taken In Developing the Statistical Model Step 1: Specify a failure model:

The Weibull distribution is the most popular statistical model of corrosion-related failure.

The Weibull cumulative probability of failure (in this'case, "detectable indications") by the time of the last inspection (t,) for the ith penetration in a specified group is:

p = 1- exp(-(t@ / a),8) (4-6)

The alpha (a) parameter is the "characteristic life" of a penetration. Due to data limitations, the beta (1) shape parameter must be inferred from other studies. Statistical analyses of PWSCC in Alloy 600 materials 33'3 4 suggest a shape value of 2.0 to 3.0. A value of 2.5 is assumed for the base case analysis; the basis for this assumption is provided below.

Step 2: Estimation of characteristiclife (alpha):

If failures exist in the data set of interest, then the value of alpha is 35:

t15 (4-7)

In - (x5 / N(47 Step 3: Predictthe unconditionalprobabilityof ith penetrationfailure between the last (EDY=t13) and next inspection (ED Y=t4):

q = exp(-(t 1 3 / dj)p) - exp(-(t1 4 / 6)) (4-8)

An indication is defined as having one or more recordable, detectable flaws in the base metal of the penetration surface of interest. This.is the probability of indications in the time interval of interest before it is known if the penetration has survived to the last inspection.

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AM-2007-011 Revision 1 Step 4: Predictthe conditionalprobability of the ih penetrationfailing between the last and next inspection, given that it survived to the last inspection:

q= (4-9) i-p This step adjusts for the fact that the penetration has survived, without detectable degradation, to the last inspection. If a nozzle surface has not survived but has been repaired, as is the case for Byron Unit 2 Nozzle 68, then the surface for that nozzle is assumed to be impervious to PWSCC for the time interval of interest here (one refueling cycle).

Step 5: Predictthe probabilityof x>O for the N penetrationsfailing between the two inspections:

probability (1 or more VHPN with flaws) = 1- Binomdist(O, N, Tr) (4-10)

In Excel, binomdist(0, N, Tr)is the function for the binomial distribution calculating the probability of zero "failures" in N trials given the probability of failure on any given trial is 1T. Thus Equation 4-9 calculates the probability of one or more VHPN with indications as one minus the probability of zero ID indications. Probabilities of any surfaces with flaws up to N can also be calculated using this distribution.

Step 6.: Calculate the probability distributiondescribingthe predicted number of penetrationshaving one or more recordable flaws in the Byron 2 reactorvessel head by the next inspection:

The probabilities of finding 0, 1, 2, ... et cetera nozzles with one or more flaws are calculated using the binomial function shown on the right side of Equation 4-10. Note that the prediction is for the number of penetrations that have one or more flaws (there may be more than one flaw, usually called an "indication" in NDE parlance, on a penetration, but this is not counted here).

4.5.2 Weibull Shape Parameter Since only one detectable defect has been found out of 1,404 cold head RVHP inspections, a shape parameter must be assumed in order to determine the Weibull "characteristic life" or scale parameter (P). The pattern of the failure rate over time determines the appropriate Weibull shape parameter. The failure rate is defined as the frequency with which a component experiences a failure at time (t) given that it has survived to that time. It is expressed as failures per unit time. A shape parameter of P<1 implies a decreasing failure rate over time consistent with component "infant mortality". A shape parameter of fr=1 implies a failure rate which is constant over time or "random" failures. When 3=2, it implies a failure rate which increases linearly with time. Shape parameter values between 1 and 2 imply an increasing failure rate with a 46 of 66

AM-2007-011 Revision 1 decreasing rate of increase. Shape parameters greater than 2 imply increasing failure rates with increasing rates of increase.

Statistical analyses of PWSCC in Alloy 600 materials (References 33 and 34) suggest a shape value of 2.0 to 3.0. The base case Weibull analyses are based on an assumed value of 2.5. Sensitivity results are provided for shape parameters of 2.0 and 3.0.

4.5.3 Results of the Statistical Analysis For the assumed base case Weibull shape parameter of 2.5, the calculated scale parameter is 35.2 EDY. This represents the time at which 63.2 percent of RVHP cold head locations would be repaired. With an increase of 0.1 EDY per calendar year of plant operation, this would be equivalent to about 352 years of operation. Table 4.8 indicates that based on these Weibull parameters, the projected mean repairs at B2R134 are 0.018% or 0.018 penetrations out of 77 RVHP. This is consistent with a 1.41%

probability that one or more RVHP repairs would be required. If the next RVHP inspection is during B2R17, these values would increase to mean repairs 0.085% or 0.065 penetrations out of 77 RVHP with a 5.00% probability that one or more RVHP repairs would be required.

Table 4-8 Weibull Analysis Base Case (Weibull Shape Parameter = 2.5 and Weibull Scale Parameter = 34.5)

Outage # 14 17 21 EDY at Outage 2.35 2.80 3.40 Mean Repairs (%) 0.018% 0.085% 0.202%

Mean Repairs (out of 77 RVHP) 0.014 0.065 0.156 Probability Of Repair(*) 1.41% 5.00% 8.65%

4.5.4 Sensitivity of Results to the Assumed Shape Parameter Sensitivity results presented in Tables 4.9 and 4.10 for assumed Weibull shape parameters from 2.0 and 3.0 indicate projected mean repairs at B2R14 between 0.013% and 0.024% or between 0.010 and 0.019 penetrations out of 77 RVHP. This is consistent with a 1.03% to 1.85% probability that one or more RVHP repairs would be required. For the next RVHP inspection during B2R17 these values would increase to mean repairs between 0.059% and 0.117% or between 0.046 and 0.090 penetrations out of 77 RVHP with a 3.46% to 6.93% probability that one or more RVHP repairs would be required.

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AM-2007-011 Revision 1 Table 4-9 Sensitivity Results for Assumed Shape Parameter (Welbull Shape Parameter = 2.0 and Weibull Scale Parameter = 712)

Outage # 14 17 21 EDY at Outage 2.35 2.80 3.40 Mean Repairs (%) 0.013% 0.059% 0.133%

Mean Repairs (out of 77 RVHP) 0.010 0.046 0.102 Probability Of Repair 1.03% 3.46% 5.50%

Table 4-10 Sensitivity Results for Assumed Shape Parameter (Welbull Shape Parameter = 3.0 and Weibull Scale Parameter = 21.3)

Outage # 14 17 21 EDY at Outage 2.35 2,80 3.40 Mean Repairs (%) 0.024% 0.117% 0.297%

Mean Repairs (out of 77 RVHP) 0.019 0.090 0.229 Probability Of Repair 1.85% 6.93% 12.98%

4.5.5 Comparison with MRP-105 Weibull Analysis Results for RPV Head Cracking MRP-105 performed a Weibull analysis based on inspection results for 30 of 69 U. S.

PWRs which had performed NDE by the end of the Spring 2003 outage season. This analysis included both hot and cold head plants, and 14 of the 30 plants had detected leakage or some form of cracking. The plants with leaks or cracking operated with head temperatures between 593.70 F and 605.00 F and had EDYs between 11.2 and 23.7 at the time of inspection. The resulting Weibull scale parameter from this study was 62.3 EDY for an assumed shape parameter of 3.0.

The projection of repairs presented in Table 4.11 indicates results lower than those in Table 4.10 for the cold head analysis by a factor of over 20.

Table 4-11 Comparison with MRP-105 Weibull Analysis (Weibull Shape Parameter = 3.0 and Weibull Scale Parameter = 62.3)

Outage # 14 17 21 EDY at Outage 2.35 2.80 3.40 Mean Repairs (%) 0.001% 0.005% 0.012%

Mean Repairs (out of 77 RVHP) 0.001 0.004 0.009 Probability Of Repair 0.07% 0.28% 0.55%

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AM-2007-011 Revision 1 4.5.6 Comparison with Weibull Analysis Results for Bottom Head Penetration Cracking Inspection results for bottom head penetrations presented in Section 2.3 indicate that out of 1,600 inspections, only two leaking penetrations were found at the South Texas plant in Spring 2003. For an assumed Weibull shape parameter of 2.5, the calculated scale parameter is 27.5 EDY. Table 4.12 presents summary results for Byron 2 RVHP if this scale parameter is taken as representative of repairable flaws in lower temperature head penetrations. This would indicate that projected mean repairs at B2R14 are 0.032% or 0.025 penetrations out of 77 RVHP. This is consistent with a 2.46% probability that one or more RVHP repairs would be required, as shown in Table 4-12. For the next RVHP inspection during B2R17 these values would increase to mean repairs 0.149% or 0.115 penetrations out of 77 RVHP with a 8.62% probability that one or more RVHP repairs would be required. These results are just slightly higher than those presented in Table 4.10 for the RVHP analysis with an assumed shape parameter of 3.0.

Table 4-12 Results for Scale Parameter for Repairable Flaws (Weibull Shape Parameter = 2.5 and Weibull Scale Parameter = 27.5)

Outage # 14 17 21 EDY at Outage 2.35 2.80 3.40 Mean Repairs (%) 0.032% 0.149% 0.355%

Mean Repairs (out of 77 RVHP) 0.025 0.115 0.273 Probability Of Repair 2.46% 8.62% 14.70%

4.5.7 Summary of Weibull Analyses Based on the Weibull analysis of cold head RVHP and low temperature bottom head penetration inspection and failure data presented in this section, the projected RVHP failures at Byron Unit 2 at the next outage (B2R14) is very low with the probability of repair of one or more penetrations at approximately 1%. These values increase over time but remain low with an expected value of repair at about 5% in six years for the base case.

5 Byron Unit 2 PWSCC Growth Projections and Flaw Tolerance This section reviews the PWSCC crack growth rates and flaw tolerance of RPV head penetrations. It summarizes the evaluation methods and residual stress fields used in the nozzle crack growth studies. The evaluation results and crack growth projections 49 of 66

AM-2007-011 Revision 1 are summarized and used to establish the recommended inspection intervals for the Byron Unit 2 reactor vessel head nozzles.

5.1 PWSCC Crack Growth Rates.

PWSCC crack growth rates for Alloy 600 material used in these growth projections have been defined in MRP-55 36 and accepted by the industry in ASME Section Xl, Appendix 037 . The PWSCC growth rates have been determined to be directly dependent on temperature, i.e. increasing temperature increases the crack growth rate.

Temperature monitoring of the Byron Unit 2 reactor vessel head has demonstrated the operating temperature is below 5580 F. Two Reactor Vessel Level Indication System (RVLIS) Probes were installed for determination of the vessel water level during an accident condition. The RVLIS Probes contain 8 thermocouple sensors. Two of these sensors, the upper sensors, are located in the head area above the Upper Internal Support Plate 38 . Sensor 1 is located as close as possible to the top of the head and the next lower sensor, Sensor 2, is located just above the Upper Internal Support Plate.

Additionally, the two upper sensors have limited interaction with the lower sensors by way of a divider disk39 . This separation ensures that a true representation of head temperature is measured. Measurements from Sensors 1 and 2 since startup of Unit 2 Cycle 14 (current operating cycle) are presented in Figure 5-1. The maximum average temperature for the head based on these measurements is 545 0F. These measurements confirm that using a temperature of 558 0 F is conservative when calculating crack growth in the head nozzles.

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AM-2007-011 Revision I Byron Unit 2 RVUS TC #1 &#2 Channels A and B

£ I

I 42M8/007WOW 8/707 W127/07 7/17/07 8/8(07 DATE Figure 5-1: Byron Unit 2 Reactor Vessel Head Operating Temperature for Fuel Cycle 14 The following equation was taken from the ASME code, Reference 37, and is used for the crack growth projections.

rf~1 it=ex{ jag-(! T')aK - ~ (5-1) where

= the crack growth rate at temperature, T, in m/s Q, = Thermal activation energy for crack growth, 130 kJ/mole R = universal gas constant, 8.314 x 10.3 kJ/mole-OK T = Absolute operating temperature, "K Trf = absolute reference temperature used to normalize data, 598.15 0 K a = crack growth rate coefficient,2.67 x 10-12 for units of m/s and stress intensity factor units of MPa'm K, = crack tip stress intensity factor, MPa4m K,h = crack tip stress intensity factor threshold for SCC, 9 MPa4m

,8 =exponent, 1.16 51 of 66

AM-2007-011 Revision 1 Using this equation, comparisons of the crack growth rates for the Byron Unit 2 head temperature of 545 0 F, the 558°F head temperature used for the crack growth predictions, and a typical hot head temperature of 600°F can be performed. Figure 5-2 presents these comparisons for a range of stress intensity factors. Based on the magnitude of the weld residual stresses driving PWSCC cracks and the crack sizes that can be detected, the stress intensity factor would be expected to range from 20 to 60 MPa'm.

From these comparisons, the crack growth rate for a typical hot reactor head temperature of 600°F is three times greater than the rate used in these crack growth predictions at a temperature of 5580 F for a given K1. It should also be noted that the crack growth rate at 558°F is approximately 1.43 time greater than the rate at 5450 F, the Byron Unit 2 measured head temperature.

11-00 I.E-la I

I.E-1Il I.E-12 a 10 20 30 40 so 60 70 80 Stre WIafty Factor, &4(MP*/m)

Figure 5-2: PWSCC Growth Rate Comparison for Cold vs. Hot RPV Head Temperatures 52 of 66

AM-2007-011 Revision 1 5.2 Byron Unit 2 PWSCC Growth Projections 5.2.1 Head Penetration Stresses To perform the PWSCC crack growth projections, the stress fields from operating conditions and welding residual stress at the postulated flaw locations are needed.

These stress fields were calculated using finite element analyses for the Byron Unit 2 head nozzles in Reference 13. Figure 5-3 displays the hoop direction stresses for the 470 head nozzle subjected to operating and weld residual stress loads. The maximum tensile stresses are located along the uphill and downhill locations around the circumference of the nozzle at the J-groove weld. At the uphill location, the largest tensile hoop stresses extend through the thickness of the nozzle and to the top of the J-groove weld and below the bottom of it. Above and below the J-groove weld, the hoop stresses reduce significantly and become negative along the outside surface. Although the extent of the large tensile hoop stresses is smaller in the downhill side of the nozzle, large hoop stresses similar to the uphill side are found here and this is the location of the flaw found in Nozzle 68. One of the contributors to the initiation and growth of the flaw in Nozzle 68 was the location of the lack of fusion being in this high tensile stress field.

Figure 5-4 displays the axial direction stresses for the 470 head nozzle subjected to operating loads and-weld residual.stress. Again the maximum tensile stresses are located along the uphill and downhill locations around the circumference of the nozzle at the J-groove weld. The amount of material with the highest axial tensile stress is much less than in the hoop direction and generally the magnitude of the axial tensile stresses is less than in the hoop direction, so axial flaws are significantly more likely than circumferential flaws. Figure 5-5 presents the axial stress through wall, along the plane formed by the top of the J-groove weld. This distribution shows a large part of the circumference is subjected to a compressive stress, which would prohibit further circumferential growth.

Details of the methods and material properties used to calculate these stress fields and the stress fields for the remaining head nozzles can be found in Reference 13.

The methodology used to estimate the weld residual stress in the head penetrations and combine it with the operating loads was independently assessed4 °. In this study, vessel head penetration weld residual stress was calculated using two different and independent methods and compared the results. The study concluded that the method used to calculate the stress used here, i.e. using a stress-strain curve for the Alloy 600 nozzle material based on cyclic stress-strain data, produced stresses that were similar or higher than the-altemate method. The alternate method was developed Engineering Mechanics Corporation of Columbus for the U.S. NRC. This comparison provides additional confidence in the methodology used to calculate the stress distributions and the stress distributions used to predict the crack growth.

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AM-2007-011 Revision I AM2 2002 0515S'IrI

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..rar.,tu Figure 5-3: Typical Operating Plus Weld Residual Hoop Stress Field Used for Crack Growth - RPV Head 470 Nozzle (psi)

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Figure 5-4: Typical Operating Plus Weld Residual Axial Stress Field Used for Crack Growth - RPV Head 470 Nozzle (psi) 54 of 66

AM-2007-011 Revision 1 ZSI'. 4".

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Figure 5-5: RPV Head 470 Nozzle Operating Plus Weld Residual Axial Stress Along the Top of the J-Grove Weld (psi) 5.2.2 Nozzle Outside Surface Axial Flaws The inspection results of the Byron Unit 2 vessel head, as summarized in Section 2.2, and the conclusions drawn from the metallurgical examination of the flaw in Nozzle 68 have provided assurances that the probability of PWSCC degradation at this time is very small. Any PWSCC flaws that may exist would be smaller than the detectable limit of the examinations performed. Based on these inspection results, a flaw tolerance analysis is performed to determine the appropriate inspection interval for the next inspection. The initial size of the postulated flaw used in the evaluation was based on the threshold of detection for the nozzle volumetric examination technique. As justified in Section 2, the initial depth and length of the postulated flaw was defined as 0.075" and 0.15" respectively. This was the initial flaw size specified in the axial flaw growth projections documented in Reference 4141, which performs flaw growth projections for the 00, 25.40, 42.80, 43.80 and 470 nozzle groups, defined in Reference 13. Figure 5-6 shows the axially oriented flaw located on the uphill side of the nozzle at the highest hoop stress location on the outside diameter. Surface flaws were postulated on the outside diameter of the nozzle at both the uphill and the downhill sides. The initial flaw was centered at the highest stressed area in the nozzle material to be consistent with the flaw found in Nozzle 68; and with the higher hoop stresses at this location, it will grow faster than in other locations above or below the weld.

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AM-2007-011 Revision 1 I

BOTrOM Wor a

Figure 5-6: RPV Head Nozzle Schematic with Postulated Flaw Location Flaws at these uphill and downhill positions were postulated to address other nozzle welds that may have weld defects similar to those found in Nozzle 68 and PWSCC initiated, but at less than the minimum detectable flaw size. Postulated flaws in these positions were grown in depth and length until the upper crack tip reached the top of the J-groove at which a leak path would be established. Stress intensity factors for semi-elliptical, part-through wall surface cracks in a cylinder were calculated at the deepest and the surface points along the crack front using Reference 4242. These stress intensity factors were used to calculate the change in crack depth and length of the postulated flaw. They would conservatively represent the crack driving force because the assumed surface flaw is restrained against crack opening by the J-groove weld, The leak path was chosen, as the crack size limit since the axial flaw size for the leak path is significantly smaller than the critical flaw size. Additional details of the evaluation methods used to calculate the projected crack growth are documented in Reference 41.

The results of these evaluations are summarized in Table 5-1. For each postulated flaw location, the operating time for the flaw to grow to its leakage limit is presented. The minimum time for a postulated axially oriented flaw located on the nozzle outside diameter at the highest hoop stress locations to grow in length and initiate a leak path is greater than 6 fuel cycles or 9.09 years of hot operation.

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AM-2007-O11 Revision 1 Table 5-1 Operating Time for A Postulated Axial Flaw at the J-groove Weld to Grow Its Limit Available Operating Window Nozzle Group & Location (Fuel Cycles)'

0.00 Nozzle 7.30 25.40 Nozzle; Downhill 9.05 25.40 Nozzle; Uphill 6.06 42.80 Nozzle; Downhill 11.69 42.80 Nozzle; Uphill 6.37 43.80 Nozzle; Downhill 12.26 43.80 Nozzle; Uphill 6.42 47.0c Nozzle; Downhill 13.75 47.00 Nozzle; Uhill 6.67 Note 1.Afuel cycle was assumed to be 18 months with a 98% capacity factor. Hot operating time conversion is 1.5 years/fuel cycle.

5.2.3 Nozzle Inside Surface Axial Flaws Other postulated flaw locations in the nozzle were evaluated in Reference 43 43. The crack growth projections in this evaluation used the same PWSCC growth rate as defined in Section 5.1 and the same operating and residual stress fields defined in Reference 13. In calculating the crack growth projections, the evaluation assumed a fixed aspect ratio of 6:1 for the flaw length and calculated the growth in the depth direction. For axially oriented flaws this is a very conservative assumption because the projected flaw lengths will extend well beyond the large tensile hoop stresses caused by the weld residual stress. Once the crack tip is beyond the weld residual stresses, growth in the length direction will be significantly slower than in the depth direction.

Also, by assuming an initial flaw size with an aspect ratio of 6, the postulated flaw will be predicted to grow more rapidly in the depth direction then a flaw with a smaller aspect ratio because there would be less restraint on the crack tip. For an axially oriented surface flaw on the inside surface of the nozzle the most rapid growth is predicted to be on the uphill side of the J-groove weld for a flaw located at the weld. From Figure 5-7 and again using an initial flaw depth of 0.075" with a length of 0.45" the postulated flaw in the worst case, nozzle angle of 470 is predicted to grow to a depth ratio of less than 0,7 in 6 years of operation. Since the flaw is growing from the inside surface, a leak path is not possible, and the flaw depth of 0.431" is less than the ASME Section XI code3 7 acceptance criteria of 75% through wall.

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basedro a5em-elliptical surfaeolwt witraoasccrtion ofr6a1 Thidurae, stressy Oientenst faSctgroatthe deees poirufentalong thienrac frontwas calcuozlewsaoevlated uigtecrlaions frmReference 42. Theedcrackhgropehraten waus baeld onida sthesPWstrabteeioned inth Sueto 5.,thoeer dutiel itation then crevrcacnitionserequiaredk toulexoete ou tsie otiesurface toov rectratraforof the 2el wasd aprpliaed tlonthe raeloacontformdbthe sunfcertit in the watzer hemsra re commendedtby Referencen3. The crackgrwhpoetnsee guroaceth proerctinfor thspsuated, afcooflawareshw apind Figuherae5-8.ontfr h 58 of 66

AM-2007-011 Revision 1

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.utfro Figure 5-8: PWSCC Growth Projections for an Outside Surface, Circumnferentially Oriented Flaw on the Downhill Side Above the J-groove Weld For an initial flaw size of 0.075" in depth and 0.45" in length, the postulated flaw in the worst case, nozzle angle 470, is predicted to grow to a depth ratio of 0.56 in 6 years of operation. For a nozzle thickness of 0.625", the predicted flaw depth is 0.35" with a length of 2.11", which is well within the structural integrity limits for the nozzle, i.e.

through wall and greater than 3000 (10.5") in length.

5.2.5 Head Penetration Weld Flaws Radial or circumferential cracking in the J-groove welds will propagate much more rapidly than flaws in the nozzle material. This is due to the greater crack growth rates, which are several times faster than the rates for the base metal. However, these cracks will not lead directly to rupture of the pressure boundary. They can propagate through the weld and initiate a leak path, which can lead to cracking in the nozzle base metal or wastage of the vessel head low alloy steel. In both cases the time between inspection intervals would bound the intervals previously determined for the postulated flaws in the nozzle material.

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AM-2007-011 Revision 1 5.3 Reactor Vessel Head Inspection Intervals The postulated flaw PWSCC growth studies performed for an axial flaw on the outside surface of the nozzle at the location of the highest hoop stress, i.e. at the J-groove weld, has determined that it would take 9.09 years of operation to grow in length and initiate a leak path. The other postulated flaw locations and orientations in the nozzle have been evaluated and were shown to satisfy nozzle acceptance criteria after 6 years of hot operation. These evaluations were based on a postulated initial flaw depth of 0.075" and a 0.15" flaw length, which was determined to be the threshold of detection for the volumetric examinations being performed. The evaluations performed included margins in the crack growth rates to account for uncertainties and variations in the vessel head temperature. Conservative flaw shapes were assumed when calculating the crack growth times. The weld residual stress fields were determined using a methodology that was verified and determined to be similar or conservative to stress fields calculated by Engineering Mechanics Corporation of Columbus for the U.S. NRC. Based on these evaluations, a time interval of six years of operation between examinations of the head has been justified.

6 Summary and Conclusions This report describes the inspections performed at Byron Unit 2 during B2R13 in accordance with NRC Order EA-03-009, and it discusses the indications that were detected during the inspections. The report highlights the outlier nature of this finding relative to the numerous inspections that have been performed in the industry according to the Order. The following conclusions can be drawn from the information presented:

e Byron Unit 2 CRDM Nozzle 68 is the only one of over 1400 cold head nozzles inspected to have found an indication. Statistically, the likelihood of Byron Unit 2 (or any low susceptibility head) finding PWSCC at their next outage is less than 1% and is independent of the indication found in Nozzle 68.

• The presence of PWSCC in Byron Unit 2 was discovered through required inspections, and the discovery was not made as the result of through-wall leakage.

e A crevice formed by a lack-of-fusion weld defect created during original fabrication was the initiator of PWSCC in Nozzle 68. Without the lack-of-fusion defect, the three necessary elements for SCC (i.e., susceptible material, tensile stress, and critical environment) would not have been simultaneously satisfied.

0 The metallurgical failure analysis of the boat sample removed from Nozzle 68 illustrates that the direction of crack growth was from a subsurface location towards the wetted surface. None of the cracking of the tube material contained in the boat sample was connected to the wetted surface of the tube.

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AM-2007-011 Revision I

• Other examples of rounded surface indications in the industry concluded that the PWSCC associated with the indication had crack growth propagating from the wetted surface toward the interior.

" The results of the probabilistic assessments showed that the probability of having the observed 50% through-wall flaw in Nozzle 68 after 20 years of service was three orders of magnitude below that expected for flaw initiation and growth due to PWSCC in Byron Unit 2. Further, the assessments showed that the observed 50% through-wall flaw did not occur in the most likely nozzle location in Byron Unit 2.

" The conclusion of the probabilistic calculations is that the 50% through-wall flaw depth observed in vessel head penetration Nozzle 68 of Byron Unit 2 is not due to normal flaw initiation and growth by PWSCC in the Alloy 600 base metal.

Additional conditions, such as those identified in the boat sample metallurgical analysis, are needed to initiate and grow a PWSCC flaw in Nozzle 68 in 20 years of operation.

" The effect of in-service inspection after 20 years of operation is to reduce the probability of a through-wall flaw due to initiation and growth by PWSCC after 60 years of operation by a factor of almost 40 for an inspection interval of six years.

" A statistical treatment of all the available inspection results for head penetrations estimated the probability that flaws would be found in the future as a function of inspection frequency. For the base case chosen, the results show there is approximately a one percent chance of cracking in the next cycle and about a five percent chance in the next six years.

" The PWSCC crack growth rate at a given KI for a typical hot reactor head at 6000F is three times greater than the crack growth rate at 5580 F, which is the temperature that was used for the crack growth predictions. Further, the crack growth rate at 558°F is approximately 1.43 times greater than the rate at 5450 F, the Byron Unit 2 measured head temperature.

The minimum time for a postulated axially-oriented PWSCC flaw located on the nozzle outside diameter at the highest hoop stress locations to grow in length and initiate a leak path is greater than six fuel cycles, which is equivalent to approximately nine years of hot operation. The other postulated flaw locations and orientations in the nozzle were shown to satisfy nozzle inspection acceptance criteria after six years of hot operation or four fuel cycles.

The use of conservative flaw shapes and head temperatures in the crack growth studies further justify a time interval of six years of operation between examinations of the head.

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AM-2007-011 Revision 1 In summary, it was demonstrated that the flaw found in Byron Unit 2 Nozzle 68 did not originate from PWSCC. Two complementary approaches have shown that a six year inspection frequency results in a very low probability of the development of cracks in the future. Even if a flaw had been below the threshold of detection at B2R1 3, calculations show that it would remain acceptable according to the ASME Code criteria for at least six years. Based on these analyses, an inspection frequency for Byron Unit 2 that is consistent with a low susceptibility head would not significantly increase the probability of a through-wall crack and subsequent leakage on top of the RPV head; therefore, the low susceptibility inspection frequency is acceptable.

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AM-2007-011 Revision 1 7 References

1. NRC Order EA-03-009, "Issuance of First Revised NRC Order (EA-03-009)

Establishing Interim Inspection Requirements for Reactor Pressure Vessel Heads at Pressurized Water Reactors," February 20, 2004.

2. NRC Bulletin 2002-02, "Reactor Pressure Vessel Head and Vessel Head Penetration Nozzle Inspection Programs," August 9, 2002.

3. Westinghouse Nuclear Services Field Service Procedure WDI-UT-01 3, "CRDM/ICI UT Analysis Guidelines, Revision 12," Westinghouse Electric Company LLC, January 2007.

4. Exelon Nuclear NDE Report 2007-276, April 13, 2007.

5. Exelon Nuclear NDE Report 2007-315, April 23, 2007.

6. PCI Energy Services, PCI Report 900866-001, April 27, 2007.

7. PCI Energy Services, PCI Report 900866-002, April 27, 2007.

8. "Materials Reliability Program: Demonstrations of Vendor Equipment and Procedures for the Inspection of Control Rod Drive Mechanism Head Penetrations (MRP-89), EPRI, 1007831, September 2003.

9. Chynoweth, J., Exelon PowerLabs Project BYR-48053, "Metallurgical Evaluations of A 'Boat' Sample from the #68 CRDM Penetration on Byron Unit 2," May 23, 2007

10. "2005 Interim Review of the Pressurized Water Reactor Primary Water Chemistry Guidelines - Revision 5," EPRI, 1009933, December 2005.

11. Davis, J. R., editor, ASM Specialty Handbook: Nickel, Cobalt,and Their Alloys, ASM International, Materials Park, OH, 2000.

12. "Grain Boundary Coverage Estimate for the Byron 2 Alloy 600 CRDM Penetration 68," electronic mail, G. V. Rao to B. A. Bishop, September 11, 2007.

13. Byron and Braidwood Units 1 and 2 CRDM Stress Analysis, Dominion Engineering, Inc. Task 77-70, Calculation C-7770-00-1, Rev. 0, April 25, 2003.

14. Status Review of Initiation of EnvironmentallyAssisted Cracking and Short Crack Growth. EPRI, Palo Alto, CA: 2005. 1011788.

15. Bamford, Bishop, Duran and Boyle, "Background and Methodology for Evaluation of Reactor Vessel Closure Head Penetration Integrity for the Westinghouse Owners Group," WCAP-14901, Rev. 0, Westinghouse Electric Corporation, July 1997

16. Letter, J. A. Begley (APTECH) to B. A. Bishop (Westinghouse), "Review of the Westinghouse Structural Reliability Mode[ for PWSCC of RV Head Penetrations," June 23, 1997.

17. Rao and Wright, "Evaluation and Resolution of the Primary Water Stress Corrosion Cracking (PWSCC) Incidents of Alloy 600 Primary System Pressure 63 of 66

AM-2007-011 Revision I Boundary Penetrations in Pressurized Water Reactors," Proceedingsof FontevraudII Symposium: Contribution of Materials Investigation to the Resolution of Problems Encounteredin PWR Plants,Royal Abbey of Fontevraud, France, September 10-14, 1990.

18. Hall, Magee, Woodman and Melton, "Evaluation of Leaking Alloy 600 Nozzles and Remaining Life Prediction for Similar Nozzles in PWR Primary System Application," Service Experience and ReliabilityImprovement, ASME PVP-Vol. 288, 1994.

19. Gold, Fletcher and Jacko, "The Status of Laboratory Evaluations in 4000C Steam of the Stress Corrosion of Alloy 600 Steam Generator Tubing,"

Proceedingsof 2nd InternationalTopical Meeting on Nuclear PowerPlant Thermal Hydraulicsand Operations,1986.

20. Norring, Engstrom and Norberg, "lntergranular Stress Corrosion Cracking in Steam Generator Tubing, Testing of Alloy 690 and Alloy 600 Tubes," Third InternationalSymposium on EnvironmentalDegradationof Materialsin Nuclear PowerSystems - Water Reactors - Proceedings,The Metallurgical Society, 1988.

21. Ball et al., "RV Closure Head Penetration Alloy 600 PWSCC (Phase 2),"

WCAP-13525, Rev. 1, Westinghouse Electric Corporation, December 1992 (Proprietary Class 2).

22. Duran, Kim and Pezze, "Reactor Vessel Closure Head Penetration Key Parameters Comparison," WCAP-1 3493, Westinghouse Electric Corporation, September 1992 (Proprietary Class 2).

23. Rao, "Microstructural and PWSCC Assessments of Alloy 600 R. V. Head Penetration at Beznau Unit 2 Station," WCAP-15388, Westinghouse Electric Company LLC, February 2000 (Proprietary Class 2C).

24. Rao, "Microstructural Correlations with Material Certification Data in Several Commercial Heats of Alloy 600 Reactor Vessel Head Penetration Materials,"

WCAP-13876, Rev. 1, Westinghouse Electric Corporation, June 1997 (Proprietary Class 2C).

25. Grambau and Fyfitch, "Vessel Head Penet. Nozzle Data for Byron 1 & 2, Braidwood 1 & 2," Engineering Information Record 51-5014160-00, FRAMATOME ANP, August 30, 2001

26. Bamford, Foster, and Rao, "Crack Growth and Microstructural Characterization of Alloy 600 Head Penetration Materials, WCAP 13929, Rev. 2, Westinghouse Electric Corporation, November 1996 (Proprietary Class 2C).

27. Newman and Raju, "Stress Intensity Factors for Internal Surface Cracks in Cylindrical Pressure Vessels" TransactionsASME, Journalof Pressure Vessel Technology, Volume 102,1980, pp. 342-346.

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28. Bishop, 'Westinghouse Structural Reliability and Risk Assessment (SRRA)

Model for Piping Risk-Informed In-service Inspection," WCAP-14572, Revision 1-NP-A, Supplement 1, Westinghouse Electric Corporation, February 1999.

29. "Risk-Based Inspection - Development of Guidelines, Volume 1, General Document," ASME Research Task Force on Risk-Based Inspection Guidelines Report CRTD-Vol. 20-1 (or NUREG/GR-005, Vol. 1), American Society of Mechanical Engineers, 1991.

30. Harris and Dedhia, "Theoretical and User's Manual for pc-PRAISE, A Probabilistic Fracture Mechanics Computer Code for Piping Reliability Analysis,"

NUREG/CR-5864, U.S. Nuclear Regulatory Commision, July 1992.

31. Bamford, Bishop, Duran and Boyle, "Probabilistic Evaluation of Reactor Vessel Closure Head Penetration Integrity for Beaver Valley Units 1 and 2,"

WCAP-14913, Rev. 1, Westinghouse Electric Corporation, October 1997 (Proprietary Class 2C).

32. Bamford, Bishop, Duran and Boyle, "Probabilistic Evaluation of Reactor Vessel Closure Head Penetration Integrity for Farley Units 1 and 2," WCAP-14906, Rev. 1, Westinghouse Electric Corporation, October 1997 (Proprietary Class 2C)%

33. "Materials Reliability Program (MRP) Probabilistic Fracture Mechanics analysis of PWR Reactor Pressure Vessel Top Head Nozzle Cracking, (MRP-105), EPRI, April 2004.

34. Harris, John E., Turner, Arthur P., Gorman, Jeffery A., "Predicted Tube Degradation for Westinghouse Models D5 and F Type Steam Generators," EPRI, TR-1 08501, September 1997.

35. Nelson, Wayne, "Weibull Prediction of a Future Number of Failures," Quality and Reliability Engineering International, 16: 23-26, 2000.

36. "Materials Reliability Program (MRP) Crack Growth Rates for Evaluating Primary Water Stress Corrosion Cracking (PWSCC) of Thick-Wall Alloy 600 Materials," (MRP-55) Revision 1, EPRI, 1006695, November 2002.

37. ASME B&PV Code,Section XI, 2004 Edition.

38. Byron/Braidwood UFSAR, Figure E.31-5, Probe Holder Assembly and Sensor Location.

39. Byron/Braidwood UFSAR, Figure E.31-8, Normal Operating Flow Pattern with Reactor Coolant Pumps On.

40. Rudland, D., Chen, Y., Zhang, T., Wilkowski, G., Broussard, J., and White, G., "Comparison of Welding Residual Stress Solutions for Control Rod Drive Mechanism Nozzles," 2007 ASME Pressure Vessels and Piping Division Conference, PVP2007-26045, July 2007.

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41. "Evaluation of Crack Growth of a Postulated Flaw in Byron Unit 2 CRDM Nozzles by Primary Water Stress Corrosion Cracking," Exelon Report AM-2007-006, Revision 0.

42. Mettu, S.R., Raju, I. S., and Forman, R. G., NASA Lyndon B. Johnson Space Center report number NASA-TM-1 11707, "Stress Intensity Factors for Part-Through Surface Cracks in Hollow Cylinders," Structures and Mechanics Division, July 1992.

43. Westinghouse Report WCAP-1 6394-P, "Structural Integrity Evaluation of Reactor Vessel Upper Head Penetrations to Support Continued Operation: Byron and Braidwood Units I and 2," February 2005.

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ATTACHMENT 4 Evaluation of Crack Growth of a Postulated Flaw in Byron Unit 2 CRDM Nozzles by Primary Water Stress Corrosion Cracking

i.

Evaluation of Crack Growth of a Postulated Flaw in Byron Unit 2 CRDM Nozzles by Primary Water Stress Corrosion Cracking Document Number AM-2007-006 Revision 0 Nuclear EngiheeringDepartment Exelon Nuclear GeneratingCo.

Prepared by: ' ' J. S. Brihmadesam Date: I/ l,/zao 9-ft DeBoO Date: 7/S/0

--RichffWl. Date: /0-7 (Dat Issued)

AM-2007-006 Table of Contents Section Title of Section Page No.

Executive Summary 3 1.0 Background 4 2.0 Bases and Purpose 4 3.0 Analytical Method 5 3.1 Stress Distribution Determination 5 3.2 Fracture Mechanics Model 8 3.3 PWSCC Crack Growth Model 9 3.4 Method of Analysis 9 4.0 Results 13 5.0 Discussion 18 6.0 Conclusions 19 7.0 References 19 Appendix I PWSCC Crack Growth Analysis 00 Nozzle 31 pgs Appendix II PWSCC Crack Growth Analysis 25.40 Nozzle Downhill 31 pgs Appendix III PWSCC Crack Growth Analysis 25.40 Nozzle Uphill 31 pgs Appendix IV PWSCC Crack Growth Analysis 42.80 Nozzle Downhill 31 pgs Appendix V PWSCC Crack Growth Analysis 42.8' Nozzle Uphill 31 pgs Appendix VI PWSCC Crack Growth Analysis 43.80 Nozzle Downhill 31 pgs Appendix PWSCC Crack Growth Analysis 43.8' Nozzle Uphill 31 pgs VII Appendix PWSCC Crack Growth Analysis 47.00 Nozzle Downhill 31 pgs VIII Appendix IX PWSCC Crack Growth Analysis 47.0' Nozzle Uphill 31 pgs Page 2 of 19

AM-2007-006 Executive Summary The volumetric ultrasonic inspections of the control rod drive mechanism (CRDM) tubes in the reactor vessel head at Byron Unit 2, identified a single indication on the outside surface, near the J-groove weld for CRDM # 68. The metallurgical evaluation

[1] of the indication determined that primary water stress corrosion cracking (PWSCC) was the initiation and propagation mechanism for the crack in the CRDM nozzle base material. The few interdendritic cracks found in the J-groove weld metal, which had a morphology similar to PWSCC cracks, were in the fillet leg of the weld and were determined to be the continuation of the propagating PWSCC crack in the base material.

No evidence of service induced PWSCC crack initiation was found on the wetted surface of the J-groove weld. Both the field ultrasonic examination and the metallurgical evaluation [1] showed the crack initiated on the outside diameter (OD) surface of the nozzle, and it had not penetrated through the nozzle wall thickness. Fabrication welding defects existed at the crack initiation site and on the wetted surface of the J-groove weld, which facilitated primary water ingress to the nozzle outside surface.

The occurrence of a PWSCC crack in the CRDM nozzle was unexpected at this time since the analyses for the reactor vessel head (RVH) showed very low susceptibility for PWSCC under operating conditions. However, the unique situation existed, where a fabrication-induced defect changed the local environmental conditions such that PWSCC occurred. Thus, it was necessary to ascertain the propensity for PWSCC crack growth in other nozzles, which could have been subjected to similar initiating conditions (i.e. high tensile stress, susceptible material and a conducive environment resulting from fabrication defects). Detailed PWSCC crack growth analyses were performed for representative CRDM nozzles that were grouped by the reactor vessel head angular location.

For the detailed crack growth analyses, the initial flaw size was postulated to be the smallest detectable flaw, determined from the qualification of the ultrasonic test method utilized for the inspection [2]. The postulated OD surface flaw was located at the middle of the J-groove weld, such that it simulated the CRDM #68 crack [1] and was positioned at the highest tensile stress [3] locations in the nozzle. The CRDM nozzle stress analyses [3] defined the operating plus welding residual stresses for the representative CRDM nozzles. The fracture mechanics stress intensity factor formulation

[5] for a longitudinal, semi-elliptical flaw was used to describe the crack driving forces for flaw growth. The PWSCC Alloy 600 crack growth rates developed by the Electric Power Research Institute's Material Reliability Program (EPRI-MRP) [6] were used to calculate the change in flaw length and depth with time.

The results of the analyses showed that a minimum of six (6) eighteen month fuel cycles would be required to propagate a postulated flaw to the top of the J-groove weld such that a leak path would be established. Therefore, at a minimum, an additional six fuel cycles would be necessary to establish a leak path, if an undetected flaw was left in service. The results of this analysis demonstrate that the initiating conditions (similar to CRDM #68) are unlikely to exist at other nozzle locations. Hence, it was the unique occurrence of the fabrication-induced defects that produced the conditions necessary for PWSCC to initiate and propagate the crack in CRDM #68.

Page 3 of 19

AM-2007-006

1.0 Background

The volumetric ultrasonic inspections of the control rod drive mechanism (CRDM) tubes in the reactor vessel head at Byron Unit 2, identified a single indication on the outside surface, near the J-groove weld for CRDM # 68. The reported indication was a part-through wall-flaw whose dimensions were 0.52 inch long and 0.326 inch deep.

This indication was located on the downhill side of the weld. A boat sample was excavated for metallurgical examination and the results of that evaluation are presented in Reference 1. The significant findings of the evaluation were:

1) Fabrication (welding) defects existed at the indication location, which facilitated primary water ingress to the tube OD surface at some depth below the wetted weld surface.

2) A combination of the wetted crevice environment, high residual stresses from welding and a susceptible tube microstructure, together provided the necessary conditions for the initiation of primary water stress corrosion cracking (PWSCC) to initiate at this sub-surface location.

3) The cracking in the tube material had an axial orientation and the fracture surface revealed an intergranular morphology, which is typical of PWSCC.

4) In the J-groove weld metal, the observed cracking [1] showed limited interdendritic cracking but none had extended to the wetted surface. These cracks were continuation from the base metal cracking that had propagated behind the J-groove fillet leg. No service related crack initiation on the wetted surface of the weld was found.

The discovery of PWSCC in this penetration was unexpected owing to the low operating temperature of the reactor vessel head and previous industry experience and analyses had concluded that PWSCC cracking was unlikely at the time of the Byron Unit 2 refueling outage. Furthermore, similar inspections at the three other sister units (Braidwood Units I and 2, and Byron Unit 1) had not revealed any detectable indication on all the CRDM penetrations inspected by volumetric ultrasonic inspection. Bare metal visual examinations of the four reactor vessel heads at Byron and Braidwood stations, did not find any evidence of nozzle leakage. Thus, it was important to study the crack growth behavior and to rationally assess the effect on other CRDM penetrations should they be subjected to similar conditions as CRDM

1. 68. In the sections that follow, a description of the analysis purpose, analytical methods and the results obtained from the analysis are presented.

2.0 Purpose The purpose of the analysis was to study the PWSCC crack growth behavior of CRDM #68 flaw using the available stress distribution data, industry approved PWSCC crack growth formulation and a standard fracture mechanics algorithm. The analysis method developed for CRDM #68 was then applied to other important nozzle locations Page 4 of 19

AM-2007-006 where the residual stress distributions could support PWSCC initiation and propagation of postulated flaws that are oriented similar to the CRDM #68 flaw. The results of the postulated flaw analyses would allow for a rational estimate of time (eighteen month fuel cycle) for an initial flaw sized at the threshold of detection to grow to the weld root at the top of the J-groove weld and initiate a potential leak path.

3.0 Analytical Method The J-groove weld was made in four steps consisting of a root pass, followed by two steps to fill the cavity and a final step to produce the fillet. Based on the metallurgical examination [ 1], the initiation occurred between the two middle steps and on the OD of the tube. This location is about the middle of the J-groove weld.

The size of the postulated initial flaw was established based on the smallest detectable flaw size from the ultrasonic examination qualification tests [2] performed to qualify the inspection method and the inspectors. In this analysis no credit is taken for incubation time to develop a micro flaw and to propagate to the initial flaw size. The analysis method developed has three components, namely: defining of stress distribution acting on the postulated flaw, the fracture mechanics algorithm, and the PWSCC crack growth model. Details of the analysis process and the crack growth results are presented in the Appendices. In the sub-sections that follow the salient aspects of these components are described.

3.1 Stress Distribution Determination Finite element methods were used to develop the operating + residual hoop stress distributions for the CRDM penetrations in the reactor vessel head for the Braidwood and Byron stations. The stress distribution analysis results are documented in Reference 3. In the stress analysis the CRDM nozzle population was divided into five groups (0', 25.40, 42.80, 43.80 and 470) and tabulated results along with contour plots were presented. CRDM #68 was at the 43.80 location. The necessary data for the analysis presented here were available in Reference 3 in Table 5-1. The hoop stress distribution through the tube wall at six locations (20% wall thickness increments) and at five axial elevations in and adjacent to the J-groove weld was presented. To locate the exact axial elevation of the flaw in the nozzle, the data from Table 5-3a through 5-3e, representing each of the five nozzle groups was used. In this manner the axial elevations of the flaw crack front and the concomitant hoop stress data were matched. The hoop stress profiles for the five nozzle groups at both the downhill and uphill locations, are presented in Reference 3 as Figures 5-2 through 5-6. From these figures it is observed that highest stresses exist at both the uphill and downhill locations for each nozzle group. The observed cracking in CRDM # 68 was at an azimuth that was approximately 160 from the absolute downhill location. In the analysis, both the downhill and uphill locations were evaluated to determine the postulated flaw crack growth at the highest stress location. In this manner a comprehensive analysis covering all nozzle groups and at highest stressed locations could be achieved. The available data for through the thickness hoop stress Page 5 of 19

AM-2007-006 distribution existed at five axial elevations. Since the postulated axial flaw, in keeping with the findings of the metallurgical evaluation for CRDM #68, was located at the middle of the J-groove weld it was essential that the hoop stress distribution above the middle of the J-groove weld to the top of the weld and beyond be characterized with sufficient accuracy to determine the corresponding crack driving forces at the deepest point along the crack front and at the end of the crack. The hoop stress distribution data was used to develop a matrix containing both the axial elevation and the through the thickness stress distributions. This matrix was then used to develop a through the thickness hoop stress distribution at twenty different axial elevations above the postulated axial flaw location. Details of the analysis method and the stress distributions are presented in the Appendices of this report. An example of the resulting curve fit for a typical hoop stress distribution along the ID and OD surfaces is presented in Figure 1.

60

,55.812 ID

• 50 I I I II SIDi

,41.824 40 I 0 0.5 1.5 2 2.5 3 AQ Axl, Loci Figure la: Hoop stress distribution on the ID surface. The solid red line shows the input data at the five axial elevations and the dotted blue curve the resultfrom a third orderpolynomial curve fit.

L77.34Y OD son 228.30ý 0 0.5 I 1.5 2 2.5 3 IQ0 AxLoq 02.4 Figure lb: Hoop stress distributionon the OD surface. The solid red line shows the input data at the five axial elevations and the dotted blue curve the resultfrom a third orderpolynomial curve fit.

The curve fitting was performed along the axial height at all six through thickness locations. Similar stress distribution graphs are presented in the Appendices for each individual flaw evaluations. In every case it is found that the curve fit provided a Page 6 of 19

AM-2007-006 reasonable fit to the stress data. For the OD surface flaw evaluations, the through wall hoop stress distribution was arranged to match the flaw orientations at the uphill and downhill locations of the nozzle. The region of interest for flaw propagation is along the axial length towards the top of the J-groove weld. The hoop stress data from Reference 3 is coarsely defined along the axial height. In order to calculate axial crack growth, an algorithm was developed to define a through thickness hoop stress distribution that is more refined along the axial direction and extends V2 inch above and below the J-groove weld. Therefore the through the thickness hoop stress distribution is defined along the entire crack face as it propagates. In this manner the crack was subjected to a hoop stress distribution that was representative of the applied stress distribution analyzed in Reference 3. The salient details of the method are described later in this report. In addition, for the fracture mechanics analysis to determine the stress intensity factor K1, the internal reactor pressure was applied to the crack face as an additive term to the uniform coefficient of the third order polynomial.

3.2 Fracture Mechanics Model The CRDM tube dimensions [4] indicated that the mean radius-to-thickness ratio (Rm/t) to be 2.79. Thus the fracture mechanics formulation for surface cracks in cylinders subjected to an arbitrary stress distribution along the crack face from Reference 5, which was developed for Rm/t ratios ranging from 1.0 to 300, was chosen.

The model [5] provides the influence coefficients for both the deepest through wall location and for the surface point on the crack front of a semi-elliptical flaw in a cylinder. Hence the stress intensity factor, K,, at these two locations can be calculated for a give stress distribution, and therefore the crack growth at these locations can be independently calculated for a semi-elliptical surface flaw. The model used in this analysis is for an axially oriented; OD flaw and the influence coefficients for this geometry were used in the analysis. The general equation for K, in Reference 5 is as follows:

Where:

K, = Stress Intensity Factor(ksi 11n)

Q = Flaw Shape Factor,defined as Q = 1+ 1.464 * (a/c)"6 5 when a/c_*'1.0 and, Q = I + 1.464 * (c/a)'"6 S when a/c2 1.0 a = Crack depth (inch), and c = Half Crack length (inch) a, = Coefficient of Stress polynomial describingthe hoop stress variation through the crack depth, which describes the power loading on the crack face (uniform, linear, quadraticand cubic)

Page 7 of 19

AM-2007-006 Gi = Stress Intensity Correction Factors (SICF), which were obtainedfrom Tables 2 and 4 of Reference 5.

In Reference 5, the SICF is presented for both the depth point of the crack (a-tip) and for the surface point of the crack (c-tip). In these tables the SICF data is provided for each of the tube and flaw parameters IRm/t ratio, a/c ratio (crack aspect ratio), and alt ratio (normalized crack depth)). The SICF tables are large and suitable interpolation is required to accurately obtain the values for a given flaw size and shape. In order to accomplish the proper interpolation scheme a polynomial fit of the data from Tables 2 and 4 in Reference 5 was performed and used such that proper coefficients could be developed to accurately determine a conservative upper bound value for K, at both points along the crack front. The salient details for the computation of K, are discussed in a later subsection.

3.3 PWSCC Crack Growth Model To evaluate the potential for crack growth due to PWSCC, the crack growth rate equation from EPRI-MRP55 [6] was used. The crack growth rate as a function of K, with a correction for temperature effect is given by [6]:

da exp I * -

d- RT T,,

Where:

da/dt = crack growth rate at temperature T (m/s]

Qg = Thermal Activation energyfor crack growth (31.0 kcal/mole]

R = Universal Gas constant (1.103 x 10 3kcal/mole per degree RI T = Absolute operating temperatureat crack tip ( 'R)

Tref = Absolute reference temperaturefor data normalization [076.67 'RI a = Crack growth amplitude (2.67x101 ]2 K = Ki at the crack tip (Mpa '/nj Kth = Threshold Kifor crack growth (Mpa /4 n]

1. = Exponent Coefficient (1.16)

The equation above uses Metric units; therefore a conversion factor was applied to obtain the crack growth in English units (inch/hr). The reactor vessel head operating temperature [4] was defined as 588 'F. The above equation represents the 7 5 th percentile curve of the data used for the correlation.

Page 8 of 19

AM-2007-006 3.4 Method of Analysis The analysis approach followed the guidance provided in Reference 7 for performing PWSCC flaw evaluations, as follows:

1) Utilization of proper stress field in the region of interest (including residual plus operating stresses).

2) Selection of initial flaw size based on the detectability limit for the inspection method utilized.

3) Use a suitable stress intensity factor correlation for determination of the crack growth driving force.

4) Integration of the appropriate crack growth rate equation to determine the available operating time under normal operating conditions.

The analysis methodology is presented in the Appendices and summarized here.

For the analysis the first part requires two tube related landmark entries, these are; CRDM[ength.eval : the portion of the CRDM tube length for which the hoop stress data exists.

ULstrs.Dist : The location of the upper extent on the CRDM tube for which the hoop stress data exists.

Immediately below these entries is an entry defined as "val", which defines the location of the initial flaw. The description for this entry is defined above the input line.

As previously described, the input for these parameters was determined from the operating and residual stress finite element analyses for the five CRDM nozzle groups; 00, 25.40, 42.80, 43.80 and 470, documented in Reference 3.

The postulated flaw parameters (size, shape and location) were selected on the following basis:

1) Flaw size: Based on the minimum detectable flaw from NDE demonstration results [2].

2) Flaw shape: based on the flaw shape for the smallest detectable flaw (semicircular). An OD surface flaw was postulated based on the examination results from CRDM #68 (NDE and Metallurgical examination). The NDE examination results did not indicate any other indication to be found in several of the CRDM penetrations examined.

The results provided in Reference 7 indicate that a low aspect ratio tends to produce faster crack growth.

3) Flaw location: Similar to the crack found in CRDM #68. Nozzle OD surface flaw located in the middle of the J-groove weld is at the high stress location [3]. UT examination results for the four Byron and Braidwood reactor vessel heads did not detect any inside surface indications, therefore inside surface flaws were not postulated.

4) No flaw was postulated in the weld metal because: a) The metallurgical evaluation [ 1] did not reveal any PWSCC crack initiating in the weld metal; b) the low susceptibility category for the head, based on low head operating temperature, implies flaw initiation on the wetted J-groove weld surface is not plausible for some time; and c)

Page 9 of 19

AM-2007-006 the post weld heat treatment (PWHT), performed on the finished head

[8], has been shown to provide higher resistance to crack growth [7],

and by implication to flaw initiation.

The crack dimensions of 0.15 inch length and 0.075 inch depth, was determined to be the detectable limit for the ultrasonic examination technique used to examine the tubes per Reference 2. The tube geometry, internal pressure and the head operating temperature were defined in Reference 3. Since the finite element analyses used to define the stress data included the operating loads, the internal pressure was only used to prescribe the crack face pressure. The years of operation (Hot Operating time), and iteration limit are used to define the duration and the limits of the crack growth calculations and were defined to ensure the postulated flaw length grew beyond the top of the J-groove weld.

The hoop stress data matrix (AllData) for the specific nozzle group being analyzed was obtained from Table 1 of Reference 3.The axial stress distribution along the ID and OD tube surfaces has been plotted to facilitate selection of appropriate data used in the analysis. In the present analyses all the data has been used.

The first step in the analysis segment is the determination of the hoop stress distribution that would be applied across the crack face. This is required because the coefficients provided in Reference 5 are defined for a power law loading with the polynomial order of three. In addition, the required orientation of the stress distribution for an OD initiated flaw [5] is from the OD surface to the ID surface. The stress distribution variation along the length of the CRDM covered by the J-groove weld is not uniform. Hence, if a single stress distribution defined at the initial flaw location were used, the K, would not be correct and the crack growth calculation would be wrong.

Since the calculation is performed in an iterative manner the likelihood of compounding errors becomes high, which in turn would lead to erroneous operating time estimates. To minimize errors arising from improper stress distribution application the following scheme was developed:

1) For the initial crack location the hoop stress distribution at the two surface crack tips and at the crack center was averaged to produce a single distribution that was representative of the loading on the crack face.. This method is considered reasonable since it is similar to the superposition principle used in finite element based K, determination.

2) The remaining portion of the CRDM tube, above the upper crack surface tip to the top of the hoop stress distribution extent (half inch above the top of the weld), is divided into twenty equal segments.

3) The hoop stress distribution in the first segment, above the upper crack tip, is an arithmetic average of the first three initial crack region distributions (lower, middle and upper) plus the distribution in the first segment. Thus when the crack propagates into the first segment the magnitude of the stress distribution is appropriately adjusted to reflect the condition of the applied distribution from the finite element results [3]. Likewise as the crack propagates upward towards the J-groove weld root, the stress hoop stress distribution is appropriately adjusted. The small extent of axial length between the adjacent segments ensures that conformance with the stress distribution of Reference 3 is maintained.

Page 10of 19

AM-2007-006 To accomplish this averaging scheme, the nodal stresses at the six nodal locations through the thickness and its variation along the length of the tube are individually regressed with a third order polynomial. The regression is performed at each of the six through the thickness locations. To ensure that the regression is proper, a graphic display after this regression is provided as Figure 1.

Once the six polynomial equations for the axial variation of the hoop stress distribution are established, the through wall hoop stress distribution for the three locations defined by the initial crack and the twenty segments above the top of the initial crack are established. The hoop stress distribution at the twenty-three locations are subjected to a third order polynomial regression to obtain the four coefficients describing the through wall distribution at these locations. These coefficients are used within the recursive calculation loop to assign the influence coefficients based on current crack location.

For the OD surface crack the SICF coefficients were incorporated in two data tables. The first table, defined as 'jsb" contains the geometry data (Rm../t, a/c, and a/t) and the second table, defined as "Sambi" contains the SICF data for the appropriate cylinder and crack geometry. The values for the data were obtained from Reference 5, Tables 2 and 4. The data contained in the two tables were concatenated such that for each value of Rm/t there are three values for "~a/c" and finally for each "alc" there are five SICF values for each "alt"'ratio. The table entries were regressed and formulated into function statements with an appropriate polynomial order. The function statements corresponded to the third order polynomial coefficients derived for the stress distributions (i.e. the uniform, linear, quadratic and cubic stress terms of the third order polynomial). Therefore four function statements for each of the two crack growth points were developed. The data for cylinder geometries for Ra/t ranging from 1.0 to 4.0 were regressed with a third order polynomial and remainder with a second order polynomial. Using these polynomial definitions the function statement prediction was always marginally higher than the corresponding table value (presented in Figure 2), indicating that the resulting K, would be a conservative upper bound value. The interpolation equation was defined outside the recursive loop and a function call was made inside the loop using the pertinent variables at the time of the call.

The recursive loop contains the crack growth calculation scheme, which determines the crack growth for a defined period of time. For the twenty-four year calculation the time step is about seven hot operating hours. Thus, as the iteration limit remains constant, a lower value for the calculation years would produce a shorter time for the crack growth period. In the recursive loop the first few statements are loop initialization parameters. The calculation algorithm begins with the assignment of the through wall stress coefficients based on the current crack location. Once the four coefficients (uniform, linear, quadratic and cubic) are assigned, the through wall stress distribution along the crack face are defined. The stresses representing the crack face values (that is within the crack envelope) are then regressed with a third order polynomial to obtain the stress coefficients (the cOi values) that are used in the K, determination. At this point, the internal pressure acting on the crack face is added to the stress coefficient for the uniform term (ao).

Page I I of 19

AM-2007-006 Following the determination of the stress coefficients, the function call to obtain the four SICF coefficients (Gi) is made. In the current analysis two function calls are needed to accommodate the four coefficients for each of the crack front locations being analyzed (i.e. a-tip and c-tip locations). The flaw shape parameter "Q" is then computed using the appropriate crack dimensions. The K, is calculated separately for the "a-tip" and the "c-tip" crack front locations using the stress coefficients, the appropriate SICF values and the crack dimensions.

The calculated K, is converted to metric unit for the computation of the incremental crack growth using the EPRI-MRP model, Reference 6. The crack growth rate is computed based on the prevailing K, at the appropriate crack tip being evaluated.

Once this is accomplished, a conditional branch statement is used to compute the crack growth within a prescribed time increment. This growth extent is converted to English units and added to the crack dimensions from the previous iteration step to determine the new crack dimensions for the next iteration cycle. The other parameters are suitably incremented and the values need for displaying the results are assigned to matrix elements of an output array defined as "CGRsambi". The plots provided at the end of the worksheet are used to determine the extent of PWSCC crack propagation and the time required for the initial crack to grow to the predetermined size.

"a-tip" Uniform Coefficients Rm/t = 2 "c-tip" Uniform Coefficients Rm/t =2 4 2 2,2. q.) 3 U fýJAý 2 W14

.0 . 0.

1) 91.2 11.4 0.6 0.S 0 0.2 11.4 1.6 11S

.Q. I atls20A"is30a0 AI 0lJ0lj-a A.

Normalized Flaw Depth Normalized Flaw Depth IM0a/c =0.2; Data 00Ma/c = 0.2; Data

.... a/c --0.2; Fit ----a/ = 0.2; Fit VON a/c = 0.4; Data x"t a/c = 0.4; Data

- a/c = 0.4: Fit --. a/c = 0.4: Fit al = 1.0; Data WA a/c = .O: Data

.... alc = 1.0; Fit a/c = 1.0; Fit Figure 2: Comparison between influence coefficient datafrom Reference 3 (solid lines) and curve fit used in the analysis (broken lines)

Page 12 of 19

AM-2007-006 4.0 Results The analysis was performed for the five nozzle groups. For the zero degree nozzle location only one analysis was needed as the nozzle is at the center of the reactor vessel head thereby the nozzle geometry and stress fields are symmetric about the vertical axis.

The other four groups are removed from the center of the head and thus have two locations where the hoop stress varies in magnitude about the nozzle circumference and with axial position. Thus, these nozzle groups required separate analyses for the "downhill" or zero degree location and the "uphill" or one hundred and eighty degree location of the nozzle. A total of nine crack growth analyses were executed and are presented in the Appendices.

The initial crack size was established by the minimum detectable flaw size in the performance demonstration test [2], which was 0.075 inch deep and 0.15 inch long. The location of this initial crack was based on the results of the metallurgical evaluation [1],

which was at the middle of the J-groove weld. This initial location also centers the postulated flaw in the maximum hoop stress position for the nozzle. Thus, the extent of crack growth from PWSCC was the difference between the axial elevation of the top of the J-groove weld (weld root) and that of the upper "c-tip" of the initial crack. The initial results from the nine analysis sets showed two different behaviors. The analysis for the "downhill" side of the weld showed flaw propagation to be gradual until the upper "c-tip" of the crack reached the top of the J-groove weld (weld root). The crack growth on the uphill side of the weld was more aggressive and instability in the analysis (a rapid increase in K1 ) occurred prior to the crack reaching the top of the J-groove weld. Typical graphical results for the "downhill" side are shown in Figure 3 and that for the "uphill" side in Figure 4.

In these figures the behavior of the K, for the two crack tips are used to determine the hot operating time, defined in fuel cycles (eighteen month cycle with a capacity factor of 0.98). When the behavior of the K, values shows a gradual increase with time (Figure 3), the crack propagation in the length direction is chosen to establish the time to reach the J-groove weld root. Figure 3 represents the condition for CRDM #68, which was located at the 43.80 head angle. At the "downhill" location it was found that the instability of K, occurred after the upper "c-tip" of the crack had progressed past the top of the weld. The K, at the "c-tip" is always higher than at the "a-tip", which implies that crack growth is faster along the surface. This is corroborated by the findings from the evaluation of the flaw found in CRDM #68.

The alternative behavior, when the K, curves show an abrupt increase in slope (Figure 4), before the upper "c-tip" has reached the top of the J-groove weld, the limit for operating time (based on analysis) is chosen to be at the time when the K, plot shows the abrupt change in slope. Once again crack growth in the length direction is observed to be faster than along the depth direction. After the instability point the crack's "c-tip" propagates rapidly to the top of the weld. Hence, truncating the analysis at the instability point ensures that a conservative estimate of the available operating time is achieved. As was the case for the "downhill" side, the crack front in the depth direction does not reach the ID surface.

Page 13 of 19

AM-2007-006 Stress Intensity Factors so 6U 11226 CGR sambi 40 CR.,992tk.6 20 0 2 4 6 9 20 12 14 M6

,5i.227X 10 CGR snb Operating Time ifeci'ules)

Depth Point

-Surf-w¢Pnint "a" Stress Intensity Factors Flaw Growth in Length Direction

.9

.~ R~j,,

0 A

0) 2 4 6 8 In 12 14 J.127Xs 10- CORanl. 6 Operating Time (fuelc,elns }

"b" Crack Growth in Length Direction Flaw Growth in Depth Direction

,075 0 24 0 H

,12217.10- , CUR _b Operating Tin. ( fioelael. I "c" Crack Growth in Depth Direction Figure 3: Typical resultsfor the "downhill" side of the weld. Plots used to determine operatingtime window for PWSCC crack propagation. The K, plot in "a" shows a gradualincreaseover time and the crack growth in the length direction ( plot "b "')shows that the allowable propagationlimit to have reachedprior to any instability in K, behavior. The crack growth in the depth direction is shown in c ". At the time when the upper "c-tip" reaches the top of the J-groove weld. the deepest penetration of the crack has not reached the ID surface of the tube.

Page 14 of 19

AM-2007-006 CGR _athi I CGR _umhi kt a J.7.497,I 6 x I 2 k 16

.. 613nlO-* CGR sonhi k, to Opetaling Time { lcee)

- Depih Pint

..... Surf-¢ Point "a" Stress Intensity Factors Flaw Growth in Length Direction

.9 CGRRamhik,1 0.5 I 1.5 2 2.5 3 3.5

. ,613x I0 -* CGRenm tIL.tO Opertilng Tirne {fuelcyclesl "b" Crack Growth in Length Direction Flaw Growth in Depth Direction 2

12 a

0 01 1.5 2 2.5 3,5

,2.6110410-4 CGR Wamnhih,,

Operating Time (feel -ycten(

"c" Crack Growth in Depth Direction Figure 4: Typical resultsfor the "uphill" side of the weld. Plots used to determine operating time window for PWSCC crack propagation.The K, plot in "a" shows an abruptslope change at 6.06fuel cycles. The crack growth in the length direction (plot "b ") shows that the allowable propagationlimit was not achieved prior to the instability in K, behavior.The crack growth in the depth direction is shown in "c ". At the time of K, instability, the deepest penetrationof the crack has not reached the ID surface of the tube.

Page 15 of 19

AM-2007-006 The instability, observed in the analysis for the "uphill" side is believed to be caused by the higher stress field at this location, which in turn would create a higher stress distribution applied on the crack face resulting in higher K, and the attendant higher crack growth. Figure 5 [3] shows the stress distribution for nozzle group "25.4"' for the "downhill and "uphill" side. It is clear from this figure that the high stress contour "red color" (range from 50ksi to 100 ksi) extends for a significantly larger region on the "uphill" side than on the "downhill" side.

ANSYS 5.7 APR 21 200) 20:43 03 PLWoTNO. 3 Powor~rlphics HFACET=1 NAT NUN NODAL SOLUTION TIME-4004 SY (AVO)

RSYS.11 Powarcraphica SFACET- 1 AVRBB=Mat EM .!409298 SM :-19942 SKX =9199

-19942

-10000 Uphill Side 0_

- 10000

- 20000 30000 40000 O50000 100000 DownillSide By~rCRIl(25.4eCYC 88.4/2.75.0,A) - Operating Figure 5: Stress contoursfor nozzle group 25.4 . The high stresses, red colored contourprevails over p" a larger region than that at the "downhill" side. Note that the stress contours in between these two importantlocationsis not as intense.

Therefore a crack on the uphill side is bound to grow faster and reach the instability point on the influence coefficient curve. The behavior of the influence coefficients with respect to operating time is provided in the Appendices. The results for the "uphill" and "downhill sides of nozzle group "25.4"' is presented in Figure 6.

The instability (rapid rise) of the influence coefficients occurs much earlier in time for the "uphill" analysis than for the "downhill" analysis. As a consequence, an OD initiated crack on the "uphill" side is likely to progress faster and reach the top of the J-groove weld in a shorter operating time.

Page 16 of 19

AM-2007-006 Influence Coelicients - Flaw Influence Coefficients - Flaw 0 I 2 3 4 5 6 7 2 4 6 8 10 12 13nX0 -*

6.2 CGR sa'bk, 7 ,i.2:'f10- t CGR ,.,, 12 Opcrtinl inc lfuel P :rYd Operatinglice Ifuel ydcls "11"-Tip - Urnt "W" - Tip-- Unihnna

..... .a"-Tip -- Liner ..... "- Tip - Linear

- - Tip-- .kthi.k - - "a"- Tip- Qwatkawin "a'

- V -Tip- Cubic ... " -Tip-. Cubic V - Tip-- Utifocrn V - Tip- Unifor.

.. Tip .. Linar - Tip - Linea. -'

"- " -Tip- Q. dic - "- - Tip -. Q IadraWi4 V -Tip-- Cubic * - Tip -- Cubic V

"Uphill Side" "Downhill Side" Figure 6: Influence coefficient plots for nozzle group "25.4 0." The instabilityfor the" uphill" side is observed to occur at 6.06fiel cycles, whereasfor the "downhill" side it occurs at 9.05 fuel cycles (right dashed vertical line).

The available operating time (fuel cycles) from the nine analysis sets is summarized below.

Nozzle Group & Location Available Operating Window (Fuel Cycles)

"0.0" Degree Nozzle 7.30 "25.4" Degree Nozzle; Downhill 9.05 "25.4" Degree Nozzle; Uphill 6.06' "42.8" Degree Nozzle; Downhill 11.69 "42.8" Degree Nozzle; Uphill 6.37" "43.8" Degree Nozzle; Downhill 12.26 "43.8" Degree Nozzle; Uphill 6.42" "47.0" Degree Nozzle; Downhill 13.75 "47.0" Degree Nozzle; Uphill 6.67"

"*" Available Operating Window limited by Instability of K, The above results indicate that the lowest available operating window is more than six (6) eighteen month fuel cycles or 8.91 hot operating years.

Page 17 of 19

AM-2007-006 5.0 Discussion The analysis presented in this report is based on the existence of a postulated flaw whose initial size is predicated to be equal to the smallest detectable flaw by the volumetric inspection method utilized for the current inspections. Furthermore, this initial flaw location was based on the findings from the metallurgical evaluation for CRDM #68 in the Byron Unit 2 reactor vessel head [1] and the maximum hoop stress locations for the nozzle. The analysis used the residual plus operating hoop stress distribution for the CRDM tubes, obtained by finite element analyses [3]. The crack growth model was obtained from EPRI-MRP 55, which proposed a conservative upper bound formulation at the 7 5 1h percentile. The fracture mechanics model was developed using the generalized formulation developed by the National Aeronautics and Space Administration (NASA)

[5]. The NASA formulation provided the necessary cylinder and flaw parameters that were suited to the CRDM tube analysis. In the analysis, the restraining effect of the J-groove weld on the OD crack mouth opening was not considered, which implies that the estimated K, values would be higher than the value if the constraint effect of the weld was simulated.

The conservative assumptions in this analysis would result in a lower bound estimate for the operating time window. Therefore the results of this analysis provide the lowest time estimate for a hypothetical initial flaw to reach a size where an initial leak path can develop (flaw tip reaching the top of the J-groove weld).

The postulation of the initial flaw would require the existence of a fabrication defect, similar to that discovered in CRDM #68 at Byron Unit 2 reactor vessel head. This is a necessary condition for the occurrence of PWSCC (i.e. the third prerequisite - corrosive environment). Given the knowledge obtained from the metallurgical evaluation [1] and the results of the present analysis, two significant inferences can be drawn. These inferences are:

1) Had there been fabrication defects similar to that discovered in CRDM #68, this analysis shows that the likelihood for their detection by the current inspection method would be very high. This is because the analysis shows that these other hypothetical flaws at other important locations would have grown to a much larger size in the same period that the flaw in CRDM #68 propagated to a larger than detectable size and would have been easily detected.

2) If it is assumed that at the start of the current operating cycle, that flaws of the size assumed in the analysis (smallest detectable flaw size) at the important locations, there would be at the very minimum nine (9) hot operating years before the crack would reach a size where an initial leak path could develop.

The significance of the constraint effect is important because the metallurgical evaluation showed that the crack in the weld metal was the result from a PWSCC crack propagating in the tube (wrought) material and then penetrating the backside of the fillet leg of the J-groove weld. The fillet leg of the J-groove weld is thin and as the PWSCC crack reached the fusion line between the fillet leg and the tube, the K, at that instant would have been significantly higher (both due to flaw size and prevailing residual plus Page 18 of 19

AM-2007-006 operating hoop stress) and hence continued propagation into the weld was facilitated.

Since no indication of PWSCC initiation in the weld was discovered from the metallurgical evaluation [1], the likelihood of extensive weld metal cracking is very low.

This observation suggests that the J-groove weld would offer significant constraint, thereby reducing the magnitude of the prevailing K, in this region. Therefore, not considering the constraint effect in the analysis results in an upper bound estimate for K1.

6.0 Conclusions The analysis performed, which was presented in the preceding sections support the following conclusions:

1) The likelihood for pre-existing defects, similar to that discovered in CRDM

1. 68 in the Byron Unit 2 reactor vessel head, at other CRDM locations is considered to be very low.

2) The analysis demonstrates that a conservative lower bound for an operating window to be six (6) fuel cycles.

7.0 References

1) "Metallurgical Evaluation of a Boat sample from the #68 CRDM Penetration on Byron unit 2"; Exelon Powerlabs Project BYR-48053; Exelon Powerlabs LLC; May 2007.

2) "Materials Reliability Program: Demonstrations of Vendor Equipment and Procedures for the Inspection of Control Rod Drive Mechanism Head Penetrations (MRP-89)," EPRI Report 1007831, September 2003.

3) "Byron and Braidwood Units 1 and 2 CRDM Stress Analysis"; Dominion Engineering, Inc.; Task No. 77-70; Calculation No. C-7770-00-1, Rev. 0; April 2003.

4) "e-mail correspondence from Jim Lee (Exelon) to Richard Hall etal. (Exelon)",

Subject:

"Byron boat sample analysis"; May 04, 2007

5) "Stress Intensity Factors for Part-through Surface cracks"; NASA TM- 111707; July 1992.

6) "Materials reliability Program (MRP) Crack growth rates for Evaluating Primary water stress corrosion Cracking (PWSCC) of thick-Wall Alloy 600 Materials";

(MRP - 55NP), NRC ADAMS Accession No. ML023010510.

7) "Development of Crack Growth Rate Disposition Curves for Primary Water Stress Corrosion Cracking (PWSCC) of Alloy 82, 182, and 132 Weldments";

White G. A., etal; Proceedings of Environmental Degradation Conference, Snowbird Utah, The Minerals, metals and Materials society; August 2005.

8) AREVA Engineering Information Record 51-5014160-001, Vessel Head Penet.

Nozzle Data For Byron I & 2, Braidwood 1& 2, Dated 5/11/07.

Page 19 of 19

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - 00 Surface Flaw D3eveloped by: J. S. Be*hmadesam

References:

1) "StressIntensity factors for Part-throughSurface cracks," NASA TM-111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion EngineeringCalc. C-7770-00-1, Rev.0, "Byron/Braidwood CRDM PenetrationResidual Stress Evaluation."

Byron NuclearStation Unit 2 Reactor Vessel CRDM -"0.0" Degree Nozzle, "0" Degree Azimuth ("Downhill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed, as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 75th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is applied during the determination of the crack extension to obtain the value in English units (inch/hr).

Note :- I) Use of SICFtables from Reference I for External flaws (Tables 2 and 4).

2) The stress distributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to OD).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5" below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL Str.Dit) on the CRDM where the through wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Pant) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the 'Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix I Page 1 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 CRDMLength.evai:= 2.24 CROM Tube Length for Crack Growth Calculation, Use the length of the tube where the through wall stress distributionswill be defined.

ULStrs.Dist := 2.24 Upper extent of the Stress bistribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint :=

22 To place the flaw with respect to the reference point, the flaw tips or flaw 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 'r - tip " located at the reference point (Enter 3).

Val := 2 Input Data :-

1 := 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint:= 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years:= 16 Number of Hot Operating Years for Analysis Appendix I Page 2 of 31

Appendix I Evaluation of PWSCC Crock Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 rim := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

aO0c 2.67 A0- 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg 31.0 Thermal activation Energy for Crack Growth; [MRP-55 Rev. 1)

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 1) od id 0 2 Rid ::- t:= Ro -Rid RM ~id+2 Timopr:= Years.365-24 Timopr Ilim[ 1 Rm CFinhr := 1.417.105 Cblk : Pmtblk := 1-5 20= Rt :=

Ilim t Qg ( t I oQ 1.103-1 THead+459.67 T+459.67 0 c Temperature Correction for Coefficient Alpha C0 1 : =e.O CC= C0 1 75 th percentile MRP-55 Revision 1 Appendix I Page 3 o! 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input all availableNodal stress data in the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recordedon data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress data at each Elevation (ksi)

Column "6" = OD Stress Data at each Elevation (ksi) 0.0 45.364 41.204 34.776 28.376 20.175 9.755 0.5 38.925 40.447 42.012 47.066 59.932 72.896 AllData := 1.12 28.976 32.43 41.249 51.066 62.753 69.448 1.74 50.06 48.288 47.810 48.037 54.095 58.235 2.24 50.065 44.607 42.606 43.168 36.062 14.709 EDAI1 := AllData(1>

AXLen := AllData(°) ODAI1 := AIlData(6Q Stress Distribution 1DA1I (jm U/

ODAII 0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix I Page 4 of 31

Appendix I Evaluation of PWSCC CrackGrowth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Observingthe stress distributionselect the region In the table above labeled DataN, that representsthe region of interest This needs to be done especiallyfor distributionsthat have a large compressive stress at the nozzle bottom andhigh tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Date" statement below and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insert the same to the rightof the MathcadEquals sign below (paste symbol).

0.0 45.364 41.204 34.776 28.376 20.175 9.755 0.5 38.925 40.447 42.012 47.066 59.932 72.896 Data := 1.12 28.976 32.43 41.249 51.066 62.753 69.448 1.74 50.06 48.288 47.810 48.037 54.095 58.235 2.24 50.065 44.607 42.606 43.168 36.062 14.709 AxI := Data(0) ID :=Data( I) Twty:= Data(2) Frty := Data(3)

Sxty :=Data (4) Egty := Data(5) OD := Data(6)

RID :=regress (Axl, ID, 3) RTwty regress(Axl, Twty, 3) RFrty := regress(AxI, Frty, 3)

RSxty: regress(AxI,SXty,3) REgty regress(Axl,Egty, 3) ROD:= regress(Axl,OD,3)

FLntr := Refpoint -co if Val= 1 Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise Appendix I Page 5 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 1 -Strs.Dist UTip UTip :- FL~Cntr + co Inc -

InStrs.avg 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locationsfor stress profiles Loco := FLCntr- I i:= i..N+3 Incri CO if i< 4 Incstrs.avg otherwise Loci := Loci-, + Incri 2 3 SIDi RI+

=RD I4 "Loci + R 5 (Loci) I(Loci) 0+R 6I5(~i STwtyi := RTwty3 + RTwtY4 Loci + RTwty "(Loci) 2 + RTWtY6. (Loci) 3 SFrtyi RFrty3 + RFrty4. Loci + RFrty. (Loci) 2 + [ RFrtY6. (Loc i)3]

SSxtyi RSxty3 + RSxtY4 -Loci + Rsxty (Loci) 2 + [ RSxtY6.(Loci)3]

Appendix I Page 6 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 SEgtyi := REgty3 + REgtY4 -Loci + REgty -(Loci) 2 + REgtY6 (Loci) 3 SODi:: ROD 3 + ROD 4Loci + ROD "(Loci) 2 + ROD 6"(Loci),

Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 50 SIDi4 30 20 I I I I 0 0.5 1 1.5 2 2.5 AxI, Loci t100 I I I OD SODI 50 0

0 0.5 1 1.5 2 2.5 Axl,Loci Appendix I Page 7 of 31

Appendix I Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j := i..N 5

STwtyj + STwtyj+l + STwtyj+ 2 if =

S-d id s% + SIDj+, + sIIj+2 iif Twt.

3 .1 3 Sid:_ .(j + 1) + SIDj+ 2 STwtyj-" (j + i) + STwtyj+ 2 otherwise otherwise j+2 j+2

-ISSXtYj + SSXtYj+i + SSXtYj+ 2 _

Frtyj SFrtyj + SFrtyj+l 3 + SFrtyj+ 2 if j Ismty it J = I YJ 3 SFrtyj_ .(j + 1) + SFrtyj+ 2 SSxtyj-, (i + 1) + SSXtYj+2 JUL[Il W ac; j+2 )therwise j+2 SODj + SODj+1 + SODj+2 if j j=I SEgtyj + SEgtyj+l + SEgtyj+2 Sod. :=

SEgtyj := if j= 3 3 J S o d_- -(j

+ l) + SODj+ 2 SEgtyj_.( + I) + SEgtyj+ 2 i-I j otherwise j+2 j+2 Eleva&Jon-Averaged lHoop Stress Distributioinflor OD Flaws (i.e. Stress distribuftion changed fTrom~ OD~ to §D.)

U0 := 0.000 U1 := 0.20 U2 := 0.40 U3 := 0.60 U4 := 0.80 U5 := 1.00 Appendix I Page 8 of 31

Appendix I Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Y :=stack(u 0'uj1U,u 2 3 ,u4 ,u5)

SIG1 stc ( o,51~y S~y ~t, SwySd)G 2 stack(Sod 2 , SEgty ,S Sxty2'S~rty,,STwty2,Sid2)

S G3 stack(Sod, SEgty3 ,,SSxty, ,SFrty3, STwty3 , Sid3) SIG4 stack( Sod 4 , SEgty4, SSxty4, SFry, STwty4, Sid 4)

SIG 5 stack(Sods,SEgty 5 ,SSxty5, SFrty5, STwty5,Sid) SIG6 stack(Sod6, SEgty6, SSxty6 , SFrty6, STwty6, Sid6)

SIG 7 stack(Sod7, SEgty7, SSxty7 ' SFrty7, STwty,, Sid,) SIG 8 := stack( Sod, SEgty SSxtys, SFrtYs, STwty, Sid 8)

SIG9 stack(Sod9 SEgtyg,SSxtyg, SFrtyg, STwty9 ,Sid9 ) SIG 1 0 stack(Sodio, SEgtylo, SSxtYlo SFrtyl0'STwtylo' Sid o)

SIG1 1 stack(Sod 1, SEgty, I,SSxty,1 ,,SFrty ,,' STwty, I Sid,) SIG 1 2 stack (Sod 1 2' SEgty 12 ' SSxty1 2 'SFrty1 2' STwty1 2' Sid 2)

S1G 13 stack(Sod ,SEgty3, SSxty, 3 , SFrtY, 3 , STwty13) Sid13) SIG 1 4 stack( S o d 14 SEgtyJ 4 , SSxtyI 4 ' SFrty)4' STwty 1' Sid 14)

SIG 15 :stackSod15 ' SEgty, 5 'SSxty 5', SFrty15 , STwty 5, S'id 5 ) SG16 :=stack(Sod16 SEgty1 6 'SSxtylbSFrty1 6 STwty 6,Sid,6)

SIG 1 7 stack(Sod17' SEgty 17 SSxty,7 'SFrty1 STwty171 Sid 17 ) SIG 1 8 stack(Sod18, SEgty 18, SSxtys , SFrty, ' STwty' ,Sid 8)

SIG 1 9 := stack (Sod 1SEgtygSSxty 5Frty wty'idj SIG 2 0 stack(Sod 2 O SEgtY2o SSxY Frty 2 o, STwty2 0 ,Sid2 0 )

Appendix I Page 9 of 31

Appendix t Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDAMnozzles at Byron Unit 2 AM-2007-006 Regression on Through Wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 regress(Y,SIG 1 ,3) ODRG 2 := regress (Y, SIG2 ,3)

ODRG 3 regress(Y, SIG 3 ,3) ODRG 4 := regress(Y,SIG4 ,3)

ODRG 5 regress(Y, SIG5 ,3) ODRG 6 regress(Y, SIG6,3)

ODRG 7 := regress(Y ,SIG 7 ,3) ODRG 8 regress(Y, SIG 8 ,3)

ODRG 9 := regress(Y,SIG 9 ,3) ODRG 1 0 := regress(Y, SIG 1 0 ,3)

ODRG 1 1 regress(Y,SIG 1 1 ,3) ODRG1 2 := regress(Y,SIGl 2 ,3)

ODRG 1 3 regress(Y, SIG 1 3 ,3) ODRG 14 := regress (Y,SIG 14 ,3)

ODRG 1 5 := regress(Y,SIG 1 5 ,3) ODRG 16 := regress(Y,SIG 1 6 ,3)

ODRG 17 := regress(Y,SIG 17 ,3) ODRG1 8 regress(Y,SIG1 8 ,3)

ODRGI 9 := regress(Y,SIG1 9 ,3) ODRG 2 0 regress(Y, SIG 2 0 ,3)

Appendix I Page 10 of 31

Appendix I Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Stress Distribution in the tube. Stress influence coefficients obtained from thirdorderpolynomial curve fit to the through wall stress distribution PrOkenIgth : ULStrs.Dist - FLCntr - c 0 - 0.5 TProLength 0.545 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-111707-SC04 Model)

{NO INPUT Required)

Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb :=

0 1 2 7he Table on the left "Jsb" consistsof the cylinder andflaw mechanical 0 1.000 0.200 0.000 parametersas follows:

1 1.000 0.200 0.200 Column "0" :- Contains the mean-radiusto thickness ratio (Rm It) of the Cylinder 2 1.000 0.200 0.500 3 1.000 0.200 0.800 Column "1"V-Contains the Flaw Aspect Ratio (a/c)

Column "2":- Contains the Flaw Depth-to- Tube- Thickness ratio (alt) 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 Appendix I Page 11 of 31

A 15 2.000 0.200 0.000 tion of PWSCC Crack Growth of PostulatedFlaw in CRDM noazzles at Byron Unit 2 AM-2007-006 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 0.800 34 4.000 0.200 1.000 35 4.000 0.400 0.000 36 4.000 0.400 0200 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000

(.5-1. 10.000 0.400 0,2001 Appendix I Page 12 of 31

A 2 5ion of PWSCC Crack Growth of Postulated Flaw in CRDM nozzles at Byron Unit 2 AM-20(Y7-O06 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 571 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 74 300.000 1.000 1.000 The Table below "Sambi"containsthe Flaw Influence coefficients as follows:

Column "0":- Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip)

Column "I":-Contains the influence coefficients for Linear Loading at themaximum depth of the flaw ("a"-tip)

Column "2".:- Contains the influence coefficients for QuadraticLoadingat themaximum depth of the flaw ("a"-tip)

Column "3" :- Contains the influence coefficients for Cubic Loading at the maximum depthof the flaw ("a"-tip)

Column "4" :- Contains the influence coefficients for Uniform Loading at the surfacepoint of the crack front ("c" tip)

Column "5" :- Contains the influence coefficients for LinearLoading atthe surfacepoint of the crack front ("c'"-tip)

Column "6" :- Contains the influence coefficients for QuadraticLoading atthesurface point of the crack front ("c" tip)

Column "7":-Contains the influence coefficients for Cubic Loading atthe surface point of the crack front ("c"-tip)

Appendix I Page 13 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Sambi:=

0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 1Append* te 14 of 3!1.16 0.242 0.097 0.051

Appendix I 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 AM-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0,113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix I Pa ge 15 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulaiedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 In the declarationsbelow, dummy variablesare defined in order to develop a continuous function for the various influence coefficients. A continuous function can then be readilyused inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysis with a thirdorderpolynomial for Rm /t less than 4.0 anda second orderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters R. It ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb ',> is a column array containing the Rn /t ratio, which is also Column "0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W := Jsb(o) X :=Jsb(I> Y :=Jsb(2) au Sambi(O) aL:= Sambi([> aQ Sambi (2) ac Sambi(3) cu Sambi4) cL:= Sambi(5) cQ Sambi(6) cc Sambi.(7) n:= 13 if Rt<4.0 Order of polynomial selected based on R m t ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

Fau (W,X,Y) which is the standard nomenclature is Fau (R , /t, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (R,

/t, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix I Page 16 of 31

Appendix I Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM nozzles at Byron Unit 2 AM-2007-M*

"a- Tip" Coefficients "a-tip" Uniform Term MaU:= augment(W,X,Y) VaU := aU RaU := regress(MaU, VaU 'n) faU(WXY):=interp RaU, MaU, VaU{ X}

fa~(WXY "a-tip" Linear Term MaL:= augment(WX,Y) VaL:= aL R:=regress (MaL ,Va, n) faL(W,X,Y) := interp RaL, MaL, VaL,{X "a-tip" Quadratic Term MaQ:= augment(W,X,Y) VaQ:= a RaQ :=regress (MaQ, VaQ, n) faQ(W,XY) : MaQ' VaQLXj "a-tip" Cubic Term MaC:= augment(W,X,Y) VaC:= aC RaC := regress(Mac, VaC, n) faC(WXY):=interp[RaC, MaC, VaC{XjJ fa~(WXY "c" Tip Coefficients "c-tip" Uniform Term MCU: augnient(W,X,Y) VCU := Cu RCU := regress (MCU, VcU, n) fcU (W,X,Y) : nepRU CVU Appendix I Page 17 of 31

Appendix I Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 "c-tip" Linear Term McL:= augment(W,X,Y) VcL := CL RcL := regress (McL, VcL, n) fcL(W, X,Y) : nepRL CVL "c-tip" Quadratic Term McQ:= augment(W,X,Y) VCQ := CQ RC =regress (MCQ 2VCQ~n) fC Q (W ,X ,Y ) :

n ep R Q M Q V Q I "c-tip" Cubic Term McC:= augment(WX,Y) VC:-Ccc R~CC: regress (MCC,V~cC,n) fCC (W, X, Y) :=interp RcCMCC, VcC {X1 Appendix I Page 18 of 31

Appendix I Evaluation ofPWSCC Crack Growth of PostulatedFlaw in CRDM nozdes at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculationof PWSCC Crack6rowth as a function of Hot Operating Time j4-o CGRsambi :=

ao<-ao co(-- cO NCB 0 <-- Cblk while j < Ilim Yo +<- ODRGI3 if Cj <Co ODRG2 3 if co < cj < co + Incstrs.avg ODRG 3 3 if co + lncstrs.avg < Cj < co + 2-Incstrs.avg ODRG4 3 if Co + 2-IncStrs.avg < Cj < co + 3.Incstrs.avg ODRG 5 3 if co + 3-Incstrs.avg < Cj < Co + 4Ilncstrs.avg ODRG 6 3 if CO+ 4-InCStrs.avg < Cj 5 co + 5.IncStrs.avg ODRG 7 3 if co + 5.lncStrs.avg < Cj < co + 6.lncstrs.avg ODRG 8 3 if co + 6-lncStrs.avg < Cj < co + 7-Ilncstrs.avg ODRG 9 3 if CO+ 7.IncStrs.avg < cj 5 co + 8.IncStrs.avg ODRG 1 0 3 if CO + 8.Insctrs.avg < cj co+ 9+Incstrs.avg ODRGll3 if cO+9-lncStrs.avg < cj < CO+ 10.IncStrs.avg ODRG 1 2 , if CO + 1o.IncStrs.a*pnit*, '*blCStrs.avg

Appe m Unit 2 AM.2007-006 ODRG 1 3 3 if CO+ I'I ncstrs.avg < cj <Co+ 12-IncStrs.av g

ODRG 1 4 3 if CO+ 12"lncstrs.avg < cj <Co+ 13"Incstrs.av g

ODRG 15 3 if Co+ 13"lncstrs.avg < Cj <Co+ 14-lncStrs.av/g ODRG 16 3 if CO + 14-lncstrs.avg < Cj co + 15"lncStrs.av /g C

ODRG 17 3 if Co + 15.Incstrs.avg < cj <co + 16.IlncStrs.av Ig 9g ODRG 18 3 if Co + 16-Ilncstrs.avg < Cj <Co + 17Ilncstrs.av ig ODRG 1 9 3 if co+ I7Ilncstrs.avg < Cj <Co+ 18-lncstrs.av ODRG2 0 3 otherwise ODRG1 4 if cj <CO ODRG2 4 if Co < cj < co + IncStrs.avg ODRG 3 4 if Co + Incstrs.avg < ci <Co + 2-Incstrs.avg ODRG4 4 if Co + 2'lncstrs.avg < Cj < co + 3-lncStrs.avg ODRG5 4 if Co + 3.ICsctrs.avg < cj <CO + 4*Incstrs.avg ODRG6 4 if Co + 4-flcStrs.avg < cj <co + 5IlncStrs.avg ODRG7 4 if Co + 5-InCStrs.avg < Cj <CO + 6.IncStrs.avg ODRG 8 4 if Co + 6-lncstrs.avg < cj < Co + 7 Incstrs.avg ODRG9 4 if Co+ 7-1nCstrs.avg < cj <Co+ 8-lncstrs.avg ODRG1 0 4 if co++8"lncStrs.av < cj <Co+ 9-1nCstrs.avg Appendix I Page 20 of 31

)n Unit 2 AM-2007-006 Appm ODRGI1 4 if co + 9-Incstrs.avg < cj _<CO + 10*-Incstrs.avg ODRG12 4 if Co + 10*.Incstrs.avg < ci _!Co + 11.Incstrs.avg ODRG13a4f "Co+ ' 1-I ncstrs.avg < cj _5CO+ 12.Ilncstrs.avg ODRG,44 if Co + 12"Ilncstrs.avg < cj <_ý Co + 13.Inlcstrs.avg ODRG 154 if Co + 13"InCstrs.avg < Cj < Co + 14Ilncstrs.avg ODRG 1 64 if co+ t4Ilncstrs.avg < cj CO+ 15.Ilncstrs.avg ODRG 1 74 if Co + 15-lncstrs.avg < cj < CO + 16.lncstrs.avg ODRG18 4 if Co + 16-Incstrs.avg < Cj <_Co+ 1-Ilncstrs.avg ODRG194 if Co+37-hacStrs.avg < cj !5 Co+ 18Ilncstrs.avg ODRG 204 otherwise cf2 <- ODRG 15 if cj co ODRG 25 if co <cj -<ý co + Incstrs.avg ODRG35 if co + lncstrs.avg < CjCo + 2.fInCstrs.avg ODRG45 if Co+ 2-InCStrs.avg < cj 5 co + 3-Incstrs.avg ODRG55 if Co + 3.InCStrs.avg < Cj _*Co + 4Ilncstrs.avg ODRG65 if Co + 4-Incstrs.avg < cj co + 5 Ifncstrs.avg ODRG75 if Co + 5-Incstrs.avg < cj CO + 6-Incstrsoavg ODRG85 if co + 6-IlCstrs.avg < Cj Co C + 7-1fnCstrs.avg f"%r1%" _r - I -, ,-- Ap..pediA IPaqe 24oRf 31

App( kjLxJAUQ 1i Lo P-r J iStrs.avg <. -;j Z co -r "'uCStrs.avg ,nUni, 2 AM-2007-00

-5 ODRG 10 5 if co + 8Ilncstrs.avg < cj < Co + 9. lncStrs.avg ODRG 1 1 if cO + 9- IlncStrs.avg < cj SCo + 10"lncstrs.avg ODRG 12 5 if co+ 1O.Incstrs.avg < cj Sco + I1 -lncstrs.avg ODRG 13 5 if cO + 1 .Ilncstrs.avg < cj !< co+ 12flncstrs.avg

<Co + 13-Incstrs.avg

5 ODRG 14 5 if CO+ 12-Incstrs.avg < Cj ODRG 1 5 5 if co+ 13"Ilncstrs.avg < cj

• CO + 14"lncstrs.avg ODRG 1 6 5 if co+ 14-Incstrs.avg < ci *5 Co+ 15-lncstrs.avg ODRG 17 5 if co+ 15.Incstrs.avg < Cj *5 Co + 16-lncstrs.avg ODRG 1 8 5 if CO+ 16.Incstrs.avg < cj j< Co + 17- Incstrs.avg ODRG 19 5 if co+ 17-1nCstrs.avg < Cj < Co+ 18-lncstrs.avg ODRG 2 0 5 otherwise ODRG1 6 if cj < Co ODRG 2 6 if Co < cj < co + Incstrs.avg ODRG 3 6 if Co + Ilncstrs.avg < cj <c0 + 2.Incstrs.avg ODRG 4 6 if Co + 2-lncstrs.avg < cj <co + 3.lncstrs.avg ODRG 5 6 if Co + 3-IncStrs.avg < Cj <Co + 4. lncstrs.avg ODRG 6 6 if CO+ 4, lncStrs.avg < cj <CO+ 5Ilncstrs.avg ODRG 7 if CO + 5"lncstrs.ave*&jA Ij'd L1Wj ' s.avg

Appx in Unit 2 AM-2007-006 ODRG8 6 if co + 6-IlncStrs.avg < cj <co + 7-IlncStrs.avg ODRG9 f if Co + 7-lncStrs.avg < Cj <co + 8-Incstrs.avg ODRG 10 6 if cO + 8-lncstrs.avg < cj < co + 9. Incstrs.avg ODRG1 1 6 if co + 9'Ilncstrs.avg < cj < Co + 10-Incstrs.avg ODRG 12 6 if Co + 10-Incstrs.avg <cj < CO + I-I"ncstrs.avg ODRG 1 3 6 if cO+ 1 4lncstrs. avg < cj < Co + 12-1nCstrs.avg ODRG 146 if Co + 12-lnCstrs.avg < cj < Co + 13* Incstrs.avg Co + 14" Incstrs.avg ODRG 1 5 if co + 13-lncstrs.avg < cj <

6 ODRG 16 6 if Co + 14-1nCstrs.avg < cj < Co + 15-lncstrs.avg ODRG 1 7 6 if CO + 15.Incstrs.avg <cj <: Co + 16"Incstrs.avg ODRG 18 6 if Co + 16-lnCstrs.avg < cj < co + 17-lncstrs.avg ODRG19 6 if Co+ 7I1nCstrs.avg < cj S Co + 18-lIncstrs.avg ODRG2 0 6 otherwise 0 .j0 < Oa0.25aj (!.25 aj)3

ý2 <- CO0 + Co 1"--'j ) + ý _"2* +a3

ý3 *+ + o2 -T -- p +ýf "IPa- 31

Appt \ L L ] L in Uni2 AM-2007-006

ý4+* o+(l t,** +(y'

( oa j2

+03' 1. j3 X0 <-- 0.0 x +- 0.25 x2 <- 0.5 x3 <- 0.75 x4- 1.0 X +- stack(x 0 ,x I,x 2 ,x 3 ,x4 )

ST 4- c(0,14,4,4 RG ---regress(X, ST, 3) a00 <-- RG3 + Plnt a 10 - RG 4 a 20 *-RG5 Y3 0 RG6 ARj ---aj cj ATj <---aj t

Gau. +- fau(RtARj,ATj)

Gal 4-- faL(Rt,ARj,ATj)

J Gaq +- faQ(Rt,ARj, ATj)

G <--f(r(Rt,ARi ,ATi) Appendix I Page 24 of 31

Appt )n Unit 2 AM-2007-006 G:u. <- fcu(Rt,ARj,ATj)

J Gci <- fcL(Rt,ARj,ATj)

Gcq. *- fQ(Rt,ARj,ATj)

Gccji -fcC (Rt, Aj, ATj)

QJ -- 1+ 1.464 . if cj _ aj 1+I.464{(j .65K otherwise

\ 05 0~

K7,Qj 0.5 Kl Cj) 0"(100"*cu. +a l0-Gcl i+ 2 0 .Gcqj +30"Gccj)

KaC *-- Ka 1.099 K <--

• Kc. 1.099 K 9.0 if Ka 9.0 Ka i otherwise Kyj*-- 9.0 if K *j<9.0 K-yj otherwise Da -- C 0 .(Kaj -9.0)1.16 D-,. <- ID. .CF;-u,..Cu,., if K-, < ig~ndix IPage 25 of 31

AM-2007 -006 App( 6,lj I 4fIln Uj Un Unit 2 40o-'.CFinhr-Cblk otherwise D ci <--CO."(Kyj - 9.0) 1.16 Dcj - Dc ,CFinhr.Cblk if <80.0 4-.0- '.CFinhr.Cblk otherwise outputj, 0 4- j outputj, I <- aj OUtpUt j, 2 - cj - Co OUtPUtj, 3 < Dagj outputj, 4 4-- Dcgj outputj, 5- Ka.

OUtpUt j, 6 <- KC NCBj output, 7 -365.24 outputj , 8 <- Gau.

J outputj, 9 <- Gal outputj, Io <-- Gaq.

output j, ItI - G ac.

OUtPUtj, 12 <-- Gcu.J outputj, 13 - Gcl.

. . . Appendix I Page 26 of 31

Appi ULJUtuj, 14 1 Ucq 7n Unit 2 AM-2007-006 outputj, 15 <- Gcc NCBj 365.24 outputj,6* ÷ 1.5 .98 j4-j++

aj <--aj- + Dagj_

cj <-- cj- + Dcgj_.

aj<- jt if aj>t aj otherwise NCBj <- NCBj-j + Cblk output k :=0.. liim PrOPLength 0.545 Appendix I Page 27 of 31

Appendix I Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 U

-C 0

1-.

(U 0 1 2 3 4 5 6 7 8 9 10 Operating Time (Fuel Cycles)

Flaw growth in the length direction, as a function of fuel cycles. The extension of the c-tip= or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.545 inch. Thus the time available for the flaw growth by PWSCC is about 7.30 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix I Page 28 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction 0.6 0.5 0._

0.4 U'

0.3 0-0.2 0.1 0 1 2 3 4 5 6 7 8 9 10 Operating Time ( fuel cycles}

Flaw growth in the depth direction, as a function of Fuel cycles. The extension of the "a-Tip' or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 7.30 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.32 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix I Page 29 of 31

Appendix I Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Stress Intensity Factors C)

LI 0 I 2 3 4 5 6 7 8 9 10 Operating Time 4fuel cycles)

- Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher WKvalue at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix I Page 30 of 31

Appendix I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM nozzles at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 0

°s Z

E 0 The influence coefficients as a function of operating time is shown. The behavior for UUD the "a-tip' shows the effect of the flaw

°C U.

u aspect ration for the initial flaw and early C

growth. No erratic behavior of the influence U

coefficients is observed.

0 2468 I0 0 Operating time Ifuel cycles)

"a" - Tip -- Uniform

. - Tip

. a" -- Linear

. .a"- Tip -Quadratic

............ Va" - Tip -- Cubic "ic" - Tip -- Uniform ic'- Tip -- Linear tic" - Tip -- Quadratic

........... c" - Tip -- Cubic Appendix I Page 31 of 31

Appendix U Evaluation of PWSCC Crack Growthofa postulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw Developed by: J. S. grihmadesam

References:

1) "StressIntensity factors for Part-throughSurface cracks,"NASA TM- 111707, July 1992.

2) Crack Growth of Alloy 600-Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion Engineering Calc. C-7770-00-1, Rev.0, "Byron/BraidwoodCRDM PenetrationResidual Stress Evaluation."

Byron NuclearStation Unit 2 Reactor Vessel CRDM -"25.4" Degree Nozzle, "0" Degree Azimuth ("Downhill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed , as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 7 5 th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is applied during the determinationof the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference I for External flaws (Tables 2 and4).

2) The stress distributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to 00).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5" below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.evai

2) The upper axial extent (UL St,.Dit) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Point ) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the "Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix II Page I of 31

Appendix IH Evaluation ofPWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 CRDM~ength.eva1 := 2.04 CROM Tube Length for Crack Growth Calculation, Use the length of the tube where the through wall stress distributions will be defined.

ULstrs.Dist := 2.04 Upper extent of the Stress Distribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval Refpoint :2 To place the flaw with respect to the reference point, the flaw tips or flaw 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 'L- tip" located at the reference point (Enter 3).

Val := 2 Input Data :-

1:= 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 24 Number of Hot Operating Years for Analysis Appendix IIPage 2 of 31

Appendix 11 Evaluationof PWSCC Crack Growthof a postulatedFlow in CRDM Nozzles at Byron Unit 2 AM-2007-006 Ilim := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

a0c := 2.67. 10- 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 1)

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 11 R° :=- od Rid:=

id 2 t:= Ro -Rid Rm := Rid+ 2 t

Timopr:= Years.365-24 Timopr Rm

-- "'in 1 C~inh :=I.417-105 C b lk := Ihim P'Mtblk = 5 Rt := t t

-Qg r I I C 0 1 : =e" 1.103.10-3. THead+459.67 Tref+459.67) Temperature Correction for Coefficient Alpha 0

Co := Co 1 75 th percentile MRP-55 Revision 1 Appendix IIPage 3 of 31

Appendix I11 Evaluationof PWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input all availableNodal stress data in the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recorded on data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress data at each Elevation (ksi)

Column "6" = OD Stress Data at each Elevation (ksi)

(0.0 36.321 32.372 27.869 24.989 20.287 13.805) 0.5 33.296 37.212 41.845 49.59 64.931 83.065 AllData := 1.02 25.782 30.577 40.782 49.862 58.797 64.920 1.54 45.491 45.833 47.413 50.965 53.968 28.917 2.04 50.294 44.579 43.112 43.33 43.213 32.43 AXLen := AllData(0) IDAll :=A1Data(1) ODAI1:= AllData(6)

Stress Distribution 100 1.675 1.69 80 T- ------ --- -- -

ODAII 60 (1.) 40 S_ _

20 A

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix II Page 4 of 31

Appendix 11 Evaluationof PWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Observing the stress distributionselect the region in the table above labeled DataA,, that represents the region of interest. This needs to be done especially for distributionsthat have a large compressive stress at the nozzle bottom and high tensile stressesat the J-weld location. Copy the selection in the above table, click on the "Data"statement below and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (pastesymbol).

0.0 36.321 32.372 27.869 24.989 20.287 13.805 0.5 33.296 37.212 41.845 49.59 64.931 83.065 Data 1.02 25.782 30.577 40.782 49.862 58.797 64.920 1.54 45.491 45.833 47.413 50.965 53.968 28.917 2.04 50.294 44.579 43.112 43.33 43.213 32.43 )

AxI : Data(0) ID :=Data(') Twty:= Data(2) Frty :=Data (3)

Sxty := Data(4) Egty :=Data (5) OD := Data(6)

RID := regress(Axl,ID,3) RTwty regress (AxI, Twty, 3) RFrty regress(Ax],Frty,3)

RSxty := regress(Axl, Sxty, 3) REgty regress(AxI,Egty,3) ROD regress(Axl,OD,3)

FLCntr := Refpoint - co if Val=I Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 RefPoint + co otherwise Appendix II Page 5 of 31

App*endix 11 Evaluationof PWSCC Crack Growthofa postulatedFlaw in CRDM Nozzles at Byron Unit 2 AM.2007-006 ULStrs.Dist - UTip UTip := FLCntr + CO lflcSts.avg :=20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locationsfor stress profiles LOCO := FL~ntr - 1 i:= 1..N+3 Incri:= co if i < 4 Incstrs.avg otherwise Loci : Loci-, + Incri SIDi : RID + RID4 Loci + RIDS (Loci)' + R~ D. (Loci) 3 STwty1 : R~w + Rw4 *Loci + R~y *(Loci) + R It6Loci)

SFrtyi RFtY3 + RFty4 *Loci + RFIrty' .(Loci), + I R~t6 (Loci) 3]

SSxtyi R SXtY3 + R S~tY4 .Loci + RSXtY5 .(Loc,) 2 + [ R S~ty6(LOC,)3]

Appendix II Page 6 of 31

Appendix H Evaluation of PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 SEgtyi := R EgtY3 + R EgtY4 -Loci + R EgtYs- (Loci)2 + R Egtyg(Loci)3 2 3 SODi:= ROD 3 + ROD4 Loci + ROD .(Loci) + ROD 6(Loci)

Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 I I I I I I I I I 50 ED SIDi 40 30 I I I I I I I I I 20 0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 2 2.2 Ax, Loci OD SODi 0I 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 AxI, Loci Appendix II Page 7 of 31

Appendix II Evaluation of PWSCC Crack Growthofa postulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j := I..N SIDj + SIDj+i + SIDJ+ 2 ifj STwtyj + STwtyj+ 1 + STwtyj+ 2 if j =

S STwty .- '-

3 3 Sid + l) + SIDj+ 2

+(j STwtY~j- .(j +i) +STwtyj+2 otherwise otherwise j+2 j +2 Fiy SFrty + SFrtyj+2 j SSxtyj + SSxtyj+1+ SSxtyj+ 2 if j =

if j SSxty S~tJ -1 StJ 3 SFrtyj- (j + 1)+ SFrtyj+ 2 SSxtyj-1 (j + I) + SSXtyj+ 2 otherwise otherwise j+2 j+2 SODj + SODj+I + SODj+ 2 if j- 1 SEgtyj + SEgtyj+l+ SEgtyj+2 if = Sod.

5 Egtyj

- 3 J 3 Sodj-l.(j + 1) + SODj+

SEgtyj- I(j + i) + SEgtyj+2 2 Sotherwise j+2 otherwise j+2 fflevatdcn-Averaged Headop Stress Distr!ibutifon f~or OD F~l~aws (i.e. Stress distrilbutionch~angied fromn O, to 0li)

U0 := 0.000 U1 := 0.20 u2 := 0.40 U3 := 0.60 u4 := 0.80 U5 := 1.00 Appendix IIPage 8 of 31

App eudix 11 Emalmalionof PWSCC Crack Growlhofo poslulmaedFlaw in CRDM Noa~zs o.. Byron Unil 2 ALM-2007-006 Y := stack(u 0 , u1, u 2 , u 3 , u 4 , u 5 )

SIG, stack*,o SEgty,, SSxty, SFy, Twty,, Sid,) SIG2 stack( Sod2 ' 2 SFrty Egty 2 SSXty ' 2 STwty 2 Sid 2 )

SIG 3 stack( Sod 3 , SEgty 3 SSxty3 ,SFrtY3 STwty3,Sid3) SIG 4 stack( Sod4 , SEgty4' SSxty4 ' SFrty4, STwtY4,Sid4) stack (Sod 67 5 gy ,S Sxty6 ' SFrty6 STwty6, Sid6 )

SIG5 stack(Sod5 SEy SSxtY, SFrty5, STwty5, Sid5) SIG 6 SIG7= stack( Sod7 , SEgty7'SSxtY7 ,SFrty ,STwtYSid7) SIG 8 := stack (Sod, ,SEgtys ,SSxty, SFrty8 , STwty', Sid8)

SIG9 stack( Sod 9 ,SEgty9 , SS xty9, SFrty9' STwty9' Sid,) SIG 1 0 stack(Sod o, SEgty'o, Ssxtyo, SFrty, o, STwtyo, Sido)

S IGl := stack (S odl, 'SEgty i , S Sxty, 1, SFrty, 1, STwty, i,3SidlI SIG 12 -stack(Sod2'SEgty t'SSXty,2'SFrty, 2 ' STwty 2' Sidt 2 )

SIG1 3 stack(Sod13, SEgty13' SSxtY(3, SFrty3, STwty 1 3 , Sid1 3) SIG 1 4 stack(Sod 14 SEgty4,

' SSxty,4'SFrty,4' STwty 1' Sid 1 4 )

SIG1 5 stack(Sod 15 SEgtY5,SSxty, 5 SFrty , STwtY,, Sid,5) SIG 1 6 stack(Sod1 6' SEgty 6'SSxty1 6 ' SFrty1 6 ' STwty16 Sid 16)

SIG 17 5 ~J 5 Wy SIG 18 stack (Sod 18 SEgty,8,

' SSXty, 8 ' Frty, 8 'STwty18,Sid,,)

stackSod 1' SEgty 17 ' S Sxtyl7'7 SFrtyj stack(Sodl7Ey'SXy 77' STwty, Sid7) 77'Si17 SIG 19 stack( Sod9 SEgtY, 9 , SxtY9,SFrtYl S 9, STwty 9 , Sid1 9 ) SIG2 0 :-- stack (Sod 20 ' SEgty 2 o' SSxty 2 o' SFrty2 o, STwty2 o, Sid 2 .)

Appendix IIPage

Appendix H Evaluation of PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 regress(Y,SIG1 ,3) ODRG 2 regress(Y,SIG 2 ,3)

ODRG 3 regress(Y,SIG3 ,3) ODRG 4 regress(Y, SIG 4 ,3)

ODRG 5 regress(Y, SIG 5 ,3) ODRG 6 regress(Y,SIG 6 ,3)

ODRG 7 regress(Y, SIG 7 ,3) ODRG 8 regress(Y,SIG 8 ,3)

ODRG 9 regress(Y,SIG 9 ,3) ODRGi 0 := regress(Y,SIG 10 ,3)

ODRG 1 1 regress(Y, SIG 1 1 ,3) ODRG 12 regress(Y,SIG 12 ,3)

ODRG 1 3 regress(Y,SIG 1 3 ,3) ODRG 1 4 regress(Y,SIG 1 4 ,3)

ODRGI 6 regress(Y,SIG 1 6 ,3)

ODRG 1 5 regress (Y,SIG 1 5 ,3)

ODRG 1 7 regress(Y,SIGI 7 ,3) ODRG 18 regress(Y,S1G 18 ,3)

ODRG 1 9 regress(Y,SIGI 9 ,3) ODRG 2 0 regress(Y, SIG 2 0 ,3)

Appendix II Page 10 of 31

Appendix 11 Evaluation of PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles a! Byron Unit 2 AM-2007-006 Stress Distribution in the tube. Stress influence coefficients obtainedfrom third orderpolynomial curve fit to the through wall stress distribution PrOPjength ULStrs.Dist - RLCntr - C0 - 0.5 Pro~ength = 0.445 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-11l1707-SC04 Model)

{NO INPUT Required) ettu RauNew Siv EFormnan r ltws [efeece Dro u g I (lFlawe 2 and 4)

Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb :=

0 1 2 The Table on the left "Jsb"consists of the cylinder and flaw mechanical 0 1.000 0.200 0.000 parametersas follows:

1 1.000 0.200 0.200 Column "0":-Contains the mean-radiusto thickness ratio (Ra, It) of the Cylinder 2 1.000 0.200 0.500 Column "1":-Contains the FlawAspect Ratio (a/c) 3 1.000 0.200 0.800 Column "2" :- Contains the Flaw Depth-to- Tube- Thickness ratio (a/t) 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 Appendix II Page 11 of 31

App, 14 1.000 1.000 1.000 IofPWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 Appendix II Page 12 of 31

51 10.000 0.400 0.200 of PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006

App, 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 74 300.000 1.000 1.000 The Table below "Sambi"contains the Flaw Influence coefficients as follows:

Column "0":-Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip)

Column "1" :- Contains the influence coefficients for LinearLoading at themaximum depth of the flaw ("a"-tip)

Column "2":- Contains the influence coefficients for QuadraticLoading at themaximum depth of the flaw ("a"-tip)

Column "3":-Contains the influence coefficients for Cubic Loading at the maximum depthof the flaw ("a"-tip)

Column "4":- Contains the influence coefficients for Uniform Loading at the surface point of the crack front ("c "-tip)

Column "5" :- Contains the influence coefficients for Linear Loading atthe surfacepoint of the crack front ("c"-tip)

Column "6":- Contains the influence coefficients for QuadraticLoading atthe surfacepoint of the crack front ("c "-tip)

Column "7" :- Contains the influence coefficients for Cubic Loadingatthe surfacepoint of the crack front ("c "-tip)

Appendix II Page 13 of 31

Appendix H Evaluation of PWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Sambi 0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 6 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 T8 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 *Apiiý 1IPage 1416131 0.242 0.097 0.051

Appendi) 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 AM-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix: II Page 15 ol 31~

Appendix 11 Evaluation of PWSCC Crack Growthofa postulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 In the declaratinsbelow, dummy variablesare defined in order to develop a continuous function for the variousinfluence coefficients.A continuous function can then be readily used inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysiswith a thirdorderpolynomial for Rm/t less than 4,0 anda second orderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters P, It ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb 'o is a column array containing the Rm /t ratio, which is also Column T0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W :=Jsb(O) X :=Jsb~i) Y :=Jsb(2) aU Sambi(O) aL= Sambi( 0 aQ Sambi(2 aC Sambi-(3) cU Sambi(4) cL: Sambi (5) cQ Saznbi(6 CC Sambi(7) n := 13 if Rt < 4.0 Order of polynomial selected based on R m t ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

FOu (W,XY) which is the standard nomenclature is Fu (R m /t, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (P.

/t, a/c. alt) that are defined within the loop based on the results from the previous iteration.

Appendix II Page 16 of 31

Appendix II Evaluationof PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "a-Tip"Coefficients "a-tip" Uniform Term MaU:= augment(W,X,Y) VaU:= aU RaU := regress(MaU, VaU, n) faU(W ,X,Y) := interp RaU, MaUVaU, X "a-tip" Linear Term MaL:= augment(W,X,Y) VaL := aL Ra=regress (MaL ,Va, n) faL(W,X,Y):= interp RaL,MaL,VaL, "a-tip" Quadratic Term (w)_~

MaQ:= augment(W,X,Y) VaQ:= aQ RaQ := regress(MaQ,VaQ,n) faQ(WX,Y): MaQ VaQ iXH

ý,Y)J "a-tip" Cubic Term MaC := augment(W,X,Y) VaC:= aC RaC := regress(MaC ,VaC,n) faC(WX Y : iterp[RaC, MaC 3VaC{ X~

lk(WXY "c" Tip Coefficients "c-tip" Uniform Term McU := augment(W,X,Y) VCU := cU RcU := regress (McU, VcU, n) fcu(W,X,Y): interp[RCUMCUVCU{,j1 Appendix IIPage 17 of 31

Appendix H Evaluationof PWSCC Crack Growthofa postulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "c-tip" Linear Term VCLL'j MCL:= augment(W,X,Y) VcL := CL RcL :=regress( MCL)VcL,n) fcL(W IX, Y) :

"c-tip" Quadratic Term WVQ{j McQ:= augment(W,X,Y) VCQ:= CQ RC =regress (MCQIVQ, n) fCQ (W, X,Y) :

"c-tip" Cubic Term McC:= augment(W,X,Y) VcC := Cc R~CC: regress (MCC, VcC,n) IfCC(W, X,Y):=iterp RCC, MCC cC, ~ X Appendix II Page 18 of 31

Appendix 11 Evaluation of PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive loop for Calculationof PWSCC Crack 6rowth as a function of Hot Operating Time CGRsambi :` j <--o0 ao <- C 0

co <--co NCBo <-- Cblk while j Ilim 004 ODRG1 3 if cj <CO ODRG 2 3 if Co < cj < Co + IncStrs.avg ODRG 3 if co + Incstrs.avg < Cj < Co + 2.InlcStrs.avg ODRG 43 if CO + 2lncStrs.avg <cj < C0 + 3.Incstrs.avg ODRG5 3 if Co + 32InCStrs.avg < cj < co+ 4-IncStrs.avg ODRG6 3 if CO+ 4-IncStrs.avg < Cj < Co + 5-Incstrs.avg ODRG7 3 if CO + 5IlncStrs.avg < Cj Co + 65Ilncstrs.avg ODRG 8 3 if CO + 6-Ilncstrs.avg < Cj co + 7-Incstrs.avg ODRG 9 3 if CO+ 7IlncStrs.avg <cj < co + 8-IncStrs.avg ODRG 10 3 if co + 8. Incstrs.avg < cj < CO + 9 lncstrs.avg ODRGll3 if co + 9"lncstrs.avg < cj 5 CO + I0-Ilncstrs.avg ODRG 12 , if co + 10. Incstrs.~<i& " Jtif j.Strs.avg

-on Unit 2 AM-2007-006 App pnn2RGI3 ODRG if CO + I I-lncstrs.avg < Cj Co + 2-IlncStrs.av g 13 ODRG if Co+ 12.Incstrs.avg < Cj < CO+ 13.InCStrs.av g 14 3 ODRG if CO+ 13.Ilncstrs.avg < Cj CO + 14.lncStrs.av g 15 3 ODRG if Co+ 14-lncstrs.avg < ci < Co+ 15.IncStrs.av ,g 16 3 ODRG if cO+ 15"IncStrs.avg < Cj <CO+ 16-IncStrs.av ,g 17 3 ODRG if C0 + 16,Ilncstrs.avg < Cj 5 CO + 17-InCStrs.av ,g 18 3 ODRG 1 3 if Co+ I7Tlncstrs.avg < cj < co+ 18-IlncStrs.av ,g 9

ODRG 2 0 3 otherwise ODRG 1 4 if cj < Co ODRG 2 4 if co < cj < CO + Incstrs.avg ODRG 3 4 if Co + Incstrs.avg < ci < Co + 2.InCstrs.avg ODRG44 if CO+ 2.IlncStrs.avg < Cj 5 Co + 3Inlcstrs.avg ODRG 5 4 if CO + 3- Incstrs.avg < cj < Co + 4 IlncStrs.avg ODRG64 if Co + 4- Ilcstrs.avg < Cj co C + 5.Incstrs.avg ODRG 7 4 if Co + 5-Ilcstrs.avg < cj <Co + 6.Incstrs.avg ODRG 8 4 if Co+ 6IlncStrs.avg < Cj CO+ 7"IncStrs.avg ODRG 9 4 if Co+ 7IlncStrs.avg < cj <co + 8,1nCStrs.avg ODRG 1 0 4 if CO + 8-Incstrs.avg < cj < Co+ 9- n1CStrs.avg Appendix II Page 20 of 31

• -onUnit 2 AM-2007-006 App ODRGI114 if Co + 9.-Incstrs. avg < cj <ý CO + 10. Incstrs. avg ODRG 124 if CO + 10"Incstrs.avg < ci < Co + I l-Incstrs.avg ODRG13 4 if CO + II.Incstrs.avg < cj < Co + 12-Ilncstrs.avg ODRG 144 if Co+ 12-1nCstrs.avg < cj < Co+ 13 IncStrs.avg ODRG 154 if Co + 13-lncstrs.avg < Cj < Co + 14-lncstrs.avg ODRG 164 if Co + 14.InCstrs.avg < cj < Co + 15-Incstrs.avg ODRG 174 if co + 15-Ilncstrs.avg < cj < co + 164IlncStrs.avg ODRG 1 84 if Co + 16"lncsttrs.avg < cj < CO + IT-Incstrs.avg ODRG 194 if Co + IT7-nCstrs.avg < cj < co + 18-IncStrs.avg ODRG20 4 otherwise CF2 <- ODRG15 if cj <!ýCo ODRG2 5 if CO < cj <! Co + lncstrs.avg ODRG35 if Co + lIncstrs.avg < Cj

< Co + 2.Ilncstrs.avg ODRG4 5 if co + 2-Incstrs.avg < cj <co + 3-Incstrs.avg ODRG55 if Co + 3-1lnCStrs.avg < Cj < Co + 4-Ilncstrs.avg ODRG65 if Co 4, Incstrs.avg < cj h +rIcstrs.savg co + 5 ODRG75 if Co + 5 Incstrs.avg < cj co + 6-Incstrs.avg ODRG85 if co + 6.1nCstrs.avg < Cj < Co + 7,lncstrs.avg ODrG 4 :c if, 0 +, Tr_ Appenkdij 0 +Pgi4f1af 31

App UJtA.95 t 1;CO 1-'1uCStrs.avg ' 'j - CO1 -r ICStrs.avg -on Unit 2 AM-2007-006 ODRG 10 5 if co+ 8-Incstrs.avg < cj < co+9.lncStrs.av*

ODRG11 5 if Co + 9. Incstrs.avg < ci < Co + 10- Incstrs.av 9 ODRG12 5 if Co + lo-Incstrs.avg < cj <O C+ 11.Incstrs.a vg ODRG13 5 if Co + 11-I ncs trs. avg < cj o+

C< 12.Incstrs.a vg ODRG14 5 if Co + 12-Inlcstrs.avg < cj <5Co + 13-Ilncstrs.a

.vg ODRG1 55 if CO+ 13-Ilncstrs.avg < Cj < Co+ 14IlncStrs.a vg ODRG 1 65 if CO+ 14Ilncstrs.avg < Cj < Co+ 15IlncStrs.a vg ODRG 1 75 if Co+ "-Ilncstrs.avg < Cj < Co+ 16-IlncStrs.a

.vg ODRG 1 85 if Co + 16-lncstrs.avg < Cj < Co + IT-lncStrs.a

.vg ODRG 1 9 5 if CO+ 17-InCstrs.avg < Cj < CO+ 18-InCstrs.avg ODRG 2 0 5 otherwise ODRG 1 6 if cj < Co ODRG 2 6 if Co < cj < Co + Incstrs.avg ODRG3 6 if Co + Incstrs.avg < cj 5 Co + 2.IlncStrs.avg ODRG 4 6 if Co+ 2.IncStrs.avg < Cj < Co + 3"lncstrs.avg ODRG5 6 if CO+ 3-lncStrs.avg < Cj < CO + 4.1lCStrs.avg ODRG6 6 if CO + 4-lncStrs.avg < cj < co + 5.lncStrs.avg ODRG7 , if CO + 5.lncStrs.avA#W$jS6 #P*'m*g§&ft%.avg

App 0 -on Unit 2 AM-2007-006 ODRG 8 6 if co + 6. lncStrs.avg < cj < Co + 7-Ilncstrs.avg ODRG 9 6 if Co+7-lnCstrs.avg < cj <_c+ I"-lnCStrs.avg ODRG 1 0 6 if co + 8-lncstrs.avg < cj < co + 9. lncstrs.avg ODRG1 1 6 if Co + 9-IncStrs.avg < cj < Co + 1O-Incstrs.avg ODRG 12 6 if Co + 10Ilncstrs.avg < cj < Co + ldflncstrs.avg ODRG 1 3 6 if Co + I fl.ncStrs.avg < cj 5 co + i2.Ilncstrs.avg ODRG 14 6 if Co+ 12"Incstrs.avg < cj 5 Co + 'i3.Icstrs.avg ODRG 1 5 6 if Co + 13Ilncstrs.avg < Cj < Co + 14"lncstrs.avg ODRG 1 6 6 if co + 14-Ilncstrs.avg < cj < Co + 15-Ilncstrs.avg ODRG 1 7 6 if Co + 15"Incstrs.avg < cj < Co + 16.lncstrs.avg ODRG 1 8 6 if co + 16-IlncStrs.avg < Cj < co + 17*Ilncstrs.avg ODRG 1 9 6 if Co + 17'IlncStrs. avg < cj < CO + 18Ilncstrs.avg ODRG 2 0 6 otherwise I aO + Cr 0.25 aj S) +2. - J 23

(.25"aj2 -t -+03 3 05a j)(

( o* _a t -aj ) 2

! .5 aj ')

t'.5

+-o+, +t- r t (71aj2 3

ý3 <"-°O + ° " . + F2"1(o.75-ajl (o.75oaj'f

-* n l'l O-T A,( -'b

App ApL j j \, t } ni2t

-onUnit 2 AM -2007-006

ý 4 (-- oCFO + Cy 1 "(-o j + 2(1 " .0

- ,- "a j --2 + *Y3(Y10-a 3 J70(io~ao X0<-- 0.0 xI,-- 0.25 x2 -- 0.5 x3 <-- 0.75 x4 -- 1.0 X <-- stack(x 0 ,xI,x 2 ,x 3 ,x 4 )

ST <-- stack(( 0 ,l ,'ý2,'ý3,'4)

RG -- regress(X, ST, 3) oo0 - RG 3 + Pint (y10 <- RG4 (72 0 -RG 5 Y3 0 RG6 aj cj A Tj t

Gauj <-- faU(Rt,ARj,ATj)

Gal <- faL(Rt,ARj,ATj)

Gaqj & faQ(Rt,ARj,ATj)

G, - f,,r(Rt,ARi, ATi') Appendix IIPage 24 Af31

AM-2007-006

-on Unit 2 App j Gcuj 4-- fcu(Rt, ARj, ATj)

Gclj <- fcL(Rt, ARj, ATj)

Gcqj <- fcQ(Rt,ARj,ATj)

Gccj <-- fcC(Rt, ARj, ATj) c !a

( aj, 1.65 Qj 1+<-- i cj > aj

.(C)1.65 1 + 1.464- otherwise Ka. "i fj auj + O10Galj + Y20"Gaqj + F30.Gaci)

C..5(ooo cu. + a ,o.Gclj + F20.Gcq + Y30.Gccj)

Katj<- Ka..1.099 Kyj <--- Kc.. 1.099 J

K ol 1--

9.0 if Ka *.9.0 IKa otherwise Kyj--- 9.0 if K7 j *9.0 K*/j otherwise

- 9.0)1.16 Da < CO.(Koj D- <--- ID.-CF;...C,.,Ci, if K-,, <Appndix ll Page 25 of 31

App 46J I 4j lunl um uj on Unit 2 AM-2007-006 4.10- 0 -CFinhr-Cblk otherwise D c <C Co0" -- K _9.0)1."16 Dcg < Dc. CFinhr.Cblk if Ky. < 80.0 4.10- l-CFinhr.Cblk otherwise outputj , 0 <-- j outputj, <*--aj OUtPUtj , 2 <-- Cj - Co outputj, 3 - Dagj outputj , 4- Dcgj OUtpUtj, 5 -- Kaj OUtPUtj, 6 <- Kcj NCBj outputj, 7 <-÷~

365.24 OUtPUtj, 8 - Gau.

J outputj, 9 <- Gal.

J outputj, 10 - Gaqj outputj, II <-- Gac.

outputj, 12 <- Gcu.

J OUtPUtj, 13 - Gcl.

J

,., ,-. . Appendix II Page 26 of 31

UULPULj , 14 -on Unit 2 AM-2007-006 App v- -c outputj, 15 <--G .

NCBj 365-24 OUtPUtj, 16*- 1.5- .98 j -- j+1 aj <-. aj- + DagjI Cj <- Cj-I + Dcgj_

aj4- It if aj_>t aj otherwise NCBj <-- NCBj-I + Cblk output k := o.. Ilim Prokength = 0.445 Appendix II Page 27 of 31

Appendix H Evaluation of PWSCC Crack Growthof a postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 C

0.5 0

0 I 2 3 4 5 6 7 8 9 10 11 12 Operating Time Ifuel cycles}

Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.445 inch. Thus the time available for the flaw growth by PWSCC is about 9.03 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix IIPage 28 of 31

Appendix II Evaluation of PWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction 0.6 0.5 U

0.4 0~

U 0.3 0

I.-

0.2 0.1 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Operating Time Ifuel cycles I Flaw growth in the depth direction, as a function of fuel cycles. The extension of the 'a-Tip' or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 9.05 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.28 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix II Page 29 of 31

Appendixll1 Evaluation of PWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Intensity Factors Cr L6

.27 0 1 2 3 4 5 6 7 8 9 10 11 12 Operating Time {fuel cycles)

-Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher WKvalue at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix II Page 30 of 31

Appendix H Evaluationof PWSCC Crack Growthofa postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 1.4 9',.0 0 05

- 1.2 _,

E 0.8 -The influence coefficients as a function of operating time is shown. The behavior for 4_4-the 'a-tip' shows the effect of the flaw 0.6 aspect ration for the initial flaw and early U- I growth. No erratic behavior of the influence coefficients is observed. When the flaw

.depth is close to the ID surface (>80%

depth) the influence coefficients for the

______ _____ a-Tip' rise rapidly.

0 2 4 6 8 10 12 Operating time (fuel cycles "a" - Tip -- Uniform "a" - Tip -- Linear "a" - Tip -- Quadratic

. a" - Tip -- Cubic c" - Tip -- Uniform c'- Tip -- Linear "c" - Tip -- Quadratic

..c" - Tip -- Cubic Appendix II Page 31 of 31

Appendix 1H Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Prinmry Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw Developed by: J. 5. Btihmadesam

References:

1) 'Stress Intensity factors for Part-throughSurface cracks," NASA TM- 111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion EngineeringCatc. C-7770-00-1, Rev.0, 'Byron/Braidwood CRDM PenetrationResidual Stress Evaluation.*

Byron Nuclear Station Unit 2 Reactor Vessel CRDM -"25.4" Degree Nozzle, "180"Degree Azimuth ("Uphill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed , as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 75th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is applied during the determinationof the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference I for External flaws (Tables 2 and 4).

2) The stress distributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to 0O).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5' below the weld bottom and extending to 0.5' above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL st,.Dit ) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Point) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the "Val' variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix III Page 1 of 31

Appendix H1 Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM -2007-006 CRDM~ength~evai : 2.46 CRDM Tube Length for Crack Growth Calculation, Use the length of the tube where the through wall stress distributions will be defined.

ULSrs.Dist := 2.46 Upper extent of the Stress bistribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint :=2 To place the flaw with respect to the reference point, the flaw tips or flaw center can be located as follows:

1) The Upper "c- tip" locatedat the reference point (Enter 1)

2) The Center of the flaw at the reference point (Enter 2)

3) The lower 'l- tip" located at the reference point (Enter 3).

Val:= 2 Input Data :-

1:= 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 12 Number of Hot Operating Years for Analysis Appendix III Page 2 of 31

Appendix 1I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 ilm := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

(Xc := 2.67-1 012 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 11 Tref := 617 Reference Temperature for normalizing Data Deg. F; (MRP-55 Rev. 1) od id id t 0 2 Rid:= t := Ro-Rid Rm:=Rid + Timopr:= Years*-365-24 Timopr Rm C~inh :=I.417-105 Cblk:= Prrbitk 1 2 Rt -=t Ilrn .= 1 50

_Qg I I C 0 1 :=e 1.103.10- 3 THead+459.67 Tref+459.67) Temperature Correction for Coefficient Alpha

-aOtc Cc= C0 1 75 th percentile MRP-55 Revision 1 Appendix III Page 3 of 31

Appendix III Evaluationof PWSCC CrackGrowth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input all availableNodal stress data in the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recordedon data sheet (inches)

Column "1 = ID Stress data at each Elevation (ksi)

Column "2"= 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress data at each Elevation (ksi)

Column "6" = OD Stress Data at each Elevation (ksi) 0.0 57.328 50.749 44.446 40.236 39.969 38.078 0.5 48.266 48.755 49.084 53.143 63.339 66.338 AllData 1.235 41.949 45.960 52.889 61.612 71.900 75.993 1.97 52.260 49.952 50.904 49.159 50.395 62.559 2.47 48.482 43.604 34.784 26.887 12.712 -5.385 AXLen :=AIIData(0) IDA11:= AlMatP) ODAI1:= AlIData(6)

Stress Distribution 100 70 IDAll 40 LAOD I 10

-20

-50 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix III Page 4 of 31

Appendix III Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Observing the stress distributionselect the region In the tableabove labeled DataAn,that represents the region of interest. This needs to be done especially for distributionsthathave a large compressive stressat the nozzle bottom and high tensile stressesat the J-weld location. Copy the selection in the above table, click on the "Data"statementbelow and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon)then insert the same to the right of the Mathcad Equals sign below (pastesymbol).

0.0 57.328 50.749 44.446 40.236 39.969 38.078 0.5 48.266 48.755 49.084 53.143 63.339 66.338 Data := 1.235 41.949 45.960 52.889 61.612 71.900 75.993 1.97 52.260 49.952 50.904 49.159 50.395 62.559 2.47 48.482 43.604 34.784 26.887 12.712 -5.385, AxI : Data(0) ID :=Data( I) Twty: Data(2) Frty :=Data (3)

Sxty := Data(4 Egty := Data(5) OD := Data(6)

RID := regress(Axl, ID, 3) RTwty regress (Axl, Twty, 3) RFrty regress(Axl, Frty, 3)

Rsxty := regress(Axl, Sxty, 3) REgty regress (Axi, Egty, 3) ROD regress(AxI,OD,3)

Flaw center Location Location above Nozzle Bottom FLCntr ;=

Appendix III Page 5 of 31

Appendix I1l Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 ULStrs.Dist - UTip UTip :" FLCntr + co 9ss.avg" 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locations for stress profiles LOCO:= FLCntr- 1 i:= I..N+3 Incri cO if i < 4 Incstrs.avg otherwise Loci : Loci- + Incri 3

SIDi : R~ '3+ RID 4*Loci + RID 5*(Loci)' + R~ D. (Loci) 2 3 STwtyi : RTty3 + RTwtY4.Loci + RTtY*.(Loci) + RTwty6' (Loci)

SFrtyi RFtY3 + RFrty* .Loci + RFrty*.(Locj) + I RFrty6*(Loci) 3 SSxtyi RS~tY + R ~y*Loci + RS~ty5 (Loci) 2 + IRSxty6*(Loci) 3 Appendix Ill Page 6 of 31

Appendix III Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 SEgtyi := REgty3 + REgtY4 Loci + REgty *(Loci) 2 + REgtY6 "(Loci) 3 2

SODi:= ROD3 + ROD 4Loci + ROD 5(Loci) + ROD 6 "(Loci)3 Input Data and Curve Fit results of data in the Crack Propagation Analysis region ID SIDi 40 0 0.5 1 1.5 2 2.5 Axl, Loci 100 I I I OD 50 SODi 0

I I I I

-50 0 0.5 I 1.5 2 2.5 Axl, Loci Appendix III Page 7 of 31

Appendix 1I Evaluation of PWSCC Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use In Fracture Mechanics Model j:= I.. N SIDJ+ SIDj+I + SIDj+2 if j= STwtyj + STwtyj+l + STwtyj+ 2 if j Sid. 3 STwtyj 3 J

Sidj (j+ 1) + SIDj+ 2 STwty-f (j + 1) + STwtyj+ 2 otherwise otherwise j+2 j+2 SFrtyj + SFrtyj+l + SFrtyj+2 i j SSxtyj + SSxtyj+i + SSxtyj+2 if j =

SFrtY : SS~~xty 3 3

SFrtyj- I"(j + I) + SFrtyj+2 SSxtyj 5 .(j + I) + SSXtYj+2 otherwise otnerwise j+2 j+2 SODj + SODj+1 + SODj+ 2 i =

SEgtyj + SEgtyj+ 1 + SEgtyj+ 2 if = Sod.

SEgtyj := 3 3 J Sodj -*(j + 1) + SODj+ 2 SEgtyj_,-(j + 1) + SEgtyj+ 2 j otherwise otherwise j+2 j+2 Elevaion-AveragiedHoop Stress Distributionfor OD Flaws (i.e. Stress distributionchanged from OD to §D)

U0 := 0.000 u1 := 0.20 U2 := 0.40 U3 := 0.60 U4 := 0.80 U5 := 1.00 Appendix III Page 8 of 31

Appen dix IH Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 A AM-2007-006 Y := stack(u 0 ,uIu 2 ,u 3 ,u 4 1 u 5 )

SIG 1 stack(Sod! , SEgty , SSxtyl, SFrty ,STwty , Sidl) SIG 2 stack(Sod 2Egty , 2 SSxty2, SFrty.,STWtY2' Sid2)

SIG 3 stack (Sod 3 ,SEgtySSXtY3 , SFrty3, STwtY3, Sid3) SIG 4 stack(Sod 4SEgty4'SSxtY4 SFrty4,STwty4,Sid4)

SIG 5 stack (Sod5 SEgty , SSxty', SFrty5, STwty5, Sids) SIG 6 stack (Sod, 6 SEgty6' SSxty6' SFrty 6 ' STwty6, S id6)

SIG 7 := stack(Sod7 SEgty7,SSxty 7 ' SFrty7 STwtY7, Sid) SIG 8 := stack( Sod 8 , SEgtYsSSxty8 , SFrty.,STwtY, Sid8 )

SIG 9 := stack( Sod9 , SEgty 9 , SSxty9 ,SFrty 9 , STwty 9 , Sid 9 ) SIG 1 0 stack( Sod 1o, SEgty 1 oSSxty1 o' SFrty1 o'STwty1 o'Sid1 o)

SIG 1 1 := stack(Sod i, SEgty, SSxty, I, SFrty i, ,STwtY, ,, Sid,') SIG 1 2 stack(Sod 1, SEgtty2 SXtY' SFy2' STwty12' Sid12)

SIG 13 stack(Sod ,13Egty,3' S Ssxty,3,SFry,3 , STty13 ,Sid,3) SloG 4 stack (Sod1 SEgty 1 4SXty l 4 ' SFrty 14 , STwty Sid 4)

SOG15 15 stack Sod1t, gy, ,S xty,, ,S ,5 wty,,Sid,,) sG6 tack/Sod6* ty S x S Swty,6

, Si y,(, 1 S IG17 s tac k So d1 'S ,y ,SSy ,, S*wt, 17S' i*S1 SIG 1-18 stack ( Sod 18 S' E g ty S SX tY' S Fy, , STw*y ,, , 18)

SI 9 "- stack*(*d*99'*xEgty 19 SXty19 Frty,9 '5 Twty 9 ' Sid*,9) SG 20 stack (sodo2 0 ' s 20 S XtY xgty 20 SFrty 20owyos

'osTwty 2 20 )

Appendix III Page 9 of 31

Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix IlII Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 regress(Y,SIG1 ,3) ODRG 2 := regress(Y,SIG 2 ,3)

ODRG 3 regress(Y, SIG3 , 3) ODRG 4 := regress(Y,SIG4 ,3)

ODRG 5 := regress(Y ,SIG 5 ,3) ODRG6 regress(Y, SIG 6 ,3)

ODRG 7 := regress(Y, SIG7 ,3) ODRG 8 regress(Y,SIG 8 ,3)

ODRG 9 := regress(Y,SIG9 ,3) ODRG 1 0 := regress(Y,SIG 1 0 ,3)

ODRG 1 1 regress(Y, SIG 1 1 ,3) ODRG 1 2 regress(Y,SIG 1 2 ,3)

ODRG 1 3 regress(Y,SIG1 3 ,3) ODRG 14 regress(Y, SIG 1 4 ,3)

ODRG 1 5 regress(Y,SIG 1 5 ,3) ODRG 1 6 regress(Y,SIG 1 6 ,3)

ODRG 1 7 regress(Y,SIG 1 7 ,3) ODRG 1 8 regress(Y,SIG 1 8 ,3)

ODRG 1 9 regress(Y, SIG1 9 ,3) ODRG2 0 regress(Y, SIG 2 0 , 3)

Appendix III Page 10 of 31

Appendix M1 Evaluation of PWSCC Crack Growth of Postulated Flaw in CROM Nozzles at Byron Unit 2 AM-200"/.Oft Stress Distribution in the tube. Stress influence coefficients obtained from thirdorderpolynomial curve fit to the through wall stress distribution Flaw Propagation of top tip to above J-Weld top PrOPkength := ULStrs.Dist - FLCntr - Co - 0.5 PrOPLength = 0.655 Data Files for Flaw Shape Factors from NASA (NASA-TM-i 11 707-SC04 Model)

{NO INPUT Required) euaiu Nablewa fSoir Foxrmn Sfluionwto efePrtece I Flaws 2 aCnder Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb :=

0 1 2 0 1.000 0.200 0.000 The Table on the left "Jsb"consists of the cylinder and flaw mechanical 1 1.000 0.200 0.200 parametersas follows:

2 1.000 0.200 0.500 Column "0" -- Contains the mean-radiusto thickness ratio (Rm /t) of the Cylinder 3 1.000 0.200 0.800 Column "1" :- Contains the Flaw Aspect Ratio (a/c) 4 1.000 0.200 1.000 Column "2":- Contains the Flaw Depth-to-Tube- Thickness ratio(a/t) 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 Appendix III Page 11 of 31

Appendix 15 2.000 0.200 0.000 AC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 51 10.000 0.400 0.200 Appendix III Page 12 of 31

Appendix Appendix

-I 4 ~ ~41 ~ ~~~~~~~~~~

MNzleatBrnUt2 PostulatedFlaw in CRDM

'f~rr.~~k[.;mwtfntPotltdFainC Nozzles at Byron Unit 2 M20-6 AM-2007-006 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 74 300.000 1.000 1.000 The Table below "Sambi"contains the Flaw Influence coefficients as follows:

Column "0" :- Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("ý-tiq)

Column "1":- Contains the influence coefficients for Linear Loading at themaximum depth of the flaw ("a"-tip)

Column "2":- Contains the Influence coefficients for Quadratic Loading at themaximum depth of the flaw ("a" -tip)

Column "3":- Contains the influence coefficients for Cubic Loadingat the maximum depthof the flaw ("a"-tip)

Column "4" :- Contains the influence coefficients for Uniform Loading at the surface point of the crack front (icp-t)p)

Column "5":-Contains the influence coefficients for Linear Loading atthe surfacepoint of the crack front ("c"-tip)

Column "6":- Contains the influence coefficients for Quadratic Loading at the surface point of the crack front ("c"tip)

Column "7":- Contains the influence coefficients for Cubic Loadingatthe surface pointof the crack front ("c'-tip)

Appendix III Page 13 of 31

Appendix II Evaluation of PWSCC Crack Growth at Postulated Flaw in CRDM Nozzles at Byron Unit 2AM20-6 AM-2007-006 Sambi 0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.4861 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 Appe"QQI Page l4b#§' 0.242 0.097 0.051

Appendix I 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 AM-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 381 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1,747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix II Page 1503of3

Appendix III Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 In the declarationsbelow, dummy variablesare defined in order to develop a continuous function for the various influence coefficients. A continuous function can then be readily usedinside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysiswith a thirdorderpolynomial for Rm /t less than 4.0 and a second orderpolynomial for the higher ratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters Rm It ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb ,0, is a column array containing the Rm /t ratio, which is also Column "0"in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W :=Jsb(o) X :=Jsb(') Y :=Jsb(2) au Sambi(o> aL: Saxnbi( I) aQ Sambi(2) ac :=Sambi(3)

Sambi<4) CQ Sambi(6) Cc Sambi(7) cu CC= Sambi(5) n := 13 if Rt 5 4.0 Order of polynomial selected based on R m/t ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

Fau (W,X,Y) which is the standard nomenclature is Fou (R m /t, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (lr

/t, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix III Page 16 of 31

Appendix MI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "a-Tip" Coefficients "a-tip" Uniform Term MaU:= augment(W,X,Y) VaU := aU RaU := regress(MaU,VaU,n) faU(W,X,Y) :=interp[RaUMaUVaU{ Xj "a-tip" Linear Term MaL:= augment(W,X,Y) VaL:= aL Ra=regress (ML, VL, n) faLWXY):=interp RaL, MaL, VaL{X]

"a-tip" Quadratic Term MaQ := augment(W,X,Y) VaQ :=aQ RaQ :=regress (MaQ, VaQ, n) faQ (W,X,Y) : "VaQ{Xj]

"a-tip" Cubic Term MaC := augment(W,X,Y) VaC:= aC faC(W, X, Y) := interp RaC, MaC ,VaC, RaC := regress (MaC, VaC, n)

ýIY I_

"c" Tip Coefficients "c-tip" Uniform Term McU:= augment(W,X,Y) VC=Cu RcU : regress (MCU,VCU,n) fcU(W XY):=interp RCUIMCUIVCU{IXj Appendix III Page 17 of 31

Appendix H1 Evaluationof PWSCC Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit2 AM-2007-006 "c-tip" Linear Term (W f McL:= augment(W,X,Y) VCL:- CL R& :Lregress( McL,VcL,n) fcL(W,X,Y) := VcL, X

ý,Y.,

"c-tip" Quadratic Term (w )1 6eQ augment(W,X,Y)

McQ:= VCQ := CQ RCQ :=regress (MCQ 2VCQ Pn) fcQ (W X,Y) : ,McQ, VcQ jx

ýIY "c-tip" Cubic Term McC:= augment(W,X,Y) VC:Ccc R~cC: regress ( Mc,V~C,n) f~c(W,X,Y) :=interp{RcCC M~CCv , X Appendix III Page 18 of 31

Appenidix MI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculation of PWSCC Crack Growth as a function of Hot Operating Time CGRsb j <---0 ao <-- a0 CO <-- CQ NCBo < Cblk while j < Ilim ao<-- ODRG13 if Cj < CO ODRG 2 3 if CO < cj <CO + lncstrs.avg ODRG 3 3 if CO + Ilncstrs.avg < Cj 5 CO + 2. lncstrs.avg ODRG 4 3 if CO+ 2-lncStrs.avg < cj* CO+ 3-lncstrs.avg ODRG 5 3 if CO+ 3.Incstrs.avg < cj CO+ 4-lncstrs.avg ODRG 6 3 if Co + 4-lncstrs.avg < cj < Co + 5-lncstrs.avg ODRG 7 3 if Co + 5. *ICStrs.avg < cj < CO+ 6.lncstrs.avg ODRG 8 3 if Co + 6-lncStrs.avg < Cj < CO + 7-lncstrs.avg ODRG 9 3 if CO+ 7.Incstrs.avg < Cj <Co+ 8"lncstrs.avg ODRGI 0 3 if Co + 8. lncstrs.avg < cj < CO + 9. lncStrs.avg ODRG 1 1 3 if CO + 9-Ilncstrs.avg < cj <CO+ 10.lnCStrs.avg ODRG 1 2 , if Co + to. lncstrs.m* ,16dIWib,-!d ,6trs.avg

lyron Unit 2 AM-2007-006 App ODRG 1 3 3 if Co + 11 I.IcStrs.avg < Cj cO + 12. IC*Strs.avg ODRG 14 3 if Co+ 12-Ilncstrs.avg < Cj CO + !3.InCstrs.avg ODRG 1 5 3 if Co + 13-Incstrs.avg < Cj CO + 14-InCstrs.avg ODRG 1 6 3 if co + 14-Icstrs.avg < C. co + 15-InCstrs.avg Co + 16. Incstrs.avg ODRG 1 7 3 if co + 15-lncstrs.avg < Cj ODRG 1 8 3 if co + 16-IncStrs.avg < C. Co + 17I lncstrs.avg ODRG 1 9 3 if co + 17"lncStrs.avg < C. Co + 18.Ilncstrs.avg ODRG 2 0 3 otherwise F1 -- ODRG 14 if cj <-Co ODRG 2 4 if Co < cj < co + Incstrs.avg ODRG 3 4 if Co + Incstrs.avg < cj < Co + 2. 1nCstrs.avg ODRG 4 4 if Co + 2 Ilncstrs.avg < Cj < CO + 3 Ilncstrs.avg ODRG 5 4 if co + 3. Incstrs.avg < Cj < CO + 4.Ilncstrs.avg ODRG 6 4 if CO + 4fInCstrs.avg < Cj < Co + 5-InCstrs.avg ODRG 7 4 if Co + 5. InCstrs.avg < Cj < CO+66lncstrs.avg ODRG 8 4 if CO + 6, lncStrs.avg < Cj CO + 7 Ilncstrs.avg ODRG 9 4 if co + 7. IncStrs.avg < cj Co + 8 Ilncstrs.avg ODRG 1 0 4 if co + 8.IlncStrs.avg < cj <Co + 9. Incstrs.avg Appendix III Page 20 of 31

App lyron Unit 2 AM-2007-006 ODRG11 4 if co + 9InCstrs.avg < C O+ I lncstrs.avg ODRG 1 24 i Co + 10-IncStrs.avg < cj < CO + 11"Incstrs.avg ODRG 1 34 if Co+ 1-Ilncstrs.avg < cj < Co+ 12Ilncstrs.avg ODRG1 44 if Co+ 12-Incstrs.avg < Cj < Co+ 13Ilncstrs.avg ODRG 15 4 if Co + 13-Ilncstrs.avg < cj <CO + 14.Ilncstrs.avg ODRG16 4 if Co+ 14.Incstrs.avg < cj < c 0 + 15.lncstrs.avg ODRG174 if Co + l.I5lncstrs.avg < Cj < Co + 16.lnCstrs.avg ODRG184 if co + 16. lncstrs.avg < cj Co + IT7lncstrs.avg ODRG194 if Co+ 1.Ifncstrs.avg < cj < C+ 18 Ilncstrs.avg ODRG 20 4 otherwise CY2 <-- ODRG15 if cj <ý co ODRG25 if co < cI < cosa + Incstrs.avg ODRG35 if Co + Ilncstrs.avg < Cj_< Co+ 2. lncstrs.avg ODRG4 5 if Co + 2. Incstrs.avg < cj !5 co + 3-Incstrs.avg ODRG 55 if co + 3-lncstrs.avg < cj <5 Co + 4. Incstrs.avg ODRG65 if co + 4-Incstrs.avg < c < co + 5tIncstrs.avg ODRG75 if Co+ 5.ncstrs.avg < +cj co+ 6. ncstrs.avg ODRG8 5 if co + 6-IlncStrs.avg < Cj co C + 7-Ilncstrs.avg r GTN 6 -fc C ,+__F-trAppendi IjII P4g 0 5?Iof 31

Iyron Unit 2 AM-2007-006 App uuxkj9 5 11 co`1- -H'cStrs.avg -. cj ý- co -r 5"ut;Strs.avg ODRGI0 5 if co + 8' lncstrs.avg <cj !< co + 9-Incstrs.avg ODRGll15 if CO+ 9-lncstrs.avg <cj !5 Co+ lO-lncstrs.avg ODRG12 5 if co+ 10-InCstrs.avg < co + 1 *lncstrs.avg ODRG 1 35 if Co+ 1.IlncStrs.avg < cj < C+ 12-+Incstrs.avg ODRG14 5 if co + 12.Ilncstrs.avg < cj <5 Co + 13-Ilncstrs.avg ODRG 1 55 if co + 13-lncstrs.avg < Cj < Co + 14-OIncstrs.avg ODRG165 if co + 14-lncstrs.avg < ci < co + 15-Incstrs.avg ODRG175 if co + 15- Incstrs.avg < cj <- co + 16-Incstrs.avg ODRG 1 85 if Co + 16-IncStrs.avg < cj < Co + I[7Incstrs.avg ODRG 1 95 if co + 1T-InCstrs.avg < cj < co + 18Ilncstrs.avg ODRG2056 otherwise ODRG1 6 if cj < co ODRG26 if co < cj <5 co + Incstrs.avg ODRG36 if CO + Ilncstrs.avg < cj < Co

+ 2-1InCstrs.avg ODRG46 if co + 2 IlncStrs.avg < cj < Co + I.Incstrs.avg ODRG5 6 if Co + 3-1 nCstrs.avg < Cj< CO+ 4 IncStrs.avg ODRG66 if Co + 4- Ilncstrs.avg < cj < co + 5. Incstrs.avg ODRG71 if Co + 5-Incstrs.avgp <C 0+l 8Lf'iqgstrs.avgz

App lyron Unit 2 AM-2007-006 ODRG 8 6 if Co + 6-Incstrs.avg < cj < co + 7Ilncstrs.avg ODRG 9 6 if Co + 7-lncStrs.avg < cj < Co + 8-lncstrs.avg ODRG 1 0 6 if co+ 8.lnCStrs.avg < Cj < Co+ 9-1nCStrs.avg ODRG 1 1 6 if CO+ 9-lncStrs.avg < cj co + 1o-Incstrs.avg ODRG 12 6 if Co + 10.IfncStrs.avg < cj <co + I lncStrs. avg ODRG 1 3 6 if cO+ 11'Incstrs.avg < Ci Co+ 12lncstrs. avg ODRG 14 6 if co+ 12"flcStrs.avg <cj < co+ 13-InCstrs.avg ODRG 1 5 if Co+ 13.lncstrs.avg < Cj < Co+ 14.lncstrs.avg

.R 6

ODRG if co+ 14-1nCStrs.avg < cj < Co+ 15-IlncStrs.avg 16 ODRG if co+ 15-lnCstrs.avg < cj < Co+ 16.lncstrs.avg 1786 ODRG 1 6 if Co + 16.1nCstrs.avg < cj 5 co + I7-lncstrs.avg 8

if Co+ 17.Incstrs.avg < Cj < Co + 18-lncstrs.avg ODRG 19 6 ODRG2 0 6 otherwise 40 CFO0 3

O.-25.aij + 2.O2 *aj (02 i

+ (O..a (0.0a (2 3~

t2O+11+ (y2* t + + Y3- t..a

+ y2 " +2--Y3 " 30 42 + Or a 2075 f 75-ajl (Y + (Y (O.75-ajj I + e-of 31 12-'--*p-ng*i-'ag-

\p Irj \U j L n 2 lyron Unit AM-2007-006 App Go+ Yo, (4 aj a- + ( )3 t~~ ~ +)Y2 XO <.- 0.0 x4 <-- 0.25 x2 <- 0.5 x3 <- 0.75 x4 (-- 1.0 X *-- stack(x 0 , x 1 , x2 , x 3 , x 4 )

ST <-- stack(* 0 ,*l ',2,'3,44)

RG -- regress(X, ST, 3) aoo -- RG3 + Pint cy 10 -- RG4 Y2 0 -- RG 5 Y30 <- RG 6 aj ARj <--

cj aj ATj <--

t Gau"i<- faU(Rt,ARj,ATj)

Gal J <-faL(Rt, ARj, ATj)

Gaqj --faQ(Rt,ARj,ATj)

G,, <- f,,r(R,,ARi,ATi Appendix III Page 24 of 31

-.. \ L lyron Unit 2 AM-2007-006 Aplp J I-Gcu <-- fcU(Rt,ARj,ATj)

Gc l- fcL(Rt,ARj, ATj)

Gcqj - fcQ(Rt, ARj, ATJ)

Gccj <-- fcC(Rt,ARj,ATj)

(a. 1.65 Qj < I+ 1.464-+_ if cj aj

! 'j) 165 I +/'rt1.464 c6 otherwise

~a,'X

--j)J (00"Gau j,1. GG K aj

• u0 + +(o 1a Ga l + 0 Y2 a c'

- a q j + o3 0 .G K c *- --jJ) "(aOO0 Gcu j+ Oy 10 G clj+ y20 *G cqj + y30 "G cc j K . -- a *K 1.099 K Kc.J

-(-- 1.099 K a<. 9.0 if Ka <9.0 J J K a. otherwise J

K--9.0 if K7 *59.o K, j otherwise Da - Co.(Kaj -- 9.0) 1,16 I D-. <- I D- CF:-..-Cmi, if K_,. <Ap*ndix III Page 25 of 31

dLIJJHULI lyron Unit 2 A.M-2007-006 ApF UM?. 1.1

4. - '°.CFinhr-Cblk otherwise D cj <-- Co.(K j -9.0)1 ".16 Dcgj <--- Dcj 'CFinhr'Cblk if Ky < 80.0 4 o-'l.CFijnhr-Cblk otherwise outputj, 0 <-- j outputj, I <-- aj outputj, 2 <-- Cj - Co OUtPUtj, 3 <-- Dag.

OUtPUtj , 4 <- Dcgj outputj, 5 <-- Kaj OUtpUtj , 6 <-- Kci NCBj OUtPUtj , 7 -- 3652-outputj, 8 (-- Gauj outputj, 9 <- G al outputj, 10 <-- Gaqj outputj, II G ac.

J OUtPUtj, 12 -Gcu J

OUtPUtj, 13 -- Gcl.

J

• ,,,.,,. I'_Appendix Ill Page 26 of 31

App Vut Futj, 14 ' cqj lyron Unit 2 AM-2007-006 outputj, 15 -- Gcc.

NCBj outputj, 16 <'-365.24

-. -.98 1.5 -9 j <--j+ I aj <--aj-t + Dagj_I Cj (- CjI + Dcgj_

ajE-- It if aj t aj otherwise NCBj <-- NCBjI + Cblk output k :=* o..im PrOPTJeQgth = 0.655 Appendix III Page 27 of 31

Appendix 1H Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 0.5 0

LI-O- 5.5 6 6.5 7 0 0.5 I 1.5 2 2.5 3 3.5 4 4.5 5 Operating Time I fuel cycles I Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.655 inch. Thus the time available for the flaw growth by PWSCC is about 6.06 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix III Page 28 of 31

Appendix III Evaluationof PWSCC CrackGrowth of PostulatedRaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction tQ 0

0 0.5 I 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Operating Time (fuel cycles )

Flaw growth in the depth direction, as a function of fuel cycles. The extension of the 'a-Tip' or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 6.06 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.282 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix III Page 29 of 31

Appendix 1I Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Intensity Factors U

C 0~

U, 0

U U,

C C

U, U,

U O L 0 I 2 3 4 5 6 7 Operating Time {fuel cyclesi Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher "K' value at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix III Page 30 of 31

Appendix lIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzies at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 1.4

-1.2-1 0 1

0 0.8 The influence coefficients as a function of operating time is shown. The behavior for 0 0.6 _the "a-tip" shows the effect of the flaw U aspect ration for the initial flaw and early growth. In the time period of interest (6.06

= 0.4 _fuel cycles), no erratic behavior of the influence coefficients is observed.

0.2 _ _ _

0 I 2 3 4 5 6 7 Operating time lfuel cycles}

"a" - Tip -- Uniform

..... a" - Tip -- Linear

---

a" - Tip -- Quadratic "a" - Tip -- Cubic c" - Tip -- Uniform "c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Appendix III Page 31 of 31

Appendix IV Evaluationof PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit2 AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw beveloped by: 3. S. Brihmadesam

References:

1) "StressIntensity factors for Part-throughSurface cracks," NASA TM-111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion Engineering Calc. C-7770-00-1, Rev.0, "Byron/BraidwoodCRDM PenetrationResidual Stress Evaluation."

Byron Nuclear Station Unit 2 Reactor Vessel CRDM -"42.8" Degree Nozzle, "0" Degree Azimuth ("Downhill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed, as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 7 5 th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is appliedduring the determination of the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference I for Eternalflaws (Tables 2 and 4).

2) The stress distributionis from the 0D to the ID (whereas the stress distributionfrom Reference 3 is from ID to OD).

These differences arenoted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5" below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL st,.Dit) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Point ) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the "Var variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter, Appendix IV Page I of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 CRDMIengfn.eval 2.16 CROM Tube Length for Crack 6rowth Calculation, Use the length of the tube where the through wall stress distributions will be defined.

ULStrs.Dist := 2.16 Upper extent of the Stress Distribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint :=2 To place the flaw with respect to the reference point, the flaw tips or flaw 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 '1:- tip" located at the reference point (Enter 3).

Val := 2 Input Data :-

1:= 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 24 Number of Hot Operating Years for Analysis Appendix IV Page 2 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 llim:= 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

aoc := 2.67 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg ý= 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 1)

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 1) od id id t Rid:= t:= Ro-Rid R  :=Rid + Timopr := Years.365"24 0 2 M id+2 Timopr hjim Rm cFinhr := 1.417- 10, Cbl k = - i Pnflblk 15 2 Rt := t Temperature Correction for Coefficient Alpha 1.103. 10-3o ead+459.67 Tref+459.67 cX0c CO:= C 0 1 75 th percentile MRP-55 Revision 1 Appendix IV Page 3 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input all availableNodal stress data in the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recordedon datasheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5"= 80% Thickness Stress data at each Elevation (ksi)

Column "6"= OD Stress Data at each Elevation (ksi) 0.0 25.077 24.310 22.406 22.333 21.23 17.403')

0.5 32.344 38.976 47.2.18 58.184 73.827 93.625 AllData 1.08 31.291 35.811 43.669 48.323 50.278 53.147 1.66 51.15 52.895 54.793 57.58 52.053 18.002 2.16 52.974 49.828 47.349 46.170 46.703 34.672)

IDA11,:= AllData0l)

AXLen:= AllData(O) ODAI1 := AllData(6)

Stress Distribution

.'_ DAII rODAI All L

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 AXI~en Axial ht. - for Analysis [inch]

Appendix IV Page 4 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Observingthe stress distributionselect the region in the table above labeled DataAll that representsthe region of interest. This needs to be done especiallyfor distributionsthathave a large compressive stress at the nozzle bottom and high tensile stressesat the J-weld location. Copy the selection in the above table, click on the "Data"statement below and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon)then insert the same to the rightof the Mathcad Equals sign below (pastesymbol).

0.0 25.077 24.310 22.406 22.333 21.23 17.403" 0.5 32.344 38.976 47.218 58.184 73.827 93.625 Data := 1.08 31.291 35.811 43.669 48.323 50.278 53.147 1.66 51.15 52.895 54.793 57.58 52.053 18.002 12.16 52.974 49.828 47.349 46.170 46.703 34.672 Axi := Data(0) ID := Data(1) Twty:= Data(2) Frty := Data(3)

Sxty := Data(4) Egty := Data(5) OD := Data(6)

RID := regress(Axl, ID, 3) RTwty:= regress(Axl, Twty, 3) RFrty regress(Axl, Frty, 3)

RSxty := regress(Axl,Sxty,3) REgty := regress(Axl, Egty, 3) ROD regress(Axl,OD, 3)

FLCntr := RefPoint - co if Val = Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise Appendix IV Page 5 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 ULStrs.Dist - UTip UTip :- FLcntr + co IncStrs.avg := 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locationsfor stress profiles L~oco : FLCntr -l i : I.. N +3 Incri:= cO if i< 4 Incstrs.avg otherwise Loci = Loci- + Incri SIDi : RID3+RID4*Loci + RID (Loci)' + RID (Loci)'

STwtyi : RTty3 + RTty*.Loci + RTtY5 .(Loci) 2 + RTwty.-(Loci) 3 SFrtyi RFtY3 +RFrty.Loci + RFtY5.(Loci), +[IRFrty.*(Loci) 31 SSxtyi R~ty + RSxty -Loci + RSxty (LoCi) 2 +[IR SXtY 6 '(LOC) 31 Appendix IV Page 6 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 AM-2007-006 SEgtyi := REgtY3 + REgtY4 Loci + REgty 5 "(Loci)2 + REgtY6"(LoCi) 3 SODi:= ROD3 + ROD4-Lc + ROD5 (Loci)2 + ROD 6(Loci),

Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 I ..................

ID 40 SIDi

. .............. I.

20-0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 2 2.2 AxI, Loci 100 OD 50 SODi I I I I I I I II II II I I I I I I I U-0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Axi, Loci Appendix IV Page 7 of 31

Appendix IV Evaluationof PWSCC Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j:= I..N SIDj + SIDj+1 + SIDj+2 if STwtyi :

idj = 3 ST~y STwtyj + STwtyj+l 3 + STwtyj+ 2 ii j STwtyj-- (j , + 1) + STwtyj+ 2 Sidi- .(j + i) + SIDj+ 2 ji otherwise otherwise j+2 j+2 SSxtyj + SSxtyj+i + SSxtyj+ 2 if j =

SSFrtyj "- 3 + SFrtyj+ 2 if SFrtyj + SFrtyj+i

"- = SSxty.-'-

3 SFrtyj- *(j + 1) + SFrtyj+ 2 Ssxtyj.l.(i + 1) + SSXtYj+2 j otherwise UUIer W1i j+2 j+2 SODj + SODj+! + SODj+ 2 if j SEgtyj + SEgtyj+ 1 + SEgtyj+2 if j = Sodj :=

SEgtyj := 3 3

Sodj- I (j + i) + SOD j+2 SEgtyj_. (j + I) + SEgtyj+ 2 j+2 otherwise otherwise j+2 Oevlle~ n-Averaged H~oop Stress D~iseributionf~or OD ROaWS (I.e. Stress distributio~n chaniged f~rom ODU to #D,)

U0 "= 0.000 U1 := 0.20 U2 := 0.40 U3 := 0.60 U4 := 0.80 u5 := 1.00 Appendix IV Page 8 of 31

Appe ndix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Y := stack(u 0 ,uP ,u 2 ,u 3 ,u 4 ,u 5 )

SIG1 stack(Sod, SEgty ,SSxty ,SFrty ,STwtyI, Sid) SIG 2 stack(Sod2, S Egty2 Ssxty2 SFry'2, STwty 2 , Sid2)

SIG 3 stack(Sod3 SEgtY3, SSxty3, SFrty3, STwty3, Sid3) SIG4 stack( Sod 4 , SEgty4, SSxty4, SFrty4 , STwty4, Sid 4)

SIG 5 stack(Sods, SEgty 5 ' SSxty5, SFrty5, STwty5, Sid5) SIG 6 stack( Sod 6 , SEgty6 SSxtY SFrty 6 , STwty6, Sid 6)

SIG 7 stack(Sod7, SEgtY7 ' SSxty7 ,SFrtY7 , STwty 7 ,Sid7 ) SIG 8 stack(Sod 8 , SEgty8 , SSxty8, SFrty8, STwty,, Sid.)

SIG 9 := stack(Sod9, SEgty9, SSxty9, SFrtY9, STwtY, S id9)

SIG 1 0 stack(Sodo,0 SEgtyio, SSxtyloS'SFrtylo'STwtylo'Sidlo)

SIG,, st1ackSodl, y 1xty, ry,,,Swy,lSid,)G 12 (

stack SodSEgty x , ,xSFrty' Twty 2 'id 2)

SIG 1 3 stack(Sod13' SEgtY 13)S, 3 STwtY, 3 Sid13) SIG 14 stack(Sod14, SEgty '4,SSxtYI4,SFrty14' STwtY14' Sid14)

SIG 1 5  :=

stack(Sod 15, SEgtY, SSXty,5,SFrty, 5 STwty5, Sid,5) SIG16 1 ..=~Sd sc~o stack( Sod61 -gtY, S S 6 'SxtY

, 1 6 ' SrtYt

,S 6 ' STwtYl6Sidl61 SiG 17 stack(Sod,7'SEgt7y,7*Sxrty , 7 S*yy 1,Sid17) SoG 18 sck(oSod SEgy 8'SSXty,8 SFrty, 8 *Twty,, Sid,)

SIG19 :stackSod9 SEgtY9, SSxtY, SFrtYl9, STwty.9, Sid.9 SIG 2 0 stack.S o d SEgty 20 , , SFrty20 , STwtY20, Sid20 Appendix IV Page 9 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 regress(Y,SIG1 ,3) ODRG 2 := regress(Y, SIG 2 ,3)

ODRG3 regress(Y,SIG 3 ,3) .ODRG 4 := regress(Y,SIG 4 ,3)

ODRG5 regress(Y, SIG 5 ,3) ODRGI6 regress(Y,SIG 6 ,3)

ODRG7 regress(Y, SIG7 ,3) ODRG8 regress(Y,S1G 8 ,3)

ODRG 9 := regress(Y,SIG 9 ,3) ODRG 1 0 regress(Y,SIG 10 ,3)

ODRGl regress(Y,SIG 1 1 ,3) ODRG 12 regress(Y,SIG 12 ,3)

ODRG 13 regress(Y,SIGl 3 ,3) ODRG 1 4 regress(Y,SIGl 4 ,3)

ODRG 15 regress(Y,SIG 15 ,3) ODRG 16 regress(Y,SIG 16 ,3)

ODRG 17 regress(Y,SIG 17 ,3) ODRG 18 regress(Y,SIG 18 ,3)

ODRG 19 := regress(Y,SIG 19 ,3) ODRG 2 0 regress( Y,SIG20 ,3)

Appendix IV Page 10 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM -2007 -006 Stress Distribution in the tube. Stress influence coefficients obtained from third orderpolynomial curve fit to the through wall stress distribution PrOPLength :- ULStrs.Dist - FLCntr - CO- 0.5 Prokpngt = 0,505 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-111707-SC04 Model)

(NO INPUT Required)

Data RaWuN es oar Firman flaws Iof ReDPartrocu 1 (wallF 2 alnde r Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw In Cylinder Jsb :=

0 1 2 The Table on the left "J7sb" consists of the cylinder and flaw mechanical 0 1.000 0.200 0.000 parametersas follows:

1 1.000 0.200 0.200 Column "0":-Contains the mean-radiusto thickness ratio (Rm It) of the Cylinder 2 1.000 0.200 0.500 Column "1":-Contains the Flaw Aspect Ratio (a/c) 3 1.000 0.200 0.800 Column "2":-Contains the Flaw Depth-to- Tube- Thickness ratio(a/t) 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 Appendix IV Page 11 of 31

Appendix I 15 2.000 0.200 0.000 'Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 AM-2007-006 16 2.000 0.200 0.200 17 2.000 0.200 0.500 1i 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000

-501- 10.000 0.400 0.200 Appendix IV Page 12 of 31

1: f.'rark Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix I 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 0.500 731 300.000 1.000 0.800 74 300,0007 1.0001 1.000 The Table below "Sambi"contains the Flaw Influence coefficients as follows.-

Column "0" :- Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip)

Column "I":- Contains the influence coefficients for Linear Loading at themaximum depth of the flaw ("a"-tip)

Column "2" :- Contains the influence coefficients for QuadraticLoading at themaximum depth of the flaw (`"a-tip)

Column "3":-Contains the influence coefficients for Cubic Loadingat the maximum depthof the flaw ("a"-tip)

Column "4":-Contains the influence coefficients for Uniform Loading at the surface point of the crack front ("c"-tip)

Column "5" :- Contains the influence coefficients for Linear Loadingatthe surfacepoint of the crack front ("c"-tip)

Column "6" :- Contains the influence coefficients for QuadraticLoadingatthe surfacepoint of the crack front ("c"-tip)

Column "7" :- Contains the influence coefficients for Cubic Loading atthe surfacepoint of the crack front ("c"-tip)

Appendix IV Page 13 of 31

Appendix IV Evaluation ot PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 M2N740 AM-2007-006 Sambi 0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.02 1 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.2931 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0,327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 .0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 251 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 301 1.009 0.65 0.5071 0.427 0.589 0.073 0.0181 0.006 311 1.1621 0.691 0.5241 0.4341 0.612 0.08 0.0231 0.01 321 1.641 0.861 0.6131 0.4881 0.7861 0.134 0.0491 0.025 33 2.51 1.178 0.782 1Appen&*W ýage 14 AS@ 0.242 0.097 0.051

34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 AM-2007-006 Appendix 1I, 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 471 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix IV age 15o3

Appendix 1V Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 In the declarationsbelow, dummy variablesare defined in order to develop a continuous function for the variousinfluence coefficients.A continuous function can then be readily used inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysiswitr a thirdorderpolynomialfor Pm /f less than 4. 0 anda second orderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters R,, /t ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb ,o, is a column array containing the R , t ratio, which is also Column "0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W := Jsb(o) X :=Jsbý I) Y :=Jsb(2) aU Sambi(O) aL= Sambi( I) aQ Sambi(2) aC Sambi(3) cU Sambi(4) CL: Sambi (5) CQ  :=Sambi(6) cc Sambi(7) n := 13 if Rt < 4.0 Order of polynomial selected based on R m/t ratio 12 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

FOu (W,X,Y) which is the standard nomenclature is Fu (R m/t, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (Pmo

/t, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix IV Page 16 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "a-Tip" Coefficients "a-tip" Uniform Term MaU:= augment(W,X,Y) VaU := aU RaU :=regress (MaU, VaU,n) fau(WX,Y):= interp RaU,MaU,VaU, "a-tip" Linear Term MaL:= augment(W,X,Y) VaL-:= aL RL:=regress (ML, VL, n) faLWXY):=interp{RaL, MaL7V aL{Xj faL(WXY "a-tip" Quadratic Term MaQ := augment(W,X, Y) VaQ := aQ RaQ :=regress (MaQqVaQ,n) faQ(W,X,Y) : ýaQ'VaQýLX1 "a-tip" Cubic Term MaC := augment(W,X, Y) VaC := aC RaC := regress (MaC, VaC, n) faC(,X,):=interp[RaCMaCVaC{ X~

"c"Tip Coefficients "c-tip" Uniform Term McU := augment(W,X,Y) VC :-Cu RcU:: regress (MCU IVCU,n) fcU (W, X, Y) :=iterp RCU ýMcu VcU{ Xj Appendix IV Page 17 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "c-tip"Linear Term McL:= augment(W,X,Y) VcL := CL R&C -- regress( McL, VcL,n) fcL(W, X,Y) := interp RcL, McL, VcL, L(

"c-tip" Quadratic Term McQ := augment(W,X,Y) VCQ := CQ Rc =regress (MCQ IVCQ, n) fcQ(W,X,Y) : , McQ, VcQ' xH

ý'r)j "c-tip" Cubic Term McC:= augment(W,X,Y) vC:-Ccc RC =regress( MCC, VCC,n) fcc(WXY):=interp[RCC, MCC, VcC{Xj Appendix IV Page 18 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculation of PWSCC Crack6rowth as a function of Hot Operating Time CGRsabi j <--- 0 ao <-- ao Co <-- CO NCBo <-- Cblk while j < llim 0r <--- ODRGI3 if Cj <-Co ODRG2 3 if co < cj <__ co + IncStrs.avg ODRG 3 3 if co + Incstrs.avg < Cj _Co + 2- InCstrs.avg ODRG4 3 if Co +2 Incstrs.avg < cj _co + 3. Icsctrs.avg if co + 3. IncStrs.avg < cj _ Co

+ 4.

-ncstrs.avg ODRG 5 3 if co + 4- InCstrs.avg < cj 5 co + 5 Ilncstrs.avg ODRG6 3 if co + 5*IncStrs.avg < cj < co

+ 6-Incstrs.avg ODRG 7 3 if CO+ 6, IncStrs.avg < Cj < Co

+ 7- Incstrs.avg ODRG 8 3 if co + 7-1nCstrs.avg < c -Co

+ 8.Ilncstrs.avg ODRG9 3 if CO+ 8- nCStrs.avg < cj co + 9.InCstrs.avg ODRG 10 3 if co+ 9.IncStrs.avg < c_ co

+ 10-IncStrs.avg ODRG1 1 3 ODRG 12 , if co + '0-Incstrs.APA A i4 FW 4d 'dcSktrs.avg

App lyron Unit 2 AM-2007-006 ODRG 1 3 3 if CO + I I-lncStrs.avg < Cj < CO+ 12-IncStrs.avg ODRG1 4 3 if Co + 12-IlncStrs.avg < Cj < co + 13.lncstrs.avg ODRG 1 5 3 if co + i3-Incstrs.avg < Cj < Co + 14- InCstrs.avg ODRG 1 6 3 if co + 14-InCstrs.avg < Cj < co + 15.lncstrs.avg ODRG 1 7 3 if Co + 15-Ilcstrs.avg < Cj < Co + 16 Ilncstrs. avg ODRG 1 8 3 if c0 + 16-Ilncstrs.avg < < Co + 17-lncstrs.avg ODRG 19 3 if Co + 17.Incstrs.avg < Cj < co + 18-lnCsttrs.avg ODRG 2 0 3 otherwise ODRGI4 if cj < CO ODRG 2 4 if co < cj < co + Incstrs.avg ODRG 3 4 if Co + Incstrs.avg < Cj < Co + 2I-ncstrs.avg ODRG4 4 if Co+ 2-IlncStrs.avg < cj <CO+ 3.1nCstrs.avg ODRG 5 4 if co + 3. IncStrs.avg < Cj CO + 4-IlncStrs.avg ODRG6 4 if Co + 4. Incstrs.avg < cj <co + 5.IlncStrs.avg ODRG7 4 if CO+5.InCStrs.avg < cj <co+ 6IlncStrs.avg ODRG 8 4 if co + 6. IncStrs.avg < cj CO + 7. lncStrs.avg ODRG 9 4 if Co + 7.lncStrs.avg < cj <co + 8-IncStrs.avg ODRGI 0 4 if CO + 8-Inlstrs.avg < cj <co + 9"IncStrs.avg Appendix IV Page 20 of 31

lyron Unit 2 AM-2007-006 App ODRGII4 if Co + 9-Incstrs.avg < cj < CO+ loI0ncstrs.avg ODRG12 4 if CO + 1o' lncstrs.avg < cj < co + 11 --Incstrs.avg ODRG1 34 if CO+ lf.Incstrs.avg < Cj < Co+ 12Ilncstrs.avg ODRG14 4 if co + 12.Ilncstrs.avg < cj <5 Co + 13.Ilncstrs.avg ODRG1 54 if Co+ 13-Incstrs.avg < Cj < Co + 14-lncstrs.avg ODRG16 4 if co+ 14-2ncstrs.avg < cj < Co+ 15-Incstrs.avg ODRG 1 74 if co+ 15"IncStrs.avg <j Co+ 16lIncstrs.avg ODRG 1 84 if Co + 163Incstrs.avg < Cj < CO + 17-lncstrs.avg ODRG1 94 if co + 174IncStrs. avg < cj < Co + 18-Incstrs.avg ODRG20 4 otherwise ODRG1 5 if cj :5 Co ODRG2 5 if co < cj <5 co + Incstrs.avg ODRG35 if CO + Ilncstrs.avg < cj < CO+ +2 Ifncstrs.avg ODRG45 if Co + 2. Incstrs.avg < cj < Co + 3-1lCstrs.avg OR5 5 if Co lncstrs.avg < cj<C+-ncstrs.avg ODRG65 if co + 4-IlncStrs.avg < cj < Co + 5"Incstrs.avg ODRG75 if CO + 5- lncstrs.avg < cj < co + 6-Incstrs.avg ODRG85 if co + 6Ilncstrs.avg < Cj < Co + 7-IlncStrs.avg 1-rl~ylbf :r - I -IT-- APp~endi? V*PqgV* ? of 31

App U ,VA 99-,

5 ii co-I-* I'mStrs.avg -cj : UOL '*ucStrs.avg lyron Unit2 AM-2007-006 ODRG 10 5 if co + 8-IncStrs.avg < *5 CO+9.lncstrs.avg ODRG 1 1 5 if cO+ 9. IncStrs.avg < cj < CO + o-Ilncstrs.avg ODRG 1 25 if co + 10-Ilncstrs.avg < cj < co + I I*IncStrs.avg ODRG1 3 5 if Co + 11. IncStrs.avg < Cj < CO + 12-lncstrs.avg ODRG 14 5 if co + 12-lncStrs.avg < cj < co + 13-lncstrs.avg ODRG 15 5 if co + 13-IlncStrs.avg < cj < Co+ 14"IncStrs.avg ODRG 16 5 if CO+ 14-Ilncstrs.avg < Cj < co + 15.Incstrs.avg ODRG 17 5 if CO+ 15-Incstrs.avg < Cj < Co + 16. Incstrs.avg ODRG 1 8 5 if Co + 16-InCstrs.avg < Cj < CO+ 17"IncStrs.avg ODRG 1 9 5 if CO+ 17-InCstrs.avg < Cj < CO+ 18.IncStrs.avg ODRG 2 0 5 otherwise ODRG 16 if cj

• CO ODRG 2 6 if CO < cj < CO+ IncStrs.avg ODRG 3 6 if CO + Incstrs.avg < cj < CO + 2"Incstrs.avg ODRG4 6 if co + 2.IncStrs.avg < cj <CO + 3-lncstrs.avg ODRG 5 6 if co + 3 IncStrs.avg < Cj <CO + 4,1lCStrs.avg ODRG6 6 if CO+ 4.InCStrs.avg < cj < co + 5.lncstrs.avg ODRG7 if cO + 5IncStrs.avfpefili IV '"c~k tgl.av

Ap~p lyron Unit 2 AM-2007-006 ODRG8 6 if Co + 6.IlncStrs.avg < Cj < Co + 7IlncStrs.avg ODRG 9 6 if CO+7.lncstrs.avg < Cj < Co + 8. Incstrs.avg ODRG 1 0 6 if Co + 8.lncstrs.avg < cj: CO + 9 Incstrs.avg ODRG 1 16 if co + 9.*Incstrs.avg < cj CO + 10Incstrs.avg ODRG 1 2 6 if co+ 1o.Incstrs.avg < cj co + 11* Incstrs.avg ODRG13 6 if cO+ i' Ilncstrs.avg < cj Co + 12.Ilncstrs.avg ODRG14 6 if co+ i2.Incstrs.avg < cj co + 13. Incstrs.avg ODRG15 6 if co+ 13 Incstrs.avg < cj Co + 14- Incstrs.avg ODRG 1 66 if co + 14. InCstrs.avg < cj Co + 15. lncstrs.avg ODRG 1 76 if Co+ 15.Ilncstrs.avg < Cj Co + 16-Incstrs.avg ODRG186 if Co + 16"Incstrs.avg < cj Co + 17 -lncstrs.avg ODRG 1 9 6 if Co+ 7TIfnCstrs.avg < Cj _*Co+ 18-Ilncstrs.avg ODRG206 otherwise 5 aj

( 0 .2

+ - 2. 2 + 0 3.

__aj) 25 *a ) 3

( -

5t ,t ) ( I+)2 .

ý2FO+

--G _ +72 _,..r*

+<,3.

aa (o.

O. 2O.a "aj3 GO-O2"- +

ý3<+( 2--t In l age) of 3 31

App \ t] ./ k L} lyron Unit 2 AM-2007-006 (Loaj j I0 aj 1.0,

,4+- O+ 0 +1 t

. +02 (Lt +9 3 t_)

+4 0.0 x1 <-- 0.25 x2 <-- 0.5 x3 +- 0.75 x4 <- 1.0 X <-- stack(x 0 , xI, x 2 , x3 , x4 )

ST <- stack( 0 , 1 ,42, ý3, 4)

RG +- regress(X, ST, 3) o00 <- RG 3 + Pint 5 10 <-- RG4 Y2 0 <-- RG 5 a 30 <- RG6 ARj aj Cj aj t

Gau" <--- faU(Rt,ARj,ATj)

J Gal <- faL(Rt,ARj ,ATj)

Gaqj <--- faQ(Rt,ARj,ATj)

G.,. +-- f,-,(R,,ARi ,ATi)

Appendix IV Page 24 of 31

'j .'\ . yron Unit 2 AM-2007-006 App ,

Gcu - fcu(R,,ARj, ATJ)

Gcli <---fcL(Rt,ARj,ATj)

Gcqj +- fcQ(Rt, ARj,ATJ)

Gcc- fcc(Rt,ARj,ATj)

Qj <- I + i.464-aI* if cj _Žaj I + .464- 1.otherwise f~taj~

a.K i--I-(IQa~*-CO- jau +a 10G0al O -G ++'730Gacj)

+ (20Gaqj ~G j 4c- j-) (ooo.Ocu + G io.Gcl + 02o*Gcq. + *3O*Gccj)

J Ka 4-Ka - i-og K -- Kc. 1.099 J

Ka ' <-- 9.0 if Ka _*9.0 Ko j otherwise Kyj <-- 9.0 if Kj :5 90 Kyj otherwise Daj --Co.(KKa - 9.0)1.16 D-. -- ID. 'CF;.,..-C..t. if K,,- <:ApMpjidix IV Page 25 of 31

App a.j AI UUU" UIK uj lyron Unit 2 AM-2007-006 4 0°CFinhr.Cblk otherwise Dc. E-- CO0(Kyj - 9.0)1.16 Dcg D*Dcj-CFinhr.Cblk if K 7j < 80.0 4 °.CFinhr-Cblk otherwise outputj, 0 <-- j outputj, I <-- aj outputj, 2 <-- Cj - Co outputj, 3 - Dag.

OUtPUtj, 4+<- Dcg OUtPUtj, 5 <-- Ka.

outputj, 6 <.-Kcj NCBj 365-24 outputj, 8 ' Gauj outputj, 9 - Gal outputj, 1o <- Gaqj J

output j, II <-- Gacj outputj, 12 +- Gcuj outputj, 13 -- Gcl.

J

.... .... . , . _ Ap pe nd ix IV Pa g e 26 o f 3 1

App UULIULj, 14 k-- Ucqj lyron Unit 2 AM-2007-006 OUtpUtj, 15 -- Gee.

NCBj 365.24 outputj, 16 <-- 1.5 *.98 jp-j+1 aj aj_, + Dagj_l cj <- Cj-i + Dcg.j 1 aj<-- It if aj_>t aj otherwise NCBj <-- NCBjI + Cblk output k :=O.. Iiim PrOPT~ngth = 0.505 Appendix IV Page 27 of 31

Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix IV Flaw Growth in Length Direction U

~.1 0

0I 0 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Operating Time {fuel cycles}

Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.505 inch. Thus the time available for the flaw growth by PWSCC is about 11.69 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix IV Page 28 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction 0 .6

).5 -

0 0 .4-3 0 .3

.0 CU 0 .2 0.1 A F I I I I .

0 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Operating Time (fuel cycles )

Flaw growth in the depth direction, as a function of fuel cycles. The extension of the *a-Tip* or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 11.69 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.32 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix IV Page 29 of 31

Appendix IV Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Intensity Factors U

80 -

0~

60-0 U

40

[.1w C

U 20 C

U U2 00 2 4 6 8 10 12 14 Operating Time {fuel cyclesl Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher OK" value at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix IV Page 30 of 31

Appendix IV Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 1.4 1.2

.E 0.8 The influence coefficients as a function of operating time is shown. The behavior for

______ _"____-the 'a-tip" shows the effect of the flaw o 0.6 aspect ration for the initial flaw and early (growth. No erratic behavior of the influence

____* i ___t"coefficients is observed.

0.2____I___ j.II 0

o 2 4 6 8 10 12 14 Operating time (years) a" - Tip -- Uniform a" - Tip -- Linear

---

"a" - Tip -- Quadratic

........ a" - Tip -- Cubic "c" - Tip -- Uniform

........ .... c- Tip -- Linear toc" - Tip -- Quadratic oc" - Tip -- Cubic Appendix IV Page 31 of 31

Appendix V Evatuationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzis atByron Untf 2 AtNI-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw teveloped by: J. S. Brihimdesom References :

1) "StressIntensity factors for Part-throughSurface cracks," NASA TM. 111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion EngineeringCalc. C-7770-00-1, Rev.0, "Byron/BraidwoodCRDM PenetrationResidual Stress Evaluation."

Byron Nuclear Station Unit 2 Reactor Vessel CRDM -"42.8" Degree Nozzle, "180" Degree Azimuth ("Uphill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed, as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 75t percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is applied during the determinationof the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference 1 for External flaws (Tables 2 and 4).

2) The stress distributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to OD).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5' below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL Strs.Dist) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Point ) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the 'Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix V Page 1 of 31

Appendix V Evaluation of PWSCC CrackGrowth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 CRDMLength.evaI := 2.72 CRDM Tube Length for Crack Growth Calculation, Use the length of the tube where the through wall stress distributions will be defined.

ULstrs.Dist := 2.72 Upper extent of the Stress bistribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.evai RefPoint :=2 To place the flaw with respect to the reference point, the flaw tips or flaw 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 (Enter2)

3) The lower '1- tip" located at the reference point (Enter 3).

Val := 2 Input Data :-

1:= 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 12 Number of Hot Operating Years for Analysis Appendix V Page 2 of 31

Appendix V Evaluation of PWSCC CrackGrowth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 him := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

(X0c := 2.67 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 1)

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 1)

Ro :="2od Rid i7 t Rid:= t := Ro -Rid RM :=Rid+ 2 Timor: Years*365-24 Phm Rm C~inr :=1.417-101 Cbk=Tirnopr Prftbll(. 2 Rt :=

Cb1i 1 0 C0, := e 1.103.10 3 (THead+459.67 Tref+459.67 c Temperature Correction for Coefficient Alpha

. 00C CC= C 0 1 75 th percentile MRP-55 Revision 1 Appendix V Page 3 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input all availableNodal stress data in the table below. The column designationsare as follows:

Column "0"= Axial distance from minimum to maximum recordedon data sheet(inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3"= 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress data at each Elevation (ksi)

Column "6" = OD Stress Dataat each Elevation (ksi) 0.0 56.365 52.66 48.772 43.271 36.801 23.594 0.5 52.907 54.254 55.419 57.892 63.059 54.099 AllData := 1.36 52.976 58.101 64.437 69.823 74.188 72.980 40.060 51.444 L 49.881 37.328 2.22 44.528 2.72 23.980 46.123 48.861 49.445 11.633 -5.430 -23.578 AXLen := AlIData(°) IDAI1:= AllData(') ODAII:= AllData(6)

Stress Distribution 100 I '1 _ 1 70 1.075 1.69 70 .. . . . .... --.......

IDAII 40 .. __t ODAII U*

__._.20_-__"__

_ _I

~rn _ _o

_______r ______

__._ _ I ___ __ _ _ _ _ _ _

JU 0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix V Page 4 of 31

Appendix V Evaluation of PWSCC CrackGrowth of PostulatedFlaw in CROM Nozzles at Byron Unit 2 AM-2007-006 Observingthe stress distributionselect the region in the table above labeled DataA,, that representsthe region of interest. This needs to be done especially for distributionsthat have a largecompressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data"statement below and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insert the same to the right of the Mathcad Equalssign below (pastesymbol).

0.0 56.365 52.66 48.772 43.271 36.801 23.594 0.5 52.907 54.254 55.419 57.892 63.059 54.099 Data := 1.36 52.976 58.101 64.437 69.823 74.188 72.980 2.22 49.881 48.861 49.445 46.123 40.060 51.444 2.72 44.528 37.328 23.980 11.633 -5.430 -23.578)

Axl : Data(0) ID := Data(1) Twty:= Data(2) Frty := Data(3)

Sxty := Data(4) Egty := Data(5) OD:= Data(6)

RID:= regress(Axl, ID, 3) RTwty regress(Axl,Twty,3) RFrty := regress(Ax1,Frty,3)

RSxty := regress(Axl, Sxty, 3) REgty regress(Axl, Egty, 3) ROD regress(Axl,OD, 3)

FLCntr:= Refpoint - co if Val = Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise Appendix V Page 5 of 31

Appendix V Evaluationof PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 ULStrs.Dist - UTip UTip := "Cntr + C lncstrs.avg := 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locations for stress profiles Loco : FLCntr -l i := I .. N +3 Incri co if i < 4 Incstrs.avg otherwise Loci : Loci- + Incri 3

SIDi := RD +RD4-Loci +RW ._(Loci) 2 + RI .(LOC,)

3 STwtyi RTty3 + RTwtY4 .Loci + Rrwty .Lo 1) + RTwty.(Lo)

SFrtyi  : RFty3 + RFtY4*Loci + RFty. .(LOCi) 2 +[IRFtY.'(LOýci) 3]

SSxtyi RSXty + RS~ty4 Loci + RS~ty5 .(LOC,) 2 +[IR SXtY.'(Loci)31 Appendix V Page 6 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 SEgtyi := REgty 3 + REgtY -Loci + REgtY "(Loci)2 + REgty6 "(Loci)3 2

SODi:= ROD3 + ROD 4Loci + ROD 5(Loci) + ROD6.(Loci)3 Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 I I I I 55 ID 50--

SIDi 45h-I I I I 40 0 0.5 I 1.5 2 2.5 3 Axi, Loci 100 OD 50" SODi 0

-50 0 0.5 I 1.5 2 2.5 3 Axi, Loci Appendix V Page 7 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j .. N SIDj + SIIj+1 + SIDJ+ 2 jf* STwtyj + STwtyj+ 1 + STwtyj+ 2 if j STwty j 3 3 Sid_-(j. + 1) + SIDj+ 2 STwtyjf (j + 1) + STwtyj+ 2 i otherwise otherwise j+2 j+2 S SFrtyj + SFrtyj+l + SFrtyj+ 2 if j = SSxtyj + SSxtyj+l + SSxtyj+ 2 if j =

SFrtyj "- "- 3 SSxty.

3 SFrtyj -l.(j+ 1) + SFrtyj+ 2 SSxtyjl (j + 1) + SSXtyj+2 Sotherwise j+2 UI rwile j+2 5 od. SODj + SODj+1 + SODj+2 SEgtyj + SEgtyj+l+ SEgtyj+ 2 if j = if j SEgtyj.-'- Jd 3 3

5 EgtyjI Sodj l-(j + 1) + SODj+ 2 (j + I) + SEgtyj+2 otherwise j+2 otherwise j+2 IEIevation-A veraged Heaop St~ress D~istrib~utionfor OD~ Flaws (i.e. Stress distri~butionchanged from OD~ to §Di)

U0 := 0.000 U1 := 0.20 U2 := 0.40 U3 := 0.60 U4 := 0.80 u5 := 1:00 Appendix V Page 8 of 31

Appe*ndix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit2 Al-2007-006 Y := stack(uo,ul,u 2 ,u 3 ,u 4 ,u 5 )

SIG1 stack(Sod 7 ,SEgty, Ssxty' ,SFrty , STwty ,Sid,) SIG 2 stack(Sod2, SEgty 2 'SSxty2 SFry2, STwtY2, Sid2)

SIG 3 stack (Sod 3 SE , Sty 3' SFrty3,STwty3,Sid3) SIG 4 stack( Sod4 , SEgtY4 , SSxtY4' SFrty4,STwty4 Sid 4)

SIG 5 stack (Sod 5 , SEgty 5 ' SSxtY5 ' SFrtY5, STwtY, Sid5) SIG 6 stack (Sod 6 , SEgtY6 , SSxtY6 ' SFrty6, STwty6 , Sid 6)

SIG 7 stack(Sod79SEgtY7, SSxtY, SFrtY , STwty7, Sid7) SIG 8 stack(Sods, SEgty8 , SSxty, SFrtY, STwty, Sid8)

SIG 9 := stack(Sod9, SEgty9 , SSxty9 , SFrty9 , STwty9 , Sid 9 )

SIGI 0 stack (Sod'o, SEgtylo, SSXtYjo' SFrtYo' STwtYlo' Sidlo)

SIG ,1 stack(Sod I'Egty 1 ' SSxty SFrty

,' ,' STwty, I'Sid, ) SIG 12 := stack (Sod 2,SEgty'2,SSxty2' SFrty1 2 'STwty 1 2 ' Sid1 2)

SIG 1 3 stack(Sod13' SEgtY3 ,SSxty3 'SFrtYI3, STwtY13, Sid13) SIG14:= stack (Sod 1 4 ' SEgty4 SSxtyl 4 'SFrtYI 4 , STwty1 4 ',Sid14)

SIG 15 stack(Sod 15' SEgty 15'SsxtY' SFrty, 5'STwty, 5' Sid15) SIG 1 6 stack( Sod1 6 ' SEgty 6 'SSxty, 6 'SFrty 6 ' STwty1 6 Sid16)

SIG 1 7 stack(Sodi1, SEgty 7, SSxtYl7' SFrtY 1, S 7 y id17) SIG 1 8 stack(Sod s, SEgty 8'SSxty,,'SFrty'8 STwty,',Sid, 8 )

SIG 1 9 stack (Sod 9 SEgtyg,SSxty 9 ',SFrtygSTwtyl9, Sidl9) SIG 2 0 stack (Sod 20 ' SEgtY20, SSxty20 SFrtY20 ' STwtY20 ' Sid 2 0)

Appendix V Page

Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix V Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG1 regress(Y,SIGi,3) ODRG 2 regress(Y, SIG 2 ,3)

ODRG 3 regress(Y, SIG 3 ,3) ODRG4 regress(Y,SIG 4 ,3)

ODRG 5 regress(Y, SIG 5 ,3) ODRG6 regress(Y,SIG6 ,3)

ODRG7 regress(Y,SIG 7 ,3) ODRG 8 regress(Y, SIG 8 ,3)

ODRG 9 regress(Y, SIG 9 ,3) ODRGI 0 := regress(Y,SIG1 0,3)

ODRG 1 1 regress(Y,SIGI 1 ,3) ODRG 1 2 regress(Y,SIG 1 2 ,3)

ODRG 1 3 regress(Y,S1G 13 ,3) ODRG 1 4 regress(Y,SIG 1 4 ,3)

ODRG 1 5 regress(Y,SIG 1 5 ,3) ODRG 1 6 regress(Y,SIG 1 6 ,3)

ODRG 1 7 regress(Y,SIG 1 7 ,3) ODRG 1 8 regress(Y,SIG 1 8 ,3)

ODRG 9 : regress(Y,SIG1 9 ,3) ODRG2 0 regress(Y, SIG2 0 ,3)

Appendix V Page 10 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Distribution in the tube. Stress influence coefficients obtained from thirdorderpolynomial curve fit to the through wall stress distribution PrOPLength :- ULStrs.Dist - FLCntr - Co - 0.5 PrOPength = 0.785 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-1i 1707-SC04 Model)

{NO INPUT Required)

Date New Soivur Formanws from OeD arthoece wTlles I i 2inde 4 Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb :=

0 1 2 The Table on the left "Jsb"consists of the cylinder and flaw mechanical 0 1.000 0.200 0.000 parametersas follows:

1 1.000 0.200 0.200 Column "0" :- Contains the mean-radius to thickness ratio (Rm It) of the Cylinder 2 1.000 0.200 0.500 3 1.000 0.200 0.800 Column "1".:- Contains the Flaw Aspect Ratio (a/c)

Column "2" :- Contains the Flaw Depth-to- Tube- Thickness ratio (a/t) 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 Appendix V Page 11 of 31

15 2.000 0.200 0.000 3CC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendi 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 5 10.000 0.400 0.200 Appendix V Page 12 of 31

Appendi 0.400 0.500 Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 AM-2007-006 52; 52 10.000 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 0.400 0.200 67 300.000 0.400 0.500 F68 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 0.200 772 300.000 1.000 0.500 73 300.000 1.000 0.800 74 300.000 1.000 1.000 The Table below "Sambi"contains the Flaw Influence coefficients as follows.

Column "0" :- Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip)

Column "1":-Containsthe influence coefficients for LinearLoading at themaximum depth of the flaw ("a'"-tip)

Column "2" :- Contains the influence coefficients for QuadraticLoading at themaximum depth of the flaw ("a"-tip)

Column "3" :- Contains the influence coefficients for Cubic Loading at the maximum depthof the flaw (a'"-tip)

Column "4" :- Contains the influence coefficients for Uniform Loading at the surfacepoint of the crack front ("c"-tip)

Column "5" :- Contains the influence coefficients for LinearLoadingat the surfacepoint of the crack front ("c"-tip)

Column "6":-Contains the influence coefficients for QuadraticLoading atthe surface point of the crack front ("c'" tip)

Column "7":-Contains the influence coefficients for Cubic Loading atthesurface point of the crack front ("c"-tip)

Appendix V Page 13 of 31

Appendix V Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Sambi 0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 K28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 133 2.51 1.1781 0.782 Appefi&" Page 14 b0§1! 0.242 0.097 0.051

AppendixI 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 AM-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 611 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix 7Pagel 5FoT3'

Appendix V Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 In the declarationsbelow, dummy variablesare defined in order to develop a continuous function for the various influence coefficients. A continuous function can then be readilyused inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysis with a thirdorderpolynomial for Rm It less than 4.0 and a second orderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters RP /t ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb ,o> is a column array containing the R , A ratio, which is also Column "0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W Jsb(O) X :=Jsb~') Y :=Jsb(2 aU Sambi(o) aL: Sambi~l aQ Sambi (2) aC cU Sambi(4) CC= Sambi(5ý cQ Sambi(6 CC :=Sambi (7) n := 13 if Rt < 4.0 Order of polynomial selected based on R m t ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

Fau (W,X,Y) which is the standard nomenclature is Fau ( m/t, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (lR it, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix V Page 16 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM.2007-006 "a-Tip" Coefficients "a-tip" Uniform Term MaU := augment(W,X,Y) VaU :; aU RaU := regress (MaU, VaU,n) faUWXY):interp{RaUMaUVaU{ Xj

~u(W~xY "a-tip" Linear Term MaL - augment(W, X,Y) VaL:= aL Ra=regress ( Ma,VaL,n) faLW,,Y):=interp RaL, MaL9VaL{ X}

"a-tip" Quadratic Term MaQ := augment(W,X,Y) VaQ.= aQ RaQ :=regress (MaQ, VaQ, n) faQ(WXY) : 2MaQ VaQLXI "a-tip" Cubic Term MaC := augment(W,X,Y) VaC := aC RaC := regress (MaCVaCn) faC(,X,):=interp[RaCMaCVaC{ X}

"c" Tip Coefficients "c-tip" Uniform Term McU := augment(W,X,Y) VcU := CU RcU :=regress (MU, VcU, n) Icu(W,X, Y) :=interp{RCU, MCU, VCU{ XJ Appendix V Page 17 of 31

Appendix V Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM NozzJes at Byron Unit 2 AM-2007-006 "c-tip" Linear Term McL:= augment(W,X,Y) VcL := CL R&c:- regress (MCL ,VcL, n) fcL(W,X,Y) := interp RcL,McL,VcL, "c-tip" Quadratic Term McQ:= augment(W,X,Y) VcQ := CQ RCQ :=regress (MCQ IVCQ, n) fcQ(WXY): interp[RCQ7MCQVCQ{XI

{E "c-tip" Cubic Term R~CC MCC := augment(W, X, Y) V cc regress (Mc,Vcc,n) f~c (W,X, Y) :=ii vcc Appendix V Page 18 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzes at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculationof PW5CC Crack Growth as a function of Hot Operating Time CGRsambi:= j <-- 0 ao<--ao Co <-- co NCB 0 <-- Cblk while j < Ilim yo0 <-- ODRG 1 3 if cj <*Co ODRG 2 3 if CO < cj < co + Ilncstrs.avg ODRG3 3 if co + Incstrs.avg < cj <5 co + 2. lncstrs.avg ODRG4 3 if CO + 2- Incstrs.avg < cj < Co + 3-lncstrs.avg ODRG5 3 if Co + 3-ncStrs.avg < Cj < co + 4 IncStrs.avg ODRG63 if Co + 4- lncstrs.avg < Cj < Co + 5. IncStrs.avg ODRG7 3 if Co + 5- lncstrs.avg < cj <5 co + 6.-Incstrs. avg ODRG83 if Co + 6, lncstrs.avg < Cj < Co + 7. lncstrs.avg ODRG9 3 if Co + 7 lncstrs.avg S < cj _<Co + 8- Incstrs.avg ODRG103 if CO + 8-lnCStrs.avg < cj < CO + 9-IlncStrs.avg ODRG113 if CO + 9 Incstrs.avg < Cj < cO +7OfnCStrs.avg ODRG12, if co + 0. Ilncstrs.avg <C

• COl+/-lin %jt, trs.avg

lyron Unit 2 AM-2007-006 Apl ODRG 1 3 3 if co + I1I" Incstrs.avg < Cj Sco + 12flncstrs.avg ODRG 1 4 3 if Co + 12-lncStrs.avg < Cj < Co + 13*Ilncstrs.avg ODRG 1 5 3 if co + 13 lncstrs.avg < Ci < co + 14Ilncstrs.avg ODRG16 3 if CO+ 14-InCStrs.avg < C. < co + 15-lncstrs.avg ODRG 1 7

. 3 if Co + 15.IncStrs.avg <

C. _<CO + 16 Ilncstrs.avg ODRG 1 83 if co + 16.InCStrs.avg < <co + 17Ilncstrs.avg ODRG 1 93 Ci if Co + I7.lncStrs.avg < SCo + 18'lncstrs.avg ODRG20 3 otherwise ODRG 1 4 if cj Cco ODRG2 4 if Co < cj 5 co + Ilncstrs.avg ODRG3 4 if CO + Ilncstrs.avg < cj _Co + 2 Ilncstrs.avg ODRG44 if co+ 2.IncStrs.avg < cCj co + 3 Incstrs.avg ODRG5 4 if CO + 3-InCStrs.avg < Cj < Co + 4-lncstrs.avg ODRG64 if Co + 4. IncStrs.avg < cj < Co + 5-IncStrs.avg ODRG7 4 if CO+ 5 IlncStrs.avg < cj _Co + 6. IncStrs.avg ODRG84 if CO+ 6. lncStrs.avg < cj* -Co + 7*lncstrs.avg ODRG9 4 if co + 7, lncStrs.avg < cj !5 Co + 8-lncStrs.avg ODRG104 if co + 8-IncStrs.avg < c -<co0 + 9IlncStrs.avg Appendix V Page 20 of 31

App lyron Unit 2 AM-2007-006 ODRG 1 1 4 if Co + 9.lncstrs.avg < cj < co + 10- Ilncstrs.avg ODRG 1 2 4 if Co+ to-Incstrs.avg < Cj < co + 11.Incstrs.avg if CO + 1I*-Incstrs.avg <cj <5co + 12. Incstrs.avg ODRG 1 3 4 if Co+ 12- IlncStrs.avg < Cj < co+ 13IlncStrs.avg ODRG 14 4 if co+ 13. ncStrs.avg < Cj < Co+ 14Ilncstrs.avg ODRG1 5 4 ODRG 16 4 if Co+ 14-1nCstrs.avg < cj < co + 15.lncstrs.avg ODRG 17 4 if Co + 15- InCstrs.avg < Cj < Co + 16. Ilncstrs.avg ODRG 1 8 4 if Co+ 16.IlncStrs.avg < Cj < Co+ 17-lncStrs.avg ODRG 19 4 if co+ 17 lncstrs.avg < Cj < Co+ 18Ilncstrs.avg ODRG2 0 4 o therwise Y2 --- ODRG1 5 if cj - Co ODRG2 5 if CO < cj !5 cO + Ilncstrs.avg ODRG3 5 if CO + IlcStrs.avg < cj !5 Co + 2-lncStrs.avg ODRG4 5 if co + 2IlncStrs.avg < Cj 5 Co + 3-1lCStrs.avg ODRG5 5 if Co + 3IlncStrs.avg < Cj !5 Co + 4-Ilncstrs.avg ODRG6 5 if Co + 4- IncStrs.avg < Cj - Co + 5. IlncStrs.avg ODRG 7 5 if Co + 5-IfcStrs.avg < Cj <_ Co + 6-lnCstrs.avg ODRG8 5 if co + 6.lncStrs.avg < cj 5 Co + 7.InCStrs.avg r¢'rl'*n t" .1£ -, , T__ Appenai;1V Pqgq 1 of 31

%JLJMUQJ -1co 1 IiL;Strs.avFg ` Cj Uo0 &-u-l-CStrs.avg

_-- Jyron Unit2 AM-2007-006 App -5 ODRG 1 0 5 if Co + 8, lncstrs.avg < Cj < CO+ 9.lncstrs.avg ODRGI 15 if CO + 9" ncStrs.avg < ci < CO + 10'Incstrs.avg ODRG 12 5 if co+ 10-InCstrs.avg < Cj CO+ lI.Incstrs.avg ODRG 13 5 if co + I I-Incstrs.avg < cj co + 12.fncstrs.avg ODRG145 if co+ 12.Incstrs.avg < cj co+ 13.lncStrs.avg ODRG 1 5 5 if CO+ 13.Incstrs.avg < cj Co + 14.Incstrs.avg ODRG 1 6 5 if co+ 14-Incstrs.avg < Cj co + 15-lncstrs.avg ODRG 1 7 5 if co + 15. ncstrs.avg < cj < co + 16"Incstrs.avg ODRG 1 85 if co + 16-Incstrs.avg < cj < Co + I7-Incstrs.avg ODRG 19 5 if Co+ 1T Incstrs.avg < cj < CO+ 18-1nCStrs.avg ODRG 2 0 5 otherwise

<--- ODRG 1 6 if cj < Co 3

ODRG2 6 if Co < cj < Co + Incstrs.avg ODRG3 6 if co + Incstrs.avg < cj < CO+ 2-Incstrs.avg ODRG4 6 if CO + 2SIncstrs.avg < cj < co + 3-Incstrs.avg ODRG56 if co+ 3-lncStrs.avg < cj. co + 4. lncstrs.avg ODRG66 if CO+ 4. InCStrs.avg < cj < co + 5.IncStrs.avg ODRG 7 , if Co+ 5Incstrs.avkp'e ijt' i-9'tAt.avw

App* lyron Unit 2 AM-2007-006 ODRG 8 6 if co + 6.IncStrs.avg < Cj < Co + 7 Incstrs.avg ODRG 9 6 if Co+7"IlncStrs. avg < Cj < Co + 8.lncStrs.avg ODRGI 0 6 if Co+ 8-lncStrs.avg < cj < CO+9-lncstrs.avg ODRGII 6 if Co + 9.IncStrs.avg < cj < Co + Io-lncStrs.avg ODRG12 6 if co + lo'.Incstrs.avg < cj 5 co + 11 'lncstrs.avg ODRG 1 36 if co+ 1lflncstrs.avg < cj < co + 12.1nCstrs.avg ODRG 1 46 if Co+ 12-Incfstrs.avg < Cj 5 Co+ 13-lncstrs.avg ODRG 156 if Co + 13-Ilncstrs.avg < cj 5 co + 14.1lnCstrs.avg ODRG166 if co + 14.Incstrs.avg < Cj Co + 15IlncStrs.avg ODRG176 if Co + 15. ncStrs.avg < cj Co + 16-Incstrs.avg ODRG 1 86 if co+ I6.lncstrs.avg < cj Co + 1ITlncstrs.avg ODRG 1 96 if Co + 15 lncstrs.avg < Cj < Co + 18"IlncStrs.avg ODRG 2 0 6 otherwise 0 1-- 00 41 (-- GO0+ O 1I -025.aij

-- + CF(0.- 25,aj t J5 2j+ C3 ý (L---t0+j1"+ 2(L5 *aj +03" 5t a 2

0 0 0 75. aj (0.75.aj (0.75.aji G Or-aPz*.07 O +2"1 .75a'l of 31

App \ t L lyron Unit2 AM-2007-006

ý4 <-- GO + (Yl Io2 + (3" XO <-- 0.0 xX<- 0.25 x2 <-- 0.5 x3- 0.75 x4 -- 1-.0 X <-- stack(x 0 , x1 ,x 2 ,x 3 ,x 4 )

ST -stack(ý0,l,ý2,ý3,4 RG - regress(X, ST, 3) a00 -- RG 3 + Pint (y1 0 <- RG 4

'- RG 5

• 20 0 3 0 <- RG 6 ARj <aj __---

C.

ATj <--aj a t

Gau <-- faU(Rt,ARj,ATj)

J Gal <-- faL(Rt,ARj,ATj)

J Gaqj <- faQ(Rt,ARj,ATj)

G*,. 4-- f.r(R,,ARi,A~i)*

Appendix V Page 24 of 31

.- j - \ . 1 'I App lyron Unit 2 AM-2007-006 Gcu" <- fcU(Rt,ARj,ATj)

Gc ijJ <-fcL(St,A j,Arj)

Gcqj <- fcQ(Rt,ARj,ATj) ccj fc-c(RI, ARj, ATj)

Qj <- I1+1.464- if cj >aj 1 + 1.464- 65 otherwise aj0.5 K'aj < °'5(Oo0.Gau. + 10.Galj +20"Gaqj +30"Gacj)

Ka ~j 1 /j +

f \0.5 KC iKcj <- -QICj.J ., +

00'yyGcu.+a10,Gl0'Gd1+020'Gcqj + 030.Gccj)

K(X. <--- Ka. 1.099 J j Kj <- Kc: 1.099 Ko*<- 9.0 if K X*<9.0 Ka otherwise I-y <--- 9.0 if Kyj < 9.0 J J1 K~j otherwise Daj <- Co"(Kaj - 9.0) 1.16 D-. <-- I D- CF;.,i..Ci.,. if K-, <Awondix V Page 25 of 31

App lyron Unit2 AM-2007-006 4.10- 10-CFinhr.Cblk otherwise DcC -Co. (Kyj - 9.0) 116 Dcgj -- Dc. CFinhr'CblkJ if Ky < 80.0 4 0°.CFinhr.Cblk otherwise outputj, o <-- j outputj, I <-- aj OUtPUtj , 2 <7-Cj - Co OUtPUtj, 3 <- Dag OUtPUtj, 4 <- Dcg.

OUtPUtj, 5 <- Kaj outputj, 6 <-- Kc.

J NCBj 365"24 OUtPUtj, 8 <- Gauj outputj, 9 <-- Gal.

J outputj, 10 +- G aqj outputj, II <- Gac.

OUtPUtj, 12 <- Gcu.

J OUtPUtj, 13 <-Gc.

Appendix V Page 26 of 31

App UULtULj, 14 'T cq lyron Unit 2 AM-2007-006 outputj, 15 -Gcc.

j NCBi 365-24 OUtPUtj, 16 - .-- 98 1.5 j +---j +

aj -- ai + Dagj_I Cj -- cji + DcgjI aj - It if aj > t aj otherwise NCBj <- NCBj-j + Cblk output k := 0.. Iiim PrOPr1 ength = 0.785 Appendix V Page 27 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Length Direction U

C C

U 0

Q

':4 0 I 2 3 4 5 6 7 8 9 Operating Time (fuel cycles)

Flaw growth in the length direction, as a function of Fuel Cycles. The extension of the *c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.785 inch. Thus the time available for the flaw growth by PWSCC is about 6.37 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix V Page 28 of 31

Appendix V Evaluationof PWSCC CrackGrowth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction 0.6 0.5 U

0.4 0J 0.3 0.2 0.1 0

0 I 2 3 4 5 6 7 8 9 Operating Time Ifuel cycles I Flaw growth in the depth direction, as a function of Hot Operating Years. The extension of the "a-Tip" or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 6.37 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.289 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix V Page 29 of 31

Appendix V Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 U

C I-0 U

C C

cj~

0 1 2 3 4 5 6 7 8 9 Operating Time {fuel cycles}

Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results value at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in in a higher WK" depth.

Appendix V Page 30 of 31

Appendix V Evaluation of PWSCC Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 1.4 ___ 6)77

- 1.2 ,_

.E 0.8 The influence coefficients as a function of oG operating time is shown. The behavior for 0 0.6 _the "a-tip' shows the effect of the flaw o aspect ration for the initial flaw and early growth. In the time period of interest (6.37

...... fuel cycles), no erratic behavior of the 0influence ~ ~~~~~`

_____~ ________ln..___I__ A coefficients is observed.

0.2

__ _ _ t __ __ ,'_ _

0 2 4 6 8 Operating time {fuel cyclesl

- "a" - Tip -- Uniform

. "a" - Tip -- Linear

......... "a" - Tip -- Quadratic

............ a" - Tip -- Cubic "c" - Tip -- Uniform c'- Tip -- Linear c" - Tip -- Quadratic "c" - Tip -- Cubic Appendix V Page 31 of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw Developed by: J. S. Brihmadesom

References:

1) "StressIntensity factors for Part-throughSurface cracks," NASA TM-111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion Engineering Ca/c. C-7770-00-1, Rev.0, "Byron/BraidwoodCRDM PenetrationResidual Stress Evaluation."

Byron Nuclear Station Unit 2 CRDM Number 68 Reactor Vessel CRDM -"43.8" Degree Nozzle, "0" Degree Azimuth ("Downhill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed, as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 75th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is applied during the determinationof the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference I for External flaws (Tables 2 and 4).

2) The stress distributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to OD).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5" below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eva

2) The upper axial extent (UL Str.Dit ) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Point) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the "Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix VI Page I of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 CRDMLength.evaI := 2.17 CRbM Tube Length for Crack Growth Calculation. Use the length of the tube where the through wall stress distributions will be defined.

ULStrs.Dist := 2.17 Upper extent of the Stress Distribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint 2 To place the flaw with respect to the reference point, the flaw tips or flaw center can be located as follows:

1) The Upper "T- tip" located at the reference point (Enter 1)

2) The Center of the flaw at the reference point (Enter2)

3) The lower 't- tip" located at the reference point (Enter 3).

Val := 2 Input Data :-

1:= 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id:= 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 24 Number of Hot Operating Years for Analysis Appendix VI Page 2 of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Iilm := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

aOc := 2.67. IC 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 1)

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 1) od id Ro = - R m = R d +*t Timopr:= Years.365-24 id:= 2 Timopr Pinn Rm CFi.hr := 1.417-105 Cbl o:= Prfltblk = 2 Rt :=

Ilim 50 t C01 := e 1.103.10- 3 THead +459.67 Tref+459.67) .a0c Temperature Correction for Coefficient Alpha CC= C 0 1 75 th percentile MRP-55 Revision 1 Appendix VI Page 3 of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Stress Input Data Input all availableNodal stress data In the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recordedon datasheet (inches)

Column "1" = ID Stress data at each Elevation(ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4"= 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress data at each Elevation (ksW)

Column "6" = OD Stress Dataat each Elevation (ksi) 0.0 23.213 22.995 21.708 21.952 21.376 16.910 0.5 31.996 38.504 47.079 58.572 74.562 93.786 AllData := 1.085 31.138 35.697 43.417 47.731 49.137 52.363 1.67 51.215 52.910 54.625 57.142 50.518 15.624 2.17 52.880 49.825 47.238 45.965 46.358 33.890 AXLen :=A11Data(0) IDAII := A11Data< 0 ODAI1 := AlIData (6)

Stress Distribution 100 80

- IDAII 60 40 C6) 20 0-0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix VI Page 4 of 31

Appendix VI Evaluationof PWSCC Crack Growt of PostulatedFlaw in CRDM AM-2007-006 Observing the stress distributionselect the region in the table above labeled DataA,, that representsthe region of interest. This needs to be done especially for distributionsthat have a large compressivestress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data"statementbelow and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insertthe same to the right of the MathcadEquals sign below (pastesymbol).

0.0 23.213 22.995 21.708 21.952 21.376 16.910) 0.5 31.996 38.504 47.079 58.572 74.562 93.786 Data:= 1.085 31.138 35.697 43.417 47.731 49.137 52.363 1.67 51.215 52.910 54.625 57.142 50.518 15.624 2.17 52.880 49.825 47.238 45.965 46.358 33.890 Axi : Data(0) ID: Data( 1) Twty :=Data (2) Frty:= Data(3)

Sxty := Data(4) Egty := Data(5) OD := Data(6)

RID:= regress(Axl,ID,3) RTwty := regress(Axl,Twty, 3) RFrty regress(Axl,Frty,3)

RSxty:= regress(Axl,Sxty,3) REgty := regress(Axl,Egty,3) ROD regress(Axl, OD, 3)

FLCntr := RefPoint - cO if Val= I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 RefPoint + cO otherwise Appendix VI Page 5 of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007.006 ULStrs.Dist - UTip UTip :" FLCntr + c0 Ilncstrs.avg 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locations for stress profiles Loco := FLCntr- 1 i := t..N+3 Incri:= CO if i< 4 Incstrs.avg otherwise Loci := Loci-, + 1ncri 2 3 SIDi := RID3 + RID4Loci + RiD5" (Loci) + RID 6(Loci)

STwtyi := RTwty3 + RTwty4- Loci + RTwty5 "(Loci)'2+ RTwty 6 -(Loci) 3 2

SFrtyi RFrty3 + RFrtY4 Loci + RFrtY "(Loci) + [RFrtY6"(Loci)3]

SSxtyi :=Rst + RSxtY4 Loci + RSxty (Loci)2++ [2Rx (Loci) 3 Appendix VI Page 6 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 SEgtyi := REgty3 + REgty4- Loci + REgty- (Loci) 2 + REgty 6 -(Loci)3 SODi := ROD 3 + ROD 4.Loci + ROD 5(Loci) 2 + ROD6.(Loci) 3 Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 ID 40 SIDi 20' 0 0.5 I 1.5 2 2.5 Axi, Loci 100 OD 50 SODi 0*-

0 0.5 1 1.5 2 2.5 Axi, Loci Appendix VI Page 7 of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j I..N Sid .: =- SI + SIDj+1 + SIDj+ 2 if j -

ST~

STwtyj + STwtyj+l + STwtyj+ 2 if ; I J 3 Twyj 3 Sid_- *(j+ I) + SIDj+ 2 STwty,_,.(j + i) + STwtyj+ 2 otherwise otherwise j+2 j+2 5 FSy S xt i :3 SSxtyj + SSxtyj+I + SSxtyj+ 2 if j = I FrtyJ SFrtyj + SFrtyj+l + SFrtyj+ 2 if j 3 StJ 3 SFrtyj_.(j + I) + SFrtyj+ 2 SSxty_(j + 1) + SSxtyj+2 otherwise i- Iotherwise j+2 j+2 SOD + SODj+j +SODj+2 SEgytv" =.i SEgtyj + SEgtyj+1 + SEgtyj+2 f j Sod.

if i I J 3 J

SEgtyj. -(j + i) + SEgtyj+2 Sodj- .(j + i) + SODj+ 2 otherwise otherwise j+2 j+2 Elevation-AveragedHoop Stress Distributionfor OD Fl/aws (i.e. Stress distributionchanged from OD to ID)

U0 := 0.000 u 1 := 0.20 U2 := 0.40 U3 := 0.60 U4 := 0.80 u5 := 1.00 Appendix VI Page 8 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Y := stack(u0,u1 ,u 2 ,u 3 ,u 4 ,u 5 )

S Sxty,,SFrty,,STwty,,Sid, ) stack( Sod 2 )SEgty 2 ,SSxty2 , SFrty 2 , STwty2 , Sid 2)

SIG 1 stack( Sod, 'SEgty, , SIG 2 SIG 3 stack(Sod3, SEgty3' SSXty3' SFrty3 ' S id3) SIG4 stack( Sod4, SEgty4 SSxty4, SFrty4, STwty, Sid4 )

S IG5 stack So d 5, SEgtys, SSxty,'SFrty5' STwty5' Sid 5) SIG 6 stack(Sod6, SEgty 6 ,SSxty 6 ' SFrty6 , STwty6, Sid6)

SIG 7 stack(Sod ,SEgtY7SSxtY7, SFrtY7 STwty7Sid7) ' SIG 8 stack (Sod 8 SEg ty 8 ' S5xy. SFrty 8 ' STwty 8 ,Sid8)

SIG 9 stack( Sod 9 , SEgty9,'SSxty 9 , SFrty9, STwty9, Sidg) SIGI 0 stack(Sod 10o SEgty 10 , SSxty1 0, SFrtyIo, STwtyI0, Sido)

SIG1 1 stack(Sod 1, SE gty II,SSxty1 I, SFrty, , STwty, 1Sid, ) SIG1 2 stack(Sod 1SEgty 2,SSxty,2'SFrty25,STwty 2, Sid 12 )

SIG 1 3 stack(Sod 13 SE ygtY Ssxtyy3' SFrty,3 STwty13' Sid1 3) SIG 14 stack(S od14 SEgty

' 4, SSxty 4, ' SFrty ,4' STwty1 4 'Sid 14)

S id stack(Sod16' SEgty STwty 1 6 Sid 1 6 )

SIG 1 5 stack(Sod 15' SEgty 1 5 ' SsxtY1 5 ' SFrty1 5 ' STwty15' 1) SIG 16 6 'SSxty, 6 ' SFrty,6' SIG 1 7 stack(Sod 1'SEgty, 'SSxty, 7 'SFrty 7 ,STWtY17,Sid17) SIG18 :=stack(Sods18 ' SEgty1, SSxty'1FrY8 ' STwty 1 8 SidI 8)

SIG 9 : stack(Sod 1 9 'SEgty 1 9 , SSxty 9 ' SFrty 19 ' STwty1 g' Sidl 9) SIG 2 0 stack (Sod SE SSxty20 'SFrty 20 ' STwty20 ,Sid 20 )

Appendix VI Page 9 of 31

Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AMl-2007-006 Appendix V1 Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG1 regress(YS1G 11 3) ODRG2 regress(Y,SIG 2 ,3)

ODRG 3 regress (Y,SIG 3 ,3) ODRG 4 regress(Y, SIG4 ,3)

ODRG 5 regress(Y ,SIG 5 ,3) ODRG6 := regress(Y, SIG 6 ,3)

ODRG7 regress(Y, SIG7 ,3) ODRG 8 := regress(Y,SIG8 ,3)

ODRG 9 : regress(Y,SIG 9 ,3) ODRG 10 regress(Y ,S1G 10 ,3)

ODRG11I regress(Y, SIG, 1 ,3) ODRG 1 2 regress(Y,SIG 1 2 ,3)

ODRG 13 regress (YS1G 13 ,3) ODRG 14 regress(Y,S1G 14 ,3)

ODRG 15 regress( Y,SIG15 ,3) ODRG 16 regress(Y,SIGI 6 ,3)

ODRG 17 regress(Y,S1G 17 ,3) ODRG 1 8 regress(Y,SIG 1 8 ,3)

ODRG1 9 : regress(Y,SIG19 ,3) ODRG 2 0 := regress(Y, SIG 2 0 , 3)

Appendix VI Page 10 of 31

Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Appendix VI Stress Distribution in the tube. Stress influence coefficients obtainedfrom third orderpolynomial curve fit to the through wall stress distribution Proken~gt UStrs.Dist

-~- - F-Cntr - co - 0.5 Pr0Pjengffi = 0.51 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-11l1707-SCO4 Model)

{NO INPUT Required)

DattuNTabs nSir Fomteran loawsutoo eOePrettrocg (TabllesC)nde 2

Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb -=

0 1 2 The Table on the left "Jsb"consists of the cylinder and flaw mechanical 0 1.000 0.200 0.000 parametersas follows:

1 1.000 0.200 0.200 Column "0" :- Contains the mean-radius to thickness ratio (RPm It) of the Cylinder 2 1.000 0.200 0.500 Column "1" :- Contains the Flaw Aspect Ratio (a/c) 3 1.000 0.200 0.800 Column "2":-Contains the Flaw Depth-to- Tube- Thickness ratio (a/t) 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 j 5 2.000 0.200 0.000 Appendix VIlPage 11 of 31

Appendix VI -t PM Z-I Crack Growth of PostulatedFlaw in CRDM AM-2007-006 16 2.000 0.200 0.200 17 2.000 0.200 0.5001 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 511 10.000 0.400 0.200 int nnnl n Ann n* rnn AAppendix VI Page 12 of 31

Appendix VI 53 10.0.-004 0.-800 f PWSCC Crack Growth of Postulated Flaw in CROM AM-2IM07"-0076 53 10.000 0.400 0.800 54 10.000 0.400 1.000 5 10.000 1.000 0.000 57 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0,200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 74 300.000 1.000 1.000 The Table below "Sambi" contains the Flaw Influence coefficients as follows.'

Column "0":-Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip)

Column "1":-Contains the influence coefficients for LinearLoading at themaximum depth of the flaw ("a'-tip)

Column "2":-Contains the influence coefficients for QuadraticLoading at themaximum depth of the flaw ("a"-tip)

Column "3":-Contains the influence coefficients for Cubic Loading at the maximum depthof the flaw ("a"-tip)

Column "4":-Contains the influence coefficients for Uniform Loading at the surfacepoint of the crack front ("c'-tip)

Column "5":-Contains the influence coefficients for LinearLoading atthe surfacepoint of the crack front ("c"-tip)

Column "6":-Contains the influence coefficients for QuadraticLoadingatthe surface point of the crack front ("c'"-tip)

Column "7":-Contains the influence coefficients for Cubic Loading atthe surfacepoint of the crack front ("c'"-tip)

Appendix Vl Page 13 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Sambi 0 1 2 3 4 5 6 7 0 1 .244 0.754 0.564 ..454 0155 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586- 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.5a4 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 0.596 1.16 0.242 0.097 0.051

-Appe Pae4

A.pJl p.' 1.4b4 U.V20e U.b9J 1.bl /I U.00 U.016 U.U/j AM-2007-006 AppendixI 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix VI Page 15 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CROM AM-2007-006 In the declarationsbelow, dummy variablesare defined in order to develop a continuous function for the various influence coefficients. A continuous function can then be readilyused inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysiswith a thirdorderpolynomial for Rm /t less than 4.0 and a secondorderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters R, t ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb '°' is a column array containing the R ,/t ratio, which is also Column "0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W := Jsb(°) X :=Jsb~') Y :=Jsb(2) au Sambi(d) aL: Sambi~') aQ Sambi (2) ac Sambi(3 cu Sambi (4> cL= Sambi(5) CQ Sambi(6 cc Sambiý7) n := 13 if Rt < 4.0 Order of polynomial selected based on R m/t ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

F.u (WX,Y) which is the standard nomenclature is Fau (R m/t, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (Pm it, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix VI Page 16 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 "a- Tip" Coefficients "a-tip" Uniform Term MaU := augment(W, X, Y) VaU :aU RaU := regress (MaU, VaU, n) fau(W,X,Y) := interp RaUMaUVaUTX "a-tip" Linear Term MaL:= augment(W,X,Y) VaL:= aL Ra=regress (Ma7V a, n) faLWXY):=interp RaL, MaL, VaL{X]

"a-tip" Quadratic Term MaQ := augment(W, X, Y) VaQ ::- Q RaQ :=regress (MaQ ,VaQ ýn) faQ (W, X,Y) : 'aQ'VaQ{ X]

"a-tip" Cubic Term MaC := augment(W,X, Y) VaC := aC RaC := regress (MaC, VaC, n) faC (W, X,Y) : MaC, VaC{ XI "c" Tip Coefficients "c-tip" Uniform Term McU:= augment(W,X,Y) VCU := CU RcU := regress(Mcu, VcU, n) fcU(W,X,Y) := interp RCU,McU, VcU, X Appendix VI Page 17 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 "c-tip" Linear Term McL:= augment(W,X,Y) VcL := CL RcL ::-regress( McL,VcL,n) fcL(W, X, Y) : inter RcL, McL, VcL, x "c-tip" Quadratic Term McQ:= augment(W,X,Y) VCQ  :=CQ RcQ :=regress ( MCQ IVQ, n) fcQ(WXY) : 2VCQ{J ]

"c-tip" Cubic Term McC:= augment(W,X,Y) VC=Cc R~cC: regress (MCC, V~C,n) f~C(W'XY) :

vcc[Ej Appendix VI Page 18 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Calculations,: Recursive calculations to estimate flaw growth.

Recursive Loop for Calculationof PW5CCCrack Growth as a function of Hot Operating Time CGRsambi:= j <--o0 ao<-ao co <-- co NCBo (- Cblk while j < Ilim c0*-- ODRG1 3 if cj Co ODRG 2 3 if Co < cj < co + Ilncstrs.avg ODRG3 3 if Co + lncstrs.avg < cj 5 CO + 2.Incstrs.avg ODRG4 3 if co + 2SIncstrs.avg < cj < co + 3. Incstrs.avg ODRG53 if Co + 3IlncStrs.avg < Cj < CO + 4.Incstrs.avg ODRG63 if Co + 4"IncStrs.avg < Cj < Co + 5-lnCStrs.avg ODRG73 if co + 5-InCStrs.avg < cj < Co + 6. lncStrs.avg ODRG83 if co + 6.Incstrs.avg < Cj < Co + 7 IlncStrs.avg ODRG93 if co+ 7.InCStrs.avg < cj < Co+ 8-lncStrs.avg ODRG103 if Co + 8IlncStrs.avg < cj < Co + 9- Incstrs.avg ODRG 1 13 if Co+9.Incstrs.avg < Cj 5 Co+ iIflncStrs.avg ODRG12, if cO+10-lncStrs.aivg idSF lY0*

JIifll

• trs.avg

App* AM-2007-006 ODRG 1 3 3 if Co + I ll*ncStrs.avg < cj < Co + 12-InCstrs.av g

ODRG1 4 3 if Co+ 12.Ilncstrs.avg < cj < Co + 13.1lCstrs.av ,g ODRG1 5 3 if Co+ 13-Ilncstrs.avg < Cj < Co+ 14"lncstrs.av ,g ODRG 16 3 if Co+ 14.Incstrs.avg < cj < Co+ 15.IncStrs.av g ODRG 1 7 3 if Co+ 15.lncstrs.avg < cj < co+ 16"lncstrs.av ,g ODRG 1 8 3 if Co + 16-InCstrs.avg < cj < Co + 17.InCStrs.av g ODRG 1 9 3 if co+ 17-Ilncstrs.avg < cj < co+ 18-lncstrs.av ,g ODRG2 0 3 otherwise if cj < Co ODRG 2 4 if co < cj < co + lncstrs.avg ODRG 3 4 if co + lncstrs.avg < Cj < co + 2-IlCStrs.avg ODRG4 4 if co + 2-IncStrs.avg < Cj < Co + 3 IlncStrs.avg ODRG 5 4 if co + 3.IncStrs.avg < cj < Co + 4. lncstrs.avg ODRG 6 4 if co+4.IncStrs.avg < Cj co + 5-*1lCStrs.avg ODRG 7 4 if co + 5.IncStrs.avg <cCj Co + 6 Ilncstrs.avg ODRG 8 4 if co + 6.Incstrs.avg < cj co + 7.lncstrs.avg ODRG 9 4 if Co + 7.IncStrs.avg < cj co + 8-lncstrs.avg ODRG 10 4 if Co + 8. lncstrs.avg < cj < CO + 9-IfncStrs avg Appendix VI Page 20 of 31

AM-2007-006 App ODRG 1 1 4 if co + 9IncStrs.avg < cj 5 CO + 10l.ncstrs.avg ODRG12 4 if co + 10- Incstrs.avg < cj <5 co+ 11 -lncstrs.avg ODRG 134 if co + 11Ilncstrs.avg < cj Co + 12.I lncStrs.avg ODRG14 4 if Co + 12.Ilncstrs.avg < cj 5 CO + 13"Ilncstrs.avg ODRG15 4 if Co + 13-Ilncstrs.avg "- cj co + 14" lncstrs.avg ODRG 164 if co+ 14.Incstrs.avg < cj < CO+ 5- lncstrs.avg ODRG 174 if Co + 15-Incstrs.avg < cj < Co+ 16-Ilncstrs.avg ODRG 184 if Co + 16-Incstrs.avg < Cj < CO + 14 lncStrs.avg ODRG 1 94 if Co+ 1"Ifncstrs.avg < Cj < Co+ 18Ilncstrs.avg ODRG204 otherwise ODRGI 5 if cj !5 Co 4Y2 <--

ODRG2 5 if co < cj <5 co + Incstrs.avg ODRG35 if co + Ilncstrs.avg < Cj

< Co

+2 Ilncstrs.avg ODRG4 5 if CO + 2-Incs trs. avg < cj < co + 3."Incstrs avg ODRG5 5 if Co + 3-Incstrs.avg < cj <5 CO+ 4.Incstrs.avg ODRG 65 if CO + 4-Incstrs.avg < cj <5Co + 5.Incstrs.avg ODRG75 if co+ 5-lnCstrs.avg < Cj< CO+ 6"Incstrs.avg ODRG85 if co+ 6.IncStrs.avg < Cj< CO+7-Ilncstrs.avg

,*,* :4C -, . I_ - Appendi3.VI P9g9 1 of 31

App U u95 g C -Vo L -I ' UiCStrs.avg -, :tj

__O -t *. uuCStrs.avg AM-2007-006 ODRG 1 0 if CO+ 8-IlncStrs.avg < cj co + 9.Incstrs.avg to5 ODRGll5 if co+9-lncstrs.avg < cj co + io-lncstrs.avg ODRG 12 5 if Co+ 10-Ilncstrs.avg < cj < CO+ II'Incstrs.avg ODRG 1 3 5 if CO+ 11"IncStrs.avg < Cj < CO+ 12-Incstrs.avg ODRG 14 5 if Co+ 12.lncstrs.avg < cj < Co+ 13-lncstrs.avg ODRG 1 5 if Co+ I3ylncstrs.avg < Cj < CO+ 14,lncstrs.avg ODRG 1 6 5 if CO + 14-lIncstrs.avg < cj < co + 15.1nCStrs. avg ODRG 1 7 5 if CO+ 15 Incstrs.avg < cj co + 16-1nCstrs.avg ODRG 1 8 5 if CO+ 16-Incstrs.avg < cj < Co+ 17.IlncStrs.avg ODRG 1 9 5 if CO+ 17+.1nCstrs.avg < cj < co + 18lncStrs.avg ODRG2 0 5 otherwise ODRG1 6 if Cj < Co ODRG 2 6 if co < cj < Co + Ilncstrs.avg ODRG3 6 if CO + Ilncstrs.avg < cj < co + 2. InCStrs.avg ODRG 4 6 if co + 2- Incstrs.avg < cj < Co + 3-Incstrs.avg ODRG5 6 if CO + 3- IncStrs.avg < Cj < Co + 4- Incstrs.avg ODRG 6 6 if CO + 4. lncstrs.avg < Cj < CO + 5.lncstrs.avg ODRG 7 , if Co + 5.Incstrs.av4kp~eR~i<w -tigll.a

0 App AM-2007-006 ODRG 8 6 if co + 6.IncStrs.avg < Cj 5 Co + 7-Incstrs.avg ODRG9 6 if co + 7-IncStrs.avg < cj < co + 8"IncStrs.avg ODRG 1 0 6 if Co+ 8-IlncStrs.avg < c. <CO + 9-Ilncstrs.avg ODRG116 if co + 9.Incstrs.avg < cj co + 10.Incstrs.avg ODRGI2 if Co+ 10.Incstrs.avg < cj <co+ 1 -lncstrs.avg ODRG136 if CO+ 11-Incstrs.avg < cj -Co+ 12-Incstrs.avg ODRG 146 if co + 12-Ilncstrs.avg < Cj < Co + 13.Incstrs.avg ODRG 1 56 if Co + 13-Incstrs.avg < cj < CO + 14-Incstrs.avg ODRG1 66 if Co + 14.Incstrs.avg < cj Co + 15.Incstrs.avg ODRG1 76 if Co+ 15-Incstrs.avg < cj < Co+ 16-Incstrs.avg ODRG 1 8 6 if Co + 16"IncStrs.avg < cj < Co + 7ITlncstrs.avg ODRG 1 9 6 if Co + 17. lncstrs.avg < cj < Co+ 18flncstrs.avg ODRG 2 0 6 otherwise

¢ 0"25"aj '2 + 0.25.aj) 3

• • - OO + L .2* "02aj+

I__

G ( __ +0 25.at__ + (3'aL 5t 2 3"3) 2 3 (L7 5- +.75-a O+.72a"

ý3CF-- +a - + 02 T-.-Ajp~nin~ I.a"ezof 31

App I\ I j L j I\ L AMV-20W7'-006

ý 4 <- Go+a]--- +a-r+

t C2- t +} 3 tJ x 0 4- 0.0 X1- 0.25 x2 <-- 0.5 x3 <-- 0.75 x4<- 1.0 X 4- stack(x 0 ,xl,x 2 ,x 3 ,x4 )

ST (---stack(ý0,ýl,ý2,ý3,ý4)

RG <- regress(X, ST, 3) 00oo RG 3 + Pint y1 0 RG4 a 2 0 *-RG5 (T30 4-RG6 a30 ARj -

cj aj ATJ +--

t Gauj <- faU(Rt,ARj, ATj)

Gal -- faL(Rt, ARj,ATJ)

G aqj +- faQ(Rt,ARj,ATj)

G.,. - f.r(Rt,ARi,ATi) Appendix VI Page 24 of 31

--\ a App uAM-2007-006 Gcuj <'- fcU (Rt, ARj, ATj)

Gclj <-- fcL(Rt,ARj,ATj)

Gcqj <- fcQ(Rt,ARj,ATj)

Gcc fcC(RtARj,ATj) 1.65 if cj > aj Qj <- 1+1.464-

¢cja)

N1.65 I + 1.464- C)J otherwise (a,)

a. - j auj aij + 020-Gaqj + o30-GacJ Kcj G + T10"GcIj a--

q'*-J Ka.<-- Ka 1.099 J J Kyj <-- Kc.1-1.099 J j KoL.<-- [9.o if Ko*. 9.0 Ka otherwise K*j <-- 9.0 if Ky~j S<9,0 Kyj otherwise Daj <-- Co. (Koj _ 9.0)1"16 D., <-- I D,. CF;-t,.- C. 11 , if K,,_ <AupOjdix VI Page 25 of 31

App Oa j 4 i HUt UmK uj AM-2007-006 4.1o- I'.CFinhr.Cblk otherwise Dcg -Dcj-CFinhr-Cblk if Kj < 0.

4 l°.CFin.Cblk otherwise outputj , 0 <- j outputj, I aj OUtPUtj, 2 cj - Co C

OUtPUtj, 3 - Dagj OUtPUtj, 4 - Dcgj OUtPUtj, 5 -- Kaj OUtPUtj, 6 <--Kc.

J NCBj OUtPUtj, 7 <- NCB 365-24 OUtPUtj, 8 4 Gau outputj, 9 -- Gal J outputj, 10 - Gaqj outputj, 12 <- Gacj OUtPUtj, 13 <- Gcji I t--, Appendix VI Page 26 of 31

UULtULj, 14 v- %Jc-App AM-2007-006 outputj, 15 (--Gcc.

J NCBj 365-24 outputj,16*-

1 .

1.5 .98 j*-j+1 aj 4- aj_1 + Dagj_

Cj -- Cj-I + Dcgj_.

aj<-- It if aj>t aj otherwise NCBj <- NCBjI + Cblk output k :=o..Ilim ProPkength = 0.51 Appendix VI Page 27 of 31

Appendiix VI Evaluation of PWSCC Crack Growth of Postulated Flaw in CROM AM-2007-M06

._f

• 0 0.5 0

I-.

8 16 Operating Time {fuel cycles}

Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip* or 00 surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.51 inch. Thus the time available for the flaw growth by PWSCC is about 12.26 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix VI Page 28 of 31

Appendix VI Evaluationof PWSCC Crack Growth of Postulated Flaw in CRDM AM -2007 -006 Flaw Growth in Depth Direction 0.6 0.5 U

0.4 0~

U 0

0.3 0

0.2 0.1 0 2 4 6 8 10 12 14 16 Operating Time Ifuel cycles)

Flaw growth in the depth direction, as a function of Hot Operating Years. The extension of the "a-tip' or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 12.26 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.33 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix VI Page 29 of 31

Appendix VI Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Stress Intensity Factors U

0~

U, C,,

I-.

U Cu U,

C C

U, U) 0 I 0 2 4 6 8 10 12 14 16 Operating Time Ifuel cycles}

Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher "K' value at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix Vl Page 30 of 31

Appendix VI Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Influence Coefficients - Flaw 1.4 4 t212.26 S 1.2 0

E 0 The influence coefficients as a function of operating time is shown. The behavior for 0 aspect ration for the initial flaw and early growth. No erratic behavior of the influence

_ _ coefficients is observed. When the flaw 0 depth reaches 80% of wall thickness the coefficients show a departure from normal 0.2 _(expected) trends.

0.

0 10 15 Operating time {fuel cycles)

"a" - Tip -- Uniform

.................a" - Tip -- Linear "a" - Tip -- Quadratic a" - Tip -- Cubic c" - Tip -- Uniform

. c'- Tip -- Linear "c" - Tip -- Quadratic "c" - Tip -- Cubic Appendix VI Page 31 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw Developed by: 3. S. Brihmadesam

References:

1) "StressIntensity factors for Part-throughSurface cracks," NASA TM- 111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion Engineering Caic. C-7770-00-1, Rev.0, 'Byron/Braidwood CRDM PenetrationResidual Stress Evaluation.'

Byron Nuclear Station Unit 2 Reactor Vessel CRDM -"43.8" Degree Nozzle, "180" Degree Azimuth ("Uphill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed , as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 75th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is applied during the determinationof the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference I for External flaws (Tables 2 and 4).

2) The stressdistributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to OD).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5' below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL Sts.Dist ) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Poin) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the "Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix VII Page 1 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 CRDMLength.evaI := 2.75 CRDM Tube Length for Crack Growth Calculation, Mse the length of the tube where the through wall stress distributions will be defined.

ULStrs.Dist := 2.75 Upper extent of the Stress Distribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint :=2 To place the flaw with respect to the reference point, the flaw tips or flaw center can be located as follows:

1) The Upper "C- tip" locatedat the reference point (Enter 1)

2) The Center of the flaw at the reference point (Enter 2)

3) The lower "r- tip" located at the reference point (Enter 3).

Val := 2 Input Data :-

1 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 16 Number of Hot Operating Years for Analysis Appendix VII Page 2 of 31

Appendix VH Evaluation of PWSCC Crack Growth of PostulatedFlaw in CROM Nozzles at Byron Unit2 AM-2007-006 lim := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

(aOc := 2.67 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 11 Tref := 617 Reference Temperature for normalizing Data Deg. F; (MRP-55 Rev. 1)

Ro :='-od id Rid := F t:= Ro-Rid RM:id+ 2 Timopr := Years.365.24 Timopr Rm CFinhr := 1.417-105 Cblk - Prftk:= 1 501 Rt :=

Ilim 9) := 2 t

-Qg T(ef59.6 Temperature Correction for Coefficient Alpha I. 103- 10-3 THead+459.67 Tref+459.67 C 0 1 := e .- 0 C CC= C0 1 75 th percentile MRP-55 Revision 1 Appendix VII Page 3 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input allavailable Nodal stress data in the table below. The column designationsare as follows:

Column "0"= Axial distance from minimum to maximum recordedon data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress data at each Elevation (ksi)

Column "6"= OD Stress Data at each Elevation (ksi) 0.0 56.226 52.631 48.97 43.329 36.365 22.173 0.5 52.932 54.424 55.803 58.159 62.767 53.192 AllData := 1.375 53.702 58.804 65.006 70.103 74.068 72.704 2.25 49.393 48.445 48.974 45.532 39.179 50.298 2.75 43.95 36.231 22.779 10.299 -6.822 -24.958 AXLen := AllData(O) IDAI1:= AlIData(l) ODAI1:= AllData(6)

Stress Distribution 100 1.075 .69 70 _ __- _-_...........

= DAl ODAII 40 I_ ___ _ _

10 Si "20 __

1 _ _

-50 0 0.2 0.4 0.6 0.8 i 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix VII Page 4 of 31

Appendix VII Evaluationof PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Observing the stress distributionselect the region in the table above labeled DataAj 1 that representsthe region of interest. This needs to be done especially for distributionsthat have a largecompressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data"statement below and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (paste symbol).

0.0 56.226 52.631 48.97 43.329 36.365 22.173 0.5 52.932 54.424 55.803 58.159 62.767 53.192 Data:= 1.375 53.702 58.804 65.006 70.103 74.068 72.704 2.25 49.393 48.445 48.974 45.532 39.179 50.298 2.75 43.95 36.231 22.779 10.299 -6.822 -24.958 Axl := Data(0) ID :=Data(') Twty := Data(2) Frty := Data(3)

Sxty :=Data (4) Egty := Data(5) OD := Data(6)

RID :=regress(Axl,ID, 3) RTwty:= regress(Axl, Twty, 3) RFrty:= regress(Axl,Frty,3)

RSxty : regress (Axl,Sxty,3) REgty := regress(Axl, Egty, 3) ROD := regress(Axl,OD, 3)

FLCntr := Refpoint - co if ValI Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 RefPoint + cO otherwise Appendix VII Page 5 of 31

Appendix VII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 UL.LStrs.Dist - UTip UTip:= FLCntr + CO Ilncstrs.avg 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locations for stress profiles Loco:= FLCntr -1 i := .. N+ 3 Incri:= co if i< 4 Incstrs.avg otherwise Loci := Loci-, + Incri SIDi :=RD3 + RID4"Loci + RID .(Loci)2 + RID 6.(Loci) 3 STwtyi := RTwty3 + RTwtY4 Loci + RTwtY -(Loci) 2

+ RTwtY6"(Loci) 3 SFrtyi [

RFry3 + RFrtY4" Loci + RFrtY (Loci) 2 + RFrtY6 (Loci) 3 1 2 +I RSxty 6 -(Loci)3]

SSxtyi := RSXtY3 + RSxtY4 Loci + RSxty5 (Loci)

Appendix VII Page 6 of 31

Appendix VH Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 SEgtyi : REtY3 + REty4 .Loci + REty*.(Loci)' + RE9Y6.(Loci)'

SODi:= ROD3 + ROD4"Loci + ROD.'(Loc) 2 + ROD6"(Loci) 3 Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 i 55 ID SI 50 45-40I I I I 0 0.5 1 1.5 2 2.5 AxI,Loci 100 1 1 1 OD 50 SODi 0

-50 0 0.5 1 1.5 2 2.5 3 Ax, Loci Appendix VII Page 7 of 31

Appendix VII Evaluation of PWSCC CrackGrowth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use In Fracture Mechanics Model j:= I..N SIDj + SIDj+ 1 + SIDj+ 2 if j STwtyj + STwtyj+ 1 + STwtyj+ 2 if =

Sid: 3 STwty :

3 SidH_ + ,) + SIDj+ 2 STwtyj- -(j + I) + STwtyj+ 2 j+2 otherwise otherwise j+2 SFrtyj + SFrtyj+i + SFrtyj+ 2 if j SSxtyj + SSxtyj+i + SSxtyj+ 2 if j =

SFrtY : SSxty 3 Stj 3 SFrtyjl-(j + 1) + SFrtyj+ 2 SSxtyj_-*(j + 1) + SSxtyj+2 otherwise omierwise j+2 j+ 2 SODj + SODj+1 + SODj+ 2 if j SEgtyj + SEgtyj+l + SEgtyj+2 Sod.

i j 3 SEgtyj 3 J Sodj- -(j + I) + SODj+ 2 SEgtyj- ( + 1) + SEgtyj+ 2 Sotherwise odierwise j+2 j+2 Elevation-AveragedH~oop Stress DistributionVor OD Flaws (i.e. Stress distributionchanged from 0D to §Di)

U0 := 0.000 U 1 := 0.20 U2 := 0.40 U3 := 0.60 U4 := 0.80 u5 := 1.00 Appendix VII Page 8 of 31

Al ppendix VII Evaluation of PWSCC Crack Growth of PostulatedFlawin CRDM Nozzles at Byron Unit 2 ALM-2007-006 Y := stack(u0,u 1 ,u 2 ,u 3 ,u 4 ,u 5 )

SIG 1 stack(Sod, SEgty, SSxty, ,SFrty, STwty,,Sid,) SIG 2 :stack(Sod2, SEgty2,SSxty2, SFrty2, STwty2, Sid2)

SIG 3 stack( Sod 3 , SEgtY3, SSxtY',SFrty3, STwtY3, Sid3) SIG4 stack( Sod 4 2SEgty4,SSxty4, SFrtY4, STwtY4, Sid4)

SIG 5 stack( Sod 5SEgty, SSxtys,SFrty, STwtysSid5 ) SIG 6 stack( Sod 6 ,SEgtY6 SSxtY6 ' SFrtY6, STwtY6, Sid6 )

SIG 7 :=stack( Sod 7 , SEgty 7 'SSxty 7 , SFrtY7 , STwtY7, Sid,) SIG 8 stack( Sod8 SEgty8 Ssxty, FrtY y,8 STwty.,

'Sid 8)

SIG 9 := stack(Sod9 SEgtyg,'SSxtY9 ' SFrtY9 , STwty9,Sid9 ) SIG 1 0 stack (Sod 1 ,SEgty1 0 ,SSxty1o, SFrty 0o, STwty10 ' Sid, 0 )

SIG 1 1 : stack(Sod, ' SEgtY ' ,SSxty, ' SFrty, ' STwty, , Sid ) SIG 12 stack(Sod 2' SEgty12 ' SSxtY12 ' SFrty2 , STwtYi2' S'id12)

SIG 13 stack(Sod 1, SEgty, SSxty, 3 ' SFrty3 , STwty 3' Sid 13) SIG14 :=stack(Sod 1SEgty 4 ,SSxty,4' SFrty,4' STwty14' Sid14)

SIG 1 5 stack(Sod 15 SEgty 5 SSXtY15'

, SFrty15' STwty 15 Sid15) SIG 1 6 stack(Sod 1SEgty 6 ,SSxty 6'SFrty1 6, STwty1 6 6Sid 1 6)

SIG 17 stack(Sod 1, SEgtY 7, SSxtYI 7 ' SFrty1 7 ' STwtY17' Sid17) SIG 1 8 stack(Sod 1SEgty,8 ,SSxtY8, SFrty,8, STwty 18 ,Sid18)

S1G 19 :=stack (*Sod Egtyq

• 9 Sxt,, y,9,sTwty, 9 Sid19 ) SIG2o := stack (Sod*0' tg 2 0xty

'S S oSFrty 2 y20oTWty Sid 20 )

Appendix VII Page 9 of 31

Appendix VUI Evaluation of PWSCC CrackGrowth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 := regress(Y,SIG 1 ,3) ODRG 2 regress(Y, SIG 2 ,3)

ODRG 3 regress(Y, SIG 3 ,3) ODRG 4 regress(Y,SIG 4 ,3)

ODRG 5 regress(Y ,SIG 5 ,3)

ODRG 6 regress(Y,SIG 6 ,3)

ODRG 7 regress(Y,SIG 7 ,3) ODRG 8 regress(Y, SIG 8 ,3)

ODRG 9 regress(Y, SIG 9 ', 3) ODRGI 0 regress(Y, SIG 1 0 ,3)

ODRG 1 1 regress(Y,SIGl 1 ,3) ODRG 12 regress(Y,SIG 12 ,3)

ODRG 1 3 regress(Y,SIG 13 ,3) ODRG 1 4 regress(Y, SIG 14 ,3)

ODRG 1 5 regress(Y,SIG 1 5 ,3) ODRG 1 6 := regress(Y,SIGI 6 ,3)

ODRG 1 7 :- regress(Y,S1G 1 7 ,3) ODRG 1 8 regress(Y,SIG1 8 ,3)

ODRG 1 9 := regress(Y,SIG 1 9 ,3) ODRG 2 0 regress(Y, SIG2 0 ,3)

Appendix VII Page 10 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Distribution in the tube. Stress influence coefficients obtained from third order polynomial curve fit to the through wall stress distribution Pr0PTJngth :;-ULStrs.Dist - FLCnt - c0 - 0.5 Prokjength = 0.8 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-i 11707-SC04 Model)

{NO INPUT Required)

Meetu R eaNewsSivaeknar or FormaS iron ofOD euPce I (Tatoes 2 ande )

Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb :=

0 1 2 The Table on the left "Jsb"consists of the cylinder and flaw mechanical 0 1.000 0.200 0.000 praneters as follows:

1 1.000 0.200 0.200 Column "0":-Contains the mean-radius to thickness ratio (Rm It) of the Cylinder 2 1.000 0.200 0.500 Column "1":- Containsthe Flaw Aspect Ratio (a/c) 3 1.000 0.200 0.800 Column "2":-Contains the Flaw Depth-to- Tube- Thickness ratio (a/t) 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 Appendix VII Page 11 of 31

Appendix 15 2.000 0.200 0.000 XC Crac Growth of Postulate Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 ij 10.000 0.400 0.200 Appendix VII Page 12 of 31

Appendix A iGrowth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 1521 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 74 300.000 1.000 1.000 The Table below "Sambi" contains the Flaw Inflimnee toe fficient* a~ follnw*:

Column "0" :- Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip)

Column "1":-Contains the influence coefficients for LinearLoading at themaximum depth of the flaw ("a"-tip)

Column "2":- Contains the influence coefficients for QuadraticLoading at themaximum depth of the flaw ("a"-tip)

Column "3".:- Contains the influence coefficients for Cubic Loading at the maximum depthof the flaw ( `a'*"tip)

Column "4".:- Contains the influence coefficients for Uniform Loading at the surfacepoint of the crack front ("c"-tip)

Column "5":-Contains the influence coefficients for LinearLoadingatthe surface point of the crack front ("c'-tip)

Column "6" :- Contains the influence coefficients for QuadraticLoading at the surfacepoint of the crack front ("c'-tip)

Column "67 :- Contains the influence coefficients for Cubic Loading atthe surface point of the crack front ("c'"-tip)

Appendix VII Page 13 of 31

Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix VII Sambi :=

0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 03715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0,817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0,866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 01785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.511 1.178 alge 14 of!3J6 0.242 0.097 0.0511 0.782 ,ppendig.Q-

Appendix VII 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 A-M-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0,773 0,575 0,472 0-994 0.195 0,078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0,204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0,142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0,505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 ppendix VII Page 15 0131

Appendix VII Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 In the declarationsbelow, dummy variablesare defined in order to develop a continuous function for the variousinfluence coefficients.A continuous function can then be readily used inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysis with a thirdorderpolynomial for Rm /t less than 4.0 anda second orderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters Rm It ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb (),>is a column array containing the R ,/t ratio, which is also Column T0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W Jsb(o) X :=Jsb~') Y := Jsb(2) aU Sambi(O) aL= Sambi~') aQ Sambi(2) cU Sambi(4) CC= Sambi(5) CQ :Sambi(6) Cc := Sambi(7) n:= 13 if Rt<4.0 Order of polynomial selected based on R mit ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

Fau (W,X,Y) which is the standard nomenclature is Fau (R m A, a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (l,

/t, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix VII Page 16 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "a-Tip" Coefficients

'a-tip" Uniform Term MaU:= augment(W,X,Y) VaU:= aU RaU ::-regress (MaU, VaU, n) faUW,,Y):=interp{RaUMaUVaU{ Xj "a-tip" Linear Term MaL:= augment(W,X,Y) VaL:= aL R:=regress (ML, VL,n) faL(W,X,Y) := interp RaL, MaL, VaL,{X "a-tip" Quadratic Term MaQ := augment(W,X,Y) VaQ.&kaQ RaQ := regress(MaQVaQ,n) faQ(W,XY) : PaQ'VaQ)LX1 "a-tip" Cubic Term MaC:= augment(W,X,Y) VaC:= aC RaC :=regress (MaC $VaC,n) faC(W,X,Y) :=interp RaC,MaC,VaC, "c"Tip Coefficients "c-tip" Uniform Term McU:= augment(W,X,Y) VU Cu RCU : regress (MCU,vcU,n) fcU (W,X, Y) :=interp RcUJ ,Mcu VC, Appendix VII Page 17 of 31

Appendix VII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "c-tip" Linear Term McL := augment(W, X, Y) VcL := cL RcL= regress( MCL9VcL, n) fcL(W, X, Y):= interp RcL, McL, VcL, K "c-tip" Quadratic Term McQ:= augment(W,X,Y) VCQ CQ RcQ := regress(MCQ, VCQ, n) fCQ(WXY): McQ'Vc "c-tip" Cubic Term McC := augment(W,X,Y) VC:Ccc R~cC: regress ( Mc,V~c,n) fCC (W,X, Y) :ý-interp RcC, Mac, VcC {Xj Appendix VII Page 15 of 31

Appendix VH Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculationof PWSCC Crack 6rowth as a function of Hot Operating Time CGRsambi 34-0 ao<-- ao NCB0 <-- Cblk while j < Ilim (Yo<-- ODRGI3 if Cj Co ODRG 2 3 if Co < cj < co + IncStrs.avg ODRG3 3 if Co + Incstrs.avg < cj < Co + 2. Incstrs.avg ODRG4 3 if o+ 2. Ilncstrs.avg < Cj < Co+ 3-lncstrs.avg ODRG 5 3 if Co + 3. lncStrs.avg < Cj < Co + 4-Incstrs.avg ODRG6 3 if co + 4-Incstrs.avg < cj _<co + 5-Incstrs.avg ODRG73 if CO+ 5.lnCStrs.avg < Cj !5 Co+ 6,lncstrs. avg ODRG83 if Co + 6- IncStrs.avg < cj < Co + 7.ilncstrs.avg ODRG93 if Co + 7Ifncstrs.avg < Cj _<Co + 8-Incstrs.avg ODRG103 if Co+ 8.lncstrs.avg < cj < CO+ 9-Incstrs.avg ODRGll3 if Co + 9.lnCstrs.avg < cj < Co + lo0-ncStrs.avg ODRG 1 2 1 if Co+ lo.lncstrs.Ap d* I A'**'t'Sstrs.avg

App lyron Unit 2 AM-2007-006 ODRG 1 3 3 if co+ II-Ulcstrs.avg < Cj *- Co+ 12"lncstrs.avcg ODRG 1 4 3 if Co + 12-1nCstrs.avg < cj _co + 13-IncStrs.av 9g ODRG 1 5 3 if Co + 13.lncstrs.avg < cj < Co+ 14Ilncstrs.av 9g ODRG 1 6 3 if Co + 14Iflncstrs.avg < Cj Co + 15.InCstrs.av 9g ODRG 1 7 3 if Co + 15-lncstrs.avg < Cj _*Co + 16.1lCStrs.av 9g ODRG 1 8 3 if Co+ 16IlncStrs.avg <cj _Co + 17- Ilncstrs.av 9g ODRGI9

. 93 if Co+ I7Tlncstrs.avg < Cj Co+ 18"lncstrs.av 9g ODRG20 3 otherwise ODRG 1 4 Y1 <--- if cj *_ Co ODRG 2 4 if Co < cj 5 CO + IncStrs.avg ODRG3 4 if Co + Ilncstrs.avg < Cj _Co + 2-Ilncstrs.avg ODRG44 if Co+ 2.Incstrs.avg <j< C Co+ 3-Ilncstrs.avg if Co + 3. IncStrs.avg < cj co + 4- Incstrs.avg ODRG5 4 if Co + 4"Ilncstrs.avg < Cj co + 5-flncstrs.avg C

ODRG64 if CO+ 5flncStrs.avg < Cj Co + 6.lIncStrs.avg ODRG7 4 if co + 6. IncStrs.avg < Cj Co + 7-IlncStrs.avg ODRG84 if Co + 7-IlncStrs.avg < Cj Co + 8-IlncStrs.avg ODRG9 4 if Co + 8.Ilncstrs.avg < cj < Co ODRG5 4 + 9-IncStrs.avg Appendix VII Page 20 of 31

App lyron Unit 2 AM-2007-006 ODRG 11 4 if co + 9- Incstrs.avg <- cj <5 co + 10- lncstrs.avg ODRG12 4 if Co + 10o.Incstrs.avg < cj C+ I l-ncstrs.avg co ODRG 1 34 if CO+ 11'lncStrs.avg < cj CO+ 12Ilncsttrs.avg ODRGI44 if CO + 12.1nCstrs.avg < cj co + 13-Incstrs.avg ODRG154 if Co+ 13-InCstrs.avg < Cj Co + 14-Incstrs.avg ODRG 1 64 if Co+ 4-I lncstrs.avg < Cj < Co+ 15 IncStrs.avg ODRG 1 7 4 if Co + 15.lncstrs.avg < cj Co + 6.Ilncstrs.avg ODRG 1 84 if Co+ 16"lncstrs.avg < Cj CO + 17.Incstrs.avg ODRG 1 94 if Co+ 17 lncstrs.avg < cj <_ Co+ lS-IncStrs.avg ODRG204 otherwise ODRG1 5 if cj !5 Co ODRG2 5 if co < cj <5 co + Incstrs.avg ODRG3 5 if CO + Incstrs.avg < cj <5 Co + 2. Incstrs.avg ODRG45 if co + 2*lncstrs.avg < cj 5 Co+ 3-fIncstrs.avg ODRG5 5 if co +3- lncstrs.avg < cj <ý CO+4,-Incstrs.avg ODRG65 if Co + 4- lncstrs.avg < cj < Co + 5 Ilncstrs.avg ODRG75 if Co+ 5. lncstrs.avg < cj _< Co+ 6-lncstrs.avg ODRG85 if co + 6.Incstrs.avg + < cj Co + 7Incstrs. avg

,,1r1,,- :,4C , AppendixV~l. Plge,ej1f 31

App %LJ,¶J9 5 11 CO - I-ILStrs.avg . Lj 0- *1o.UICStrs.avg lyron Unit 2 AM-2007-006 ODRGI 0 5 if Co + 8.IncStrs.avg < cj < Co + 9"lncstrs.avg ODRG 1 15 if co + 9-InCStrs.avg < cj < co + 10*IncStrs.avg

!ODRG125 if co + io'lncstrs.avg < cj <ý co + IIl.Incstrs.avg ODRG13 5 if co + 11 'Incstrs.avg < cj <5 Co + 12.Ilncstrs.avg ODRG 1 45 if Co+ 12IlncStrs.avg < Cj < Co+ 13-Ilncstrs.avg ODRG15 5 if Co + 13. Incstrs.avg < cj !5 CO + 14" Incstrs.aVg ODRG 1 65 if CO + 14.lncstrs.avg < Cj < Co + 15.lncstrs.avg ODRG175 if Co+ 152lncstrs.avg < Cj < CO + 16-lncstrs.avg ODRG 18 5 if co + 16-Ilncstrs.avg < cj <CO + IT-Incstrs.avg ODRG 19 5 if Co+ T-Incstrs.avg < cj < CO+ l8"IncStrs.avg ODRG 20 5 otherwise ODRG 16 if cj <ýCo 03 <--

ODRG 26 if co < cj <5 CO + Incstrs.avg ODRG3 6 if cO + Ilncstrs.avg < Cj Co + 2- Ilncstrs.avg ODRG46 if CO + 2 lIncstrs.avg < Cj Co + 3-lncstrs.avg ODRG56 if Co + 3.lncStrs.avg < cj CO+ 4- lncstrs.avg ODRG66 if Co + 4. InCstrs.avg < Cj co + 5. Ilncstrs.avg ODRG7, if Co+ 5- Incstrs.aav ix<VCjOt& .IflCs.avg

°

App Alyron Unit 2 AM-2007 -006 ODRG 8 6 if Co + 6,IlncStrs.avg <Cj < Co + 7. Incstrs.avg ODRG 9 6 if Co + 7IlncStrs.avg <cj < Co + 8-Incstrs.avg ODRGI 0 6 if Co+ 8.1lCStrs.avg < C9 <Co+9-lncstrs.avg ODRGll6 if co + 9.lcstrs.avg < c- < Co+ 1o'lncstrs.avg ODRG12 6 if Co + 10--Incstrs.avg < ci <ý CO + II-lncstrs.avg ODRG 136 if co + 1l-IncStrs.avg < Cj < Co + 120IlncStrs. avg ODRG 1 46 if Co+ 12.lncstrs.avg < cj < Co + 13-Incstrs.avg ODRG 1 56 if co + 13.Incstrs.avg < Cj < Co + 14-InCstrs.avg ODRG166 if Co + 14- IncStrs.avg < cj < Co + 15-InCstrs.avg ODRG 1 76 if Co + 15Ilncsttrs.avg < Cj < Co + 16.InCstrs.avg ODRG 1 8 6 if co+ 16-InCstirs.avg < cj < Co+ 17.InCStrs.avg ODRG 1 96 if Co+ 17-Incstrs.avg < cj _ Co+ 18ilncstrs.avg ODRG 2 0 6 otherwise

ý0 <-- (Y0 (L.2 -1,ai (O.25.ajJ 2 (1.25.aij) 1 o5aj

-,aj l

_1.,___L 3

. 75 j -2 4"

+0 -i-01"+ _ 02 t 3 ~ 0-

App I j \1 t j \, L lyron Unit 2 AM-2007-006 j ~

/o j 2 1- a 3 "4 G 0 YI t

-- +(2 L +CY L xo(- 0.0 x1 <- 0.25 x2 <- 0.5 x3 <-- 0.75 x4- 1.0 X *--stack(x 0 ,xl ,x 2 ,x 3 ,x4 )

ST <- stack(ý0, 1,42, 3,44)

RG <-- regress(X, ST, 3) a 0 0 <- RG 3 + Pint 1 0o <- RG4 o20 +-- RG5 (Y3 0 <- RG 6 aj ARj <__--

Cj aj ATj <----

t Gau. <-- faU(Rt,ARj,ATj)

J Galj +- faL(Rt,ARj,ATj)

Gaq. 4- faQ(Rt,ARj,ATj)

G. - f ~, ATi'*

ARt, Appendix VII Page 24 of 31

,-,j ,.-  % I I '; lyron Unit 2 App AM-2007-006 Gcuj-- fcU (Rt, ARj, ATj)

Ge -- fcL(Rt, ARj, ATj)

J Gcqj <-- fcQ(Rt,ARj,ATj)

Gcc i- fcC(Rt, ARj,ATJ)

J Qj <- 1+1.464- _J if cj >_aj

+1.6 r 1 +1.464. j otherwise 0.5 K---/Tta j °5-(ao-Gauj + a l0-Galj + 020-Gaqj +30"Gacj) 0.5 KQj 'c j <0"5.i 00,-*-j

<--- 00-Gcu. +j c10. Gc. + 20 Gcqj +. 30"Gcc Ka j <- Ka.- 1.099 K j <---Kc- 1.099 K --- 9.0 if K < 9.0 Ka* otherwise J

K~jiotherwise Da <-

• C 0 -(Kai - 9.0)1.16 D__ <-- I D, .CF:._.,..-C,., if K.. <*A*Iodix VII Page 25 of 31

App I i d~ 11111 UMK u. lyron Unit 2 AM-2007-006 4.10 - 0 -CFinhr.Cblk otherwise Dc C-(Kyj - 9.0)1.16 Dcgj --- Dcj-CFinhr.Cblk if K, < 80.0 4 o.CFinhr.Cblk otherwise outputj, 0 <- j outputj, I- aj outputj, 2 -- Cj - Co OUtPUtj, 3 - Dagj OUtPUtj, 4 <- Dcgj OUtPUtj, 5 <-- Ka j

OUtpUtj , 6 +- Kc NCBj 365-24 outputj, 8 -- Gauj J

outputj,9q< Gal outputj, 10 <-- Gaqj outputj, I I <-- Gac J

OUtpUtj, 12 <- Gcu.

J OUtPUtj, 13 <-- Gcl.

• ,*,. , i,,_Apper ndix VII Page 26 of 31

App U L FUt l J, 14 v-- %.cqj 3yron Unit 2 AM-2007-006 OUtPUtj, 15 <-- Gcc.

J NCBj 365.24 outputj, 16 +-.98 1.5 j +---j + I aj*- ajI + Dagj_

Cj ** cI + Dcgj_

aj-- It if aj_>t aj otherwise NCBj +- NCBjI + Cblk output k:= 0.. Ilim ProPkflgff = 0.8 Appendix VII Page 27 of 31

Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix VII Flaw Growth in Length Direction U

~-1 0.5 0

Cu 0

0 1 2 3 4 5 6 7 8 Operating Time (fuel cycles}

Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.8 inch. Thus the time available for the flaw growth by PWSCC is about 6.42 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix VII Page 28 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction 0.61 0.5 0.4 0.3 0

0.2 CZ 0.1 0L.

0 1 2 3 4 5 6 7 8 Operating Time Ifuel cycles)

Flaw growth in the depth direction, as a function of Hot Operating Years. The extension of the 'a-Tip" or the maximum depth is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 6.42 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.293 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix VII Page 29 of 31

Appendix VLJ Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Intensity Factors "3.4 L.2 co 0 I 0 1 2 3 4 5 6 7 8 Operating Time (fuel cyclesI Depth Point Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher WKvalue at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix VII Page 30 of 31

Appendix VII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 0

E The influence coefficients as a function of operating time is shown. The behavior for "8

the "a-tip" shows the effect of the flaw U aspect ration for the initial flaw and early growth. In the time period of interest (6.42 fuel cycles), no erratic behavior of the influence coefficients is observed.

C 0 2 4 6 8 Operating time {fuel cycles}

"a" - Tip -- Uniform

. - "a" - Tip -- Linear

......... a" - Tip -- Quadratic

........... a" - Tip -- Cubic c" - Tip -- Uniform

. c'- Tip -- Linear "c" - Tip -- Quadratic c" - Tip -- Cubic Appendix VII Page 31 of 31

Appendix VIII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw beveloped by: J. S. Brihmadesom

References:

1) "StressIntensity factors for Part-throughSurface cracks,a NASA TM-111707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion EngineeringCalc. C-7770-00-1, Rev.0, "Byron/BraidwoodCRDM PenetrationResidual Stress Evaluation.0 Byron Nuclear Station Unit 2 Reactor Vessel CRDM -"47.0" Degree Nozzle, "0"Degree Azimuth ("Downhill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed, as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 75th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factor is appliedduring the determinationof the crack extension to obtain the value in English units (inch/hr).

NoAte :- 1) Use of SICFtables from Reference 1 for Emternal flaws (Tables 2 and 4).

2) The stress distributionis from the OD to the ID (whereasthe stress distributionfrom Reference 3 is from ID to 0D).

These differences are noted (in bold redprint) at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5" below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL Strs.Dist) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Pojit ) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the "Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix VIII Page 1 of 31

Appendix VIII Evaluation of PWSCC Crack Growth ol PostulatedFlaw in CRDM NozzJes at Byron Unit 2 AM-2007-006 CRDMIength.eva1 := 2.15 CRADM Tube Length for Crack Growth Calculation, Use the length of the tube where the through wall stress distributions will be defined.

ULStrs.Dist := 2.15 Upper extent of the Stress bistribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint :2 To place the flaw with respect to the reference point, the flaw tips or flaw 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 't- tip" located at the reference point (Enter 3).

Val:= 2 Input Data :-

I := 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

a0 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 24 Number of Hot Operating Years for Analysis Appendix VIII Page 2 of 31

Appendix VII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Ilim := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

(X0c := 2.67 10- 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; (MRP-55 Rev. 1}

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 11 Ro :="2od id t Rid := 2 t:= Ro - Rid Rm := Rid + Timopr:= Years.365.24

'rim 1 Rm C~inh := .417- 105 Cblk =Timopr Pmtblk :=1 50 1 Rt :=

Ilim t

- Qg ( I I Temperature Correction for Coefficient Alpha e 1.103 10- THead+459. 6 7 .67 0 CC = C0 1 75 th percentile MRP-55 Revision 1 Appendix VIII Page 3 of 31

Appendix VII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Input Data Input all availableNodal stress data in the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recordedon data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress dataat each Elevation (ksi)

Column "5"= 80% Thickness Stress data at each Elevation (ksi)

Column "6" = OD Stress Data at each Elevation (ksi) 0.0 18.582 19.647 19.958 21.730 21.285 15.119 0.5 27.445 36.287 46.454 59.529 76.537 93.935 AllData 1.075 29.803 35.298 43.181 46.293 45.767 49.986 1.65 51.366 52.738 54.092 56.267 46.012 9.509

.2.15 52.738 49.990 47.397 46.028 46.446 33.237, IDA,, := AllData(I)

AXLen := AllData(°) ODA, := AllData(6)

Stress Distribution

~All 01 1 1 I1 J 0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 2 2.2 AXLen Axial ht. - for Analysis [inch]

Appendix VIII Page 4 of 31

Appendix VUI Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Observing the stress distributionselect the region in the table above labeledDataA,, that represents the region of interest.This needs to be done especially for distributionsthat have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data"statement below and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (pastesymbol).

0.0 18.582 19.647 19.958 21.730 21.285 15.119 0.5 27.445 36.287 46.454 59.529 76.537 93.935 Data:= 1.075 29.803 35.298 43.181 46.293 45.767 49.986 1.65 51.366 52.738 54.092 56.267 46.012 9.509 2.15 52.738 49.990 47.397 46.028 46.446 33.237 Axi : Data(0) ID :=Data(]) Twty:= Data(2) Frty := Data(3)

Sxty := Data(4) Egty := Data(5) OD := Data(6)

RID:= regress(Axl,ID,3) RTwty regress(Axl, Twty, 3) RFrty := regress(Axl, Frty, 3)

RSxty := regress(Axl, Sxty, 3) REgty regress(Axl, Egty, 3) ROD:= regress(Axl,OD, 3)

FLCntr := Refpoint - co if Val = 1 Flaw center Location Location above Nozzle Bottom RefPoint if Val = 2 Refpoint + co otherwise Appendix VIII Page 5 of 31

Appendix VIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 ULStrs.Dist - UTip UTip : Cntr + C0 lncstrs.avg :p 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N := 20 Number of locationsfor stress profiles LOoj:= FLcntr- 1 i:=i..N+3 Incri:= cO if i< 4 Incstrs.avg otherwise Loci := Loci-I + Incri 2

SIDi:= RD3 + RID4"Loci + RID5 (Loci) + RID6.(Loci) 3 STwtyi := RTwty3 + RTwtY4 Loci + RTwtY- (Loci)' + RTwtY6(Loci)

SFrtyi RFrtY3 + RFrtY4 -Loci + RFrtyY5(Loci) 2

+ [ RFrtY6-(Loci)3I SSxtyi Rsxty3 + RSxtY4 "Loci + RSxtYs (Loci) 2 + [ RSxtY6 "(Loci)31 Appendix VIII Page 6 of 31

Appendix 'Vill Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 SEgtyi := REgtY3 + REgtY4 Loci + REgty -(Loci) 2 + REgtY6-(Loci) 3 SODi:= ROD 3 + ROD 4 .Loci + RODs. (Loci) 2

+ RoD6"(Loci) 3 Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 I I I I I I I I I I ID 40 SIDi 20 I I I I I I I I I I 0

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Axl, Loci 100 OD SODi 50 0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 AxI,Loci Appendix VIII Page 7 of 31

Appendix VIII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CROM Nozzles at Byron Unit 2 AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j := i .. N SIDj+SIDj+1 +SIDj+ 2 ifj STwtyj + STwtyj+j+ STwtyj+ 2 if =

Sid. 3 STwtyj.-'-

J 3 Sid .(j + I) + SIDj+ 2 STwtyj- (j + i) + STwtyj+ 2 otherwise otherwise j+2 j+2 SFrty + SFrtyj~+ +SFrtyj+2 if i=I SSxtyj + SSxtyj+i + SSxtyj+ 2 if j =

SFrtY : SSxtyj.-'

3 3 SFrtyj_ l + I) + SFrtyj+ 2 SSxtyj_I (j + 1) + SSXtYj+2 otherwise oUIICI W se; j+2 j+2 SODj + SODj+I + SODj+ 2 if j =

SEgtyj + SEgtyj+l+ SEgtyj+2 if =

5 Egtyj -"

Sod. 3 3 j Sodj_*(j + l) + SODj+

SEgtyj_ (j + 1) + SEgtyj+ 2 2 j+2 otherwise otherwise j+2 Elevzffon-A veraged Hoop Stress Distributionfor OD Flaws (i.e. Stress distributionchanged from OD to §D )

U0 := 0.000 UI := 0.20 U2 := 0.40 U3 := 0.60 u4 := 0.80 U5 := 1.00 Appendix Vill Page 8 of 31

ApIe ndix VIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 MV-2007-006 Y := stack(u 0 ,ul,u 2 ,u 3 ,u 4 ,u 5 )

SIG 1 stack(Sod, SEgty,,SSxty,, SFrty,, Twy,'Sid,) SIG 2 stack(Sod2, SEgty2'SSxty 2' SFrty2, STwtY2, Sid2)

SIG 3 stack(Sod3 , SEgty3,SSxty3 , SFrty3, STwty' ,Sid 3) SIG4 stack( Sod 4 , SEgtY4, SSxtY4, SFrty4, STwtY4, Sid,)

SIG5 stack( Sods, SEgty 5 ',SxtY5 SFrty 5 , STwty5 ,Sids) SIG 6 stack(Sod 6 ,S Egty 6 'SSxty6 SFrty6, STwty6, Sid 6)

SIG 7 := stack (Sod7 SE Egty 7, SSFrtY7' STWtY' SSd7) SIG 8 := stack (Sod 8 SEgty 8 , SSxty8, SFrty 8 , STwty8 , Sid8 )

SIG9 :=-staok(Sod9 sEgty, S~xty' SFry9 ',STwy' id9) lO- stac10(Sodo, 'Egty, 0 'Sxtyo ',Frty 1 o'Twty1 ,' Silo SIG1 1 stack(sod, SEgty, ,SSxty,,SFrty, , STwtyI, Sid,') SIG 12 stack(Sod 1SEgtY 'SSxty12 ' SFrtYz, 2 STwty,21Sid12)

SIG 1 3 stack(Sod 1, SEgty3,Ssxty,3,SFrty,3 STwty13, Sid13) SIG 1 4 (

stack Sod4 SEgty 4, SSxtYI4, SFrty14, STwty 14Sid1 4)

SIG 1 5 : stack(Sod15, SEgtY15, SSxtY.5,SFrty5, STwtY 15'Sid,5) SIG 1 6 stack(Sod16' SEgtY6 ' SSXtY, 6SFrtY.6, STwtY , Sid16 )

SIG 1 7 :stack Sod 17'SEgtY17, SsxtY17, SFrtY, 7' STwtY17, Sid17) SIG 18 stack(Sod 8, SEgty,8, SSXtY1 8 , SFrty 1 8 STwtY , 'Sid1 8)

SIG 1 9 stack (Sod 9, SEgtY19, SSxty 9 ', SFrty1 9, STwtYl 9 )Sid,9) SIG2 0 stack (Sod 2 0 SEgtY20,

' SSxtY20, SFrtY20 , STwty20, Sid20)

Appendix VIII Page 9 of 31

Appendix VIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 regress(Y,SIG 1 ,3) ODRG 2 := regress(Y,SIG 2 ,3)

ODRG 3 regress(Y, SIG 3 , 3) ODRG4 :: regress(Y,SIG 4 ,3)

ODRG 5 regress(Y, SIG5 ,3)

ODRG6 regress(Y, SIG 6 ,3)

ODRG 7 regress(Y, SIG 7 , 3) ODRG 8 regress(Y,SIG 8 ,3)

ODRG 9 := regress(Y,SIG 9 ,3) ODRGI 0 := regress(Y, SIG 10 , 3)

ODRG II: regress(Y,SIGll,3) ODRG1 2 regress(Y,SIG 12 ,3)

ODRG 1 3 regress(Y,SIG 1 3 ,3) ODRG1 4 regress(Y,SIG 1 4 ,3)

ODRGI 5 regress(Y,SIG 1 5 ,3) ODRG 1 6 regress(Y ,SIG 16 ,3)

ODRG 1 7 regress(Y,SIG 1 7 ,3) ODRG 1 8 regress(Y,SIG 1 8 , 3)

ODRGI 9 regress(Y,SIG 1 9 ,3) ODRG 2 0 regress(Y,SIG 2 0 ,3)

Appendix VIII Page 10 of 31

Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix VIII Stress Distribution in the tube. Stress influence coefficients obtained from thirdorder polynomial curve fit to the through wall stress distribution PrOPLength = 0.5 Flaw Propagation of top tip to above J-Weld top PrOPLength := ULStrs.Dist - FLCntr - Co - 0.5 Data Files for Flaw Shape Factors from NASA (NASA-TM-1 11707-SC04 Model)

{NO INPUT Required)

Date TRabewa Saur Fur aws Vrof ePrtethoce wIg allFa Cy2 4)nder Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb :=

0 1 2 ihe Table on the left "Jsb"consists of the cylinder and flaw mechanical 0 1.000 0.200 0.000 parametersas follows:

1 1.000 0.200 0.200 Column "0" :- Contains the mean-radius to thickness ratio (Im /t) of the Cylinder 2 1.000 0.200 0.500 3 1.000 0.200 0.800 Column "1":- Contains the Flaw Aspect Ratio (a/c)

Column "2".:- Contains the Flaw Depth-to- Tube- Thickness ratio (a/t) 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 Appendix VIII Page 11 of 31

AppendixI is 2.0001 0.200 0.000 1Crack Growth of PostulatedFlawin CRDM NozzJes at Byron Unit 2 AM-2007-006 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 51 10.000 0.400 0.200 Appendix VIII Page 12 of 31

AppendixI 52 10.000 0.400 0.500 Crack Growth of Postulated Flaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 74 300.000 1.000 1.000 The Table below "Sambi"containsthe Flaw Influence coefficients as follows:

Column "0":- Contains the influence coefficients for Uniform Loading at the maximum depth of the flaw ("a"-tip) 1" Containsthe influence coefficients for LinearLoading at themaximum depth of the flaw ("a"-tip)

Column I:-

Column "2" :- Contains the influence coefficients for QuadraticLoadingat themaximum depth of the flaw ("a"-tip)

Column "3" :- Contains the influence coefficients for Cubic Loading at the maximum depthof the flaw ('a"-tip)

Column "4":- Contains the influence coefficients for Uniform Loading at the surfacepoint of the crack front ("c"-tip)

Column "5" :- Contains the influence coefficients for LinearLoading atthe surfacepoint of the crack front ("c "-tip)

Column "6" :- Contains the influence coefficients for QuadraticLoading atthe surface pointof the crack front ("c "-tip)

Column "7" :- Contains the influence coefficients for Cubic Loadingatthe surface pointof the crack front ("c"-tip)

Appendix VIII Page 13 of 31

Appendix VIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Sambi 0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1.054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0.102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 2.51 1.178 0.7821 AplAAWl Vill Pagel tl*:f 31 0.242 0.097 0.051 m

Appendi 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073 AM-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1.096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 601 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendx VIII Page 150- 31

Appendix VM Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 In the declarationsbelow, dummy variables are defined in order to develop a continuousfunction for the various influence coefficients. A continuous function can then be readily used inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysiswith a thirdorderpolynomial for Rm /t less than 4.0 and a second orderpolynomial for the higherratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters k It ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsbo, is a column array containing the Rn A ratio, which is also Column "'0"in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W :=Jsb(o) X :=Jsb~') Y := Jsb(2) au :Sambi(O> aL: Sambi~i) aQ Sambi(2) ac : Sambi(3) cU Sambi(4> cL= Sambi(5) cQ Sambi(6 cc: Sambi (7) n := 1312 if hwRt 4.0 otherwise Order of polynomial selected based on R m/t ratio The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a"-tip is defined as:

Fau (W,X,Y) which is the standard nomenclature is F.u (R m. , a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (r It, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix VIII Page 16 of 31

Appendix VIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 "a-Tip" Coefficients "a-tip" Uniform Term MaU:= augment(W,X,Y) VaU := aU RaU := regr~ess (MaU 9VaU, n) fau(W,X,Y) := interp RaU,Mau,Vau, "a-tip" Linear Term MaL:= augment(W,X,Y) VaL:= aL Ra=regress ( Mayva,n) faL(W,X,Y) := inter RaLMaLVaL{X}

"a-tip" Quadratic Term MaQ:= augment(W,X,Y) VaQ := aQ RaQ :=regress (MaQ,VaQ,n) faQ(W,X,Y) : 7aQ'VaQ7LX1 "a-tip" Cubic Term MaC:= augment(W,X,Y) VaC := aC RaC :=regress( MaC, VaC,n) faC(W,X,Y) := interp RaC,MaC,VaC, X "c" Tip Coefficients "c-tip" Uniform Term MCU := augment(W,X,Y) VC =Cu RcU := regress (McU, VcU, n) fCU(,XY:=iterp[RCU7MCU 7VCUrX~J Appendix VIII Page 17 of 31

Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Appendix VHI "c-tip" Linear Term McL:= augment(W,X,Y) VcL := CL RcL := regress( McL, VcL,n) fcL(W,X, Y) := interp RcL, McL, VcL, "c-tip" Quadratic Term McQ:= augment(W,X,Y) VCQ:= CQ RCQ := regress (MCQ , VCQ ,n) XY):=interp{RCQ) MCQ' VCQ{IX~J fcQ(W fCQ(WY.)Y "c-tip" Cubic Term

('W McC:= augment(W,X,Y) VC:Ccc R~C := regress (MCC, V~C,n) fcc(W,X,Y) := VCC, X Jl_

Appendix VIII Page 18 of 31

Appendix VIII Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculationof PW5CC Crack Growth as a function of Hot Operating Time CGRsambi j <- O co c0 NCBo <- Cblk while j < Ilim a0 ODRG 1 3 if cj <Co ODRG 2 3 if Co < cj < Co + Incstrs.avg ODRG 3 3 if CO + Ilncstrs.avg < Cj < CO + 2 lncstrs.avg ODRG4 3 if Co+2,lncStrs.avg < cj 5 CO+ 3-lncstrs.avg ODRG 5 3 if CO+ 3-Incstrs.avg < Cj < Co + 4-lncStrs.avg ODRG 6 3 if Co + 4-InCstrs.avg < Cj < co + 5.lncstrs.avg ODRG 7 3 if co + 5-IncStrs.avg < cj Co + 6.IncStrs.avg ODRG 8 3 if co + 6-IncStrs.avg < Cj < Co + 7-lncstrs.avg ODRG 9 3 if Co + 7-lncstrs.avg < Cj < Co + 8 lfncstrs.avg ODRGI 0 3 if Co+ 8.1nCstrs.avg < cj < co+991nCStrs.avg ODRGII3 if Co + 9-lncstrs.avg < cj < cO + Io-Incstrs.avg ODRG1 2 , if co + jo-IncstrsWh f iCb IM'Strs.avg

App Ap lyron Unit 2 AM-2007-006 if Co + 12Ilncstrs.avg < Cj _ Co + 12-IncStrs.aav 9g if co+ 12.Ilncstrs.avg < Cj _ Co+ 13-IncStrs.av 9g if Co + t3*lncstrs.avg < cj CO + 14Ilncstrs.av 9g if CO+ 14 IncStrs.avg < cj _co+ 15.6IncStrs.av 9g 3if Co + 15-Ilncstrs.avg < cj _5Co + 16"Incstrs.av 9g if co+ 16-Ilncstrs.avg < Cj __Co+ 17.IlncStrs.av 9g if Co + 17 InCstrs.avg < c j ! Co + 18-IncStrs.av 9g otherwise if cj _Co if co < cj < co + IncStrs.avg if CO + Ilncstrs.avg < Cj 5 Co + 2- Incstrs.avg if Co+ 2-IncStrs.avg < cj_ CO+ 3-Incstrs.avg if CO+ 3IlncStrs. avg < cj _*Co + 4*Incstrs.avg if Co + 4Ilncstrs.avg < cj < co + 5-Incstrs.avg if co + 5-IncStrs.avg < cj _* co + 6.Incstrs.avg if co + 6. IncStrs.avg < cj < Co + 7. fnCstrs.avg if Co + 7 IlncStrs.avg < ci -<co + 8.IncStrs.avg if co + 8 -[nCstrs.avg < cj *_ co + 9-IncStrs.avg

.4 Appendix VIII Page 20 of 31

lyron Unit 2 AM-2007-006 App ODRGll 4 if co +9- Incstrs.avg < cj _<ý co + 1o'Incstrs.avg ODRG 1 24 if Co+ 10Ilncstrs.avg < cj _*CO+ liIncstrs.avg ODRG13 4 if co + 11 .Incs trs.avg < cj _<co + 12. Incstrs.avg ODRG14 4 if co + 12.1lnCStrs.avg < cj _5co+ 13.Ilncstrs.avg ODRG15 4 if Co + 13,InCstrs.avg < cj < co + 14-Ilncstrs.avg ODRG1 64 if C + 14b ncstrs.avg < cj _ Co+ 15.Ilncstrs.avg ODRG 1 74 if Co+ 1"5cstrs.avg < cj Co+ 16-lncstrs.avg c

ODRG1 84 if Co+ 16I*lncstrs.avg < Cj _<Co + IT-lncstrs.avg ODRG 1 94 if Co+ 17 Incstrs.avg < Cj 5 Co+ 18Ilncstrs.avg ODRG20 4 otherwise ODRG1 5 if cj <5co ODRG2 5 if co < cj _<co + Incstrs.avg ODRG35 if Co+ Ilncstrs.avg < cj _ Co+ 2-Incstrs.avg ODRG45 if co+ 2.Incstrs.avg < cj _< co+ 3.lncStrs.avg ODRG55 if co + 31 lncstrs.avg < cj <_ Co + 4Ilncstrs.avg ODRG65 if Co + 4. Incfstrs.avg < Cj _* Co+ 5. Incstrs.avg ODRG75 if CO + 5jIncstrs.avg < cj _co + 6-Incstrs.avg ODRG85 if CO + 6Ilncstrs.avg < cj co c + 7.lncStrs.avg

,rr,-, iC - .2, -Crs Apgni<xCVllC0 P,+gL,2t... 31 v

App 9 5 I CO -V " UlCStrs.avg , Cj

• 1o -t-I" ucStrs.avg JLJISA5J lyron Unit 2 AM-2007-006 ODRGI 0 5 if co + 8-lncstrs.avg < Cj _ co + 9.Incstrs.avg ODRGIIl5 if co + 9. lncstrs.avg < cj S_ co+ 10. lncstrs.avg ODRG 1 25 if Co + 10.Incstrs.avg < cj _ CO + II-Incstrs.avg ODRG13 5 if Co + 11 .Incstrs.avg < cj <_ýco + 12. Incstrs.avg ODRG 145 if Co+ 12.Ilncstrs.avg < cj _<co+ 1 3.IncStrs.avg ODRG 1 55 if co+ 13- Ilncstrs.avg < cj _ co+ 14"IncStrs.avg ODRG16 5 if co + 14.Ilncstrs.avg < ci _ CO + 15.1lnCStrs.avg ODRG 1 75 if Co+ 15I*lncstrs.avg < cj _ co+ 16.-nCstrs.avg ODRG 1 85 if Co+ 16- Incstrs.avg < Cj _ co+ 17-1nCstrs.avg ODRG195 if Co + 1I lncstrs.avg < Cj _<cO + 18-Incstrs.avg ODRG 20 5 otherwise ODRG 16 if cj !5 Co 5

ODRG 26 if co < cj _<co + Incstrs.avg ODRG36 if Co+ Incstrs.avg < cj _< Co+ 2-Incstrs.avg ODRG46 if Co+ 2 Incstrs.avg < cj _5co + 3- Incstrs.avg ODRG56 if Co+ 3. Incstrs.avg < Cj<_ Co+ 4-IncStrs.avg ODRG66 if Co + 4jIncstrs.avg < cj _<co + 5"Incstrs.avg ODRG7, if cO + 5 - +ncstrs.atWeixAIvgP*'lf@ avg

0 *lyron Unit 2 AM-2007-006 App ODRG8 6 if co + 6-IncStrs.avg < cj < Co + 7-lncstrs.avg ODRG 9 6 if co + 7*IlncStrs.avg < cj < co + 8-Incstrs.avg ODRGI 0 6 if Co+ 8-lncstrs.avg < cj < Co+9Ilncstrs.avg ODRG 1 1 if CO + 9*IncStrs. avg < cij < Co+ IoIlncStrs.avg ODRG 1 2 6 if Co + lo.ncstrs.avg < cj < cO + 11- lncStrs.avg ODRG 1 3 6 if co + I I-lncStrs.avg < cj 5 co + 12IlncStrs.avg ODRG 1 4 6 if co + 12*Incstrs.avg < Cj Co + 13 Ilncstrs.avg ODRG 1 5 6 if co + 13IlncStrs.avg < Cj CO + 14IlncStrs.avg ODRG 1 6 6 if co + 14.Incstrs.avg < Cj < Co + 15-IncStrs.avg ODRG 1 7 6 if co + 15.IncStrs.avg < cj < co + 16* ncstrs.avg ODRG 1 8 6 if co+ 16'IlncStrs.avg < cj 5 Co + 7. IncStrs.avg ODRG 19 6 if Co+ 17IlncStrs.avg < cj < Co + 18Ilncstrs.avg ODRG 2 0 6 otherwise

ý0 <-- GO L5*a 2 3 (o._25.aj) f( L 2 Oa+ (Yy O'°G 0 '2 41

ý2<--G Y + CF2J 2+0-(t -5a) 3

(~*arýJa)

.75 -aj 0.75-aj 2 0.75 3a

(

43 < +y - +O 2 1

+2 pe 6a--li&"IagtFO+in5aof 31

App lyron Unit 2 AM-2007-006

\t + \ t + 3 t x 0 (-o0.0 x, (-- 0.25 x2 <- 0.5 x3 <- 0.75 x4- 1.0 X <-- stack(x 0 ,xI ,x 2 ,x 3 ,x 4 )

ST <-- stack(ý0,ýl,ý2,3,ý4)

RG <- regress(X, ST, 3) r00*-+- RG 3 + Pint a 10 <-- RG 4 Y20 <-- RG 5 aY3 0 +- RG6 aj Cj aj ATj <_--j t

Gau. <--- fau(Rt,ARj,ATj)

Gal -- faL(Rt,ARjATj)

J Gaqj <- faQ (Rt, ARj, ATj)

G, - f,,r(Rt,ARi,ATi) Appendix VIII Page 24 of 31

sý Ia ,

App L

iyron Unit 2 AM-2007-006 Gcu"i <-- fcU(Rt,ARj,ATj)

GCi <-- fcL(Rt,ARj,ATj) j Gcqj <-- fcQ(Rt,ARjATJ) c <-- fcc(Rt,ARj,ATj)

J Qj <-- I + .464- if cj > aj kcj)

/1.65 1 + 1.464. cj 1 otherwise (aj)

Kaj<---* Qj "(aO00Gauj+ ao0Galj+20"Gaqj+ y30Gacj) 0.5 Kc- f-rCj) .(o.~ +,uiO-Gc +F 2 0-Gcq +a -G~i j

i -00"Gcu + i cq j + CY30 ccj)

K0C --Ka. *1.099 J J K j<-- Kc.-1.099 yj Ko <-- 9.o if Ka 5<9.0 J

K(Xji otherwise

<- 9.0 if K !59.0 l(j otherwise Da. (Koaj 9.0) 1'6 J

D-- <- I D- -CF:.-tCn, if K,- AMl dix Vill Page 25 of 31

App ,arj aj u"u UI tU.j Iyron Unit 2 AM-2007-006

-14.0- °-CFinhr.Cblk otherwise Dcj <-- Co-(K~ j - 9.0)1.16 Koj < 9e.i otherwise outputj , 0 <- j outputj, I <-- aj OUtPUtj, 2 <- Cj - Co outputj, 3 -- Dagj OUtPUtj, 4- Dcgj OUtPUtj, 5 <-- Ka OutPutj, 6 K-c NCBj output j, 7* -365-24 OUtPUtj, 8 - Gauj outputj, 9 --Gal.

J outputj, 10 <- Gaqj outputj, I I -- Gac.

OUtPUtj, 12 <-- Gcu.

J output j, 13 <-- Gcli Appendix VIII Page 26 of 31

yron Unit2 AM-2007-006 App UUtPULj, 4kV- Jcq Outputj, 15 <-- G cc.

J NCBj 365.24 OUtpUtj, 16 - *

-.98 j<--j+ I aj <-- aj_, + Dagj_ 1 cj <--Cj-i + DcgjI aj<-- It if aj_>t aj otherwise NCBj <- NCBj_1 + Cblk output k :=o.. Ilim PrOPiength = 0.5 Appendix VIII Page 27 of 31

Appendix VII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Length Direction I I I I II, I I3.75

.5 0.5 F 0 -..

,.,- - -- - - - - - -- - - -I-I-I-I-I - - -- - - - - ---- - - - - -- - - - ------ ----

CoI 0

0 2 4 6 8 10 12 14 16 Operating Time {fuel cycles}

Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.50 inch. Thus the time available for the flaw growth by PWSCC is about 13.75 fuel cycles. When the upper tip of the flaw reaches the weld root, a leakage path to the nozzle annulus can be established. Thus this calculation estimates the operating time to the initiation of leakage.

Appendix VIII Page 28 of 31

Appendix Vill Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Flaw Growth in Depth Direction 0.6 0.5 U

C 0.4 0.

0.3 0

I-.

0.2 0.1 0 2 4 6 8 10 12 14 16 Operating Time Ifuel cycles}

Flaw growth in the depth direction, as a function of Hot Operating Years. The extension of the 'a-Tip" or the maximum depth is shown. The available propagation depth to the ID surface is about 0.50 inch. The flaw depth at the calculated Hot Operating Time of 13.75 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.32 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix VIII Page 29 of 31

Appendix VIII Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM Nozzles at Byron Unit 2 AM-2007-006 Stress Intensity Factors

." 80 413.75

-* 60 4.

0 40 U 20 0 ,-IALo I I I , 1I 0 2 4 6 8 10 12 14 16 Operating Time (fuel cycles)

Depth Point

.......... Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher "Ka value at the surface point. The geometry of this initial flaw and the through wall stress distribution causes the flaw to grow faster in length than in depth.

Appendix VIII Page 30 of 31

Appendix V111 Evaluation of PWSCC Crack Growth of PostulatedFlaw in CROM Nozzles at Byron Unit 2 AM-2007-006 Influence Coefficients - Flaw 1.4 13.75F 1-1.2 0

E 0.8

.4_

I __ __ __ __ The influence coefficients as a function of

• 0 operating time is shown. The behavior for the "a-tip" shows the effect of the flaw 0.6 aspect ration for the initial flaw and early U

growth. No erratic behavior of the influence coefficients is observed.

0.4 C

0.2 (1

0 5 i0 15 Operating time {fuel cycles}

"a" - Tip -- Uniform "a" - Tip -- Linear Ita" - Tip -- Quadratic a" - Tip -- Cubic c" - Tip -- Uniform "c' - Tip -- Linear c" - Tip -- Quadratic "c" - Tip -- Cubic Appendix VIII Page 31 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Primary Water Stress Corrosion Crack Growth Analysis - OD Surface Flaw Developed by: 3. S. Brihmadesam

References:

1) "StressIntensity factors for Part-throughSurface cracks,"NASA TM-I11707, July 1992.

2) Crack Growth of Alloy 600 Base Metal in PWR Environments, EPRI MRP Report MRP 55 Rev. 1, 2002.

3) Dominion EngineeringCalc. C-7770-00-1, Rev.0, "ByroniBraidwoodCRDM PenetrationResidual Stress Evaluation."

Byron Nuclear Station Unit 2 Reactor Vessel CRDM -"47.0" Degree Nozzle, "180" Degree Azimuth rUphill")

Synopsis: The following PWSCC crack growth analysis predicts the growth of an OD initiated flaw, which has an initial size at the NDE detection limit. The evaluation process uses: 1) fracture mechanics model developed in Reference 1; 2) the stress distribution (welding residual + operating stresses) from Reference 2: and, 3) the crack growth law developed in Reference 3. The crack growth is computed, as a function of Hot Operating hours (time at operating temperature), to determine the growth time until the upper flaw tip reaches the root of the J-groove weld. In the analysis the flaw face is pressurized to the Operating Pressure and the crack growth law is for the 7 5th percentile curve from Reference 2.

Note : The input of data are in English units. The crack growth equation from Reference 2 is in Metric units. Therefore, a conversion factoris applied during the determination of the crack extension to obtain the value in English units (inch/hr).

Note :- 1) Use of SICF tables from Reference I for External flaws (Tables 2 and 4).

2) The stress distributionis from the OD to the ID (whereas the stress distributionfrom Reference 3 is from ID to OD).

These differences are noted (in bold red print)at the appropriatelocations.

Analysis Input:

1) The through wall stress distribution, provided in Reference 3, is for a length of CRDM tube extending from 0.5" below the weld bottom and extending to 0.5" above the top (weld root) of the weld. This distance in this analysis is defined as the CRDM Length.eval

2) The upper axial extent (UL Strs.Dist) on the CRDM where the trhough wall stress distribution exists. For the current evaluation it is the same value of the length for analysis.

3) A reference point (Ref Point) to locate the flaw is established at the midpoint of the evaluation extent.

4) The flaw can be located in one of three ways as described for the 'Val" variable. This feature provides the location for the initial flaw and is used to define the average stress distribution for fracture mechanics analysis.

5) The Input Data definitions are provided with their respective input parameter.

Appendix IX Page I of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 CRDMLength.eval1 2.80 CROM Tube Length for Crack Growth Calculation, Use the total length for the stress distribution.

ULStrs.Dist := 2.80 Upper extent of the Stress Distribution used for analysis (The Highest Elevation for which stress data exists)

CRDMLength.eval RefPoint :2 To place the flaw with respect to the reference point, the flaw tips or flaw 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 'T- tip" located at the reference point (Enter 3).

Val := 2 Input Data :-

I := 0.15 Initial Flaw Length (minimum Detectable Length by NDE); Inch.

ao 0.075 Initial Flaw Depth (minimum Detectable Depth by NDE); Inch.

od 4.00 Tube OD; From Design Information; Inch.

id 2.75 Tube ID; From design Information; Inch.

Pint := 2.235 Design Operating Pressure (internal) Used to define Crack face Pressure only; ksi.

Years := 12 Number of Hot Operating Years for Analysis Appendix IX Page 2 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006

]rim := 30000 Iteration limit for Crack Growth loop (Larger number has higher calculational accuracy)

THead := 558 Estimate of Operating Temperature of Reactor Vessel Head; Deg. F.

(Xc :=.2.67.10- 12 Constant in MRP-55 Rev. 2; PWSCC Model for 1-600 Wrought @ 617 deg. F Qg := 31.0 Thermal activation Energy for Crack Growth; {MRP-55 Rev. 1}

Tref := 617 Reference Temperature for normalizing Data Deg. F; {MRP-55 Rev. 1) od id R0 2 Rid:= t:= Ro -Rd Rm= Rid+ Timopr := Years.365.24 Timopopr Ilim 1 Rm CFinhr := 1.417.105 Cblk := Pmtblk := I"5-I 2o:= Rt : =

hlim t Temperature Correction for Coefficient Alpha 1.0-0 3 ýTHead+459.67 Tref+459.67~

C0, := e 0Oc Co := Co 1 75 th percentile MRP-55 Revision 1 Appendix IX Page 3 of 31

Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Appendix IX Stress Input Data Input all available Nodal stress data in the table below. The column designationsare as follows:

Column "0" = Axial distance from minimum to maximum recordedon data sheet (inches)

Column "1" = ID Stress data at each Elevation (ksi)

Column "2" = 20% Thickness Stress data at each Elevation (ksi)

Column "3" = 40% Thickness Stress data at each Elevation (ksi)

Column "4" = 60% Thickness Stress data at each Elevation (ksi)

Column "5" = 80% Thickness Stress dataat each Elevation(ksi)

Column "6" = OD Stress Data at each Elevation (ksi) 0.0 55.812 52.589 49.655 43.496 34.470 16.786 0.5 52.917 54.783 56.949 58.918 61.883 51.753 AllData 1.40 55.710 60.621 66.299 70.417 73.203 71.301 2.30 47.831 47.386 48.238 44.776 37.177 45.729 2.80 42.404 33.332 19.496 6.705 -10.543 -28.306)

IDAI1 := AllData(l0 AXLen:= AllData(0) ODAI1,:= AllData(6)

Stress Distribution IDAII fJ~

ODAJI C.)

I..

-50 0 0.2 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 AXLen Axial ht. - for Analysis [inch]

Appendix IX Page 4 of 31

Appendix IX Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Observing the stress distributionselect the region in the table above labeled DataAll that represents the region of interest. This needs to be done especially for distributionsthat have a large compressive stress at the nozzle bottom and high tensile stresses at the J-weld location. Copy the selection in the above table, click on the "Data"statementbelow and delete it from the edit menu. Type "Dataand the Mathcad "equal"sign (Shift-Colon) then insert the same to the right of the Mathcad Equals sign below (pastesymbol).

0.0 55.812 52.589 49.655 43.496 34.470 16.786 0.5 52.917 54.783 56.949 58.918 61.883 51.753 Data := 1.40 55.710 60.621 66.299 70.417 73.203 71.301 2.30 47.831 47.386 48.238 44.776 37.177 45.729 2.80 42.404 33.332 19.496 6.705 -10.543 -28.306)

AxI := Data(0) ID: Data( I) Twty :=Data(2) Frty := Data(3)

Sxty :=Data (4) Egty := Data(5) OD := Data(6)

RID: regress(Axl,ID,3) RTwty := regress(Axl,Twty,3) RFrty := regress(Axl,Frty,3)

RS~tY : regress(Axl,Sxty,3) REgty := regress(Axl, Egty, 3) ROD:= regress(Axl,OD,3)

FLCntr := Refpoint - co if Val = I Flaw center Location Location above Nozzle Bottom Refpoint if Val = 2 Refpoint + co otherwise Appendix IX Page 5 of 31

Appendix IX Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM A M-2007-006 ULStrs.Dist - UTip UTip : FLcntr + co Incstrs.avg := 20 No User Input is required beyond this Point Calculation to Develop Hoop Stress Profiles through wall at selected at selected elevations in the Axial Direction for Fracture Mechanics Analysis N:= 20 Number of locationsfor stress profiles Loco: FLCntr- I i:= i.. N +3 Incr : co if i< 4 IifncStrs.avg otherwise Loci := Loci-, + Incri SIDi := RID3 + RID4-Loc + RID '(Loci) 2 + RID,-(Loci) 3 STwtyi := RTwty3 + RT .ty4"Loci

+ RTwtY5"(Loci) 2 + RTwtY6"(Loci)'

SFrtyi RFrty3 + RFrtY4 Loci + RFrty -(Loci) 2 +[RFrty6-(Loci)31 SSxtyi :=RSXty3 +RSXty4. Loci + Rsxty -(Loci) 2 +I RSxtY6.(Loci)3]

Appendix IX Page 6 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 SEgtyi := REgty3 + REgtY4 Loci + REgty- (Loci) 2 + REgtY6"(LoCi) 3 2 3 SODi:= ROD 3 + ROD4"Loci + ROD "(Loci) + ROD6(Loci)

Input Data and Curve Fit results of data in the Crack Propagation Analysis region 60 ID 50 SID,,

40 0 0.5 I 1.5 2 2.5 3 AxI, Loci 100 OD 50" SODi 0 ....

...... I

-50 0 0.5 I 1.5 2 2.5 3 AxI, Loci Appendix IX Page 7 of 31

Appendix IX Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Development of Elevation-Averaged stresses at 20 elevations along the axial extent of tube for use in Fracture Mechanics Model j:= I..N SIDJ + SIDj+I + STwtyj + STwtyj+i + STwtyj+ 2 SIDJ+ 2 if if j = 1 J 3 STwtyj " 3 Sid_ *.(j+ i) + SIDj+ 2 STwtyj 1 -(j + I) + STwtyj+ 2 otherwise i-I 0*therwise j+2 j+2 SFrtyj + SFrtyj+l + SFrtyj+ 2 if = SSxtyj + SSxtyj+1 + SSxtyj+2 SFrty- SSxtyj fj =I 3 3 SFrtyj- .(j + i1) + SFrtyj+ 2 SSXty '(j + I) + SSxtyj+2 otherwise j+2 therwise j+2 SEgtyj + SEgtyj+l+ SEgtyj+ 2 if =j Sodj:3if SODj + SODj+i + SODj+ 2 j =

SEgtyj := Jd 3 3

Sod_, .(j + l) + SODj+ 2 SEgtyj- .(j + 1) + SEgtyj+ 2 j+2 otherwise otherwise j+2 ElevagionoAveragedHoop Stress DistributionFor OD F*aws (i.e. Stress distributionchanged from OD to §ID)

U0 := 0.000 Ui := 0.20 U2 := 0.40 u3 := 0.60 u4 := 0.80 U5 := 1.00 Appendix IX Page 8 of 31

Apperndix IX Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM AM-2007-O06 Y := stack(u 0 , uI 1 u2 ' u 3 ' u 4 ' u 5 )

SIG , stack(Sod, ISEgty, , SS' x y ,SF rt ' Twty, Sid,) SIG2 sta ck( Sod* 2SE t2 ' SSx t2 ' SF ry 2S Tw t , id2)

SIG 3 stack( Sod 3 5 Egty' 5 5~y3 5 ry3 5 Twty' Sid) SIG4 stack( Sod 4 , SEgty4' SSxty4 , SFrty4, STwty4, Sid4)

SIG 5 stack( So d5, SEgty 5 ,S Sxty 5, SFrty5 ,STwty 5, Sid,) SIG 6 stack( Sod61S Egty 6 ' SSxty 6 , SFrty6 ,STwty 6, Sid 6 )

SIG 8 := stack( Sod',S Egty 8 ' SSxty 8 , SFrty8 , STwty8 , Sid 8 )

SIG 7 := stack( Sod 7 S1Egty 'SSxty 7 , SFrty7 ' STWty 7 ' Sid 7)

SIG 9 :=stck(Sod978*gt,9,Ssxtyg, S rty9, STwtY9, Sid91) 8I G:o10 stack(SOdlo, SEgty , Sgxty10 ' SFrtyo0 ST w ,o' Sid,,)

SIG 1 1 stack(Sodl SEgt 'SSXt',SFr ,Sid) SIG 12 stack(Sod1 SEgty SSXty2SFrty1STwty1Sid 1 2 )

SIG 1 3 stack(Sod13,SEgty13,SSxtY[3,SFrtY13,STwtY13,Sid13) SIG 1 4 stack(Sod SEgty14 'SSXty 1 4 $Frty 14 '5 Twty 14 Sid)

SIG 1 5 stack(Sod 15 ,SEgty15 , SSxty ,, SFrty,',STwtys,5 Sid15 ) SIG 16 stack (od 1SEgtY1 6 'SSXtY 1SFrty16' STwty16' Sid 16 )

SIG17 :=stack(Sod17,SEgty 7 ,SSxtYlT, SFrty 17 , STwty 17, Sid17) SIG18 stack( Sod 18 ' SEgty18, SgXty18, SFrty 1' STwty,8, Sid18)

SIG 1 9 stack(Sod 19 ' SEgty 9,gSxtyl 9 ,SFrty1 9,STwty9,Sid 1 9) SIG2 0 stack(Sod 20 ,SEgty 2 0 'SSxty 20 , SFrty 20 ,STwly2, Sid 2 0 )

Appendix IX Page 9 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Regression on Through wall Stress distribution to obtain Stress Coefficients through wall using a Third Order polynomial ODRG 1 regress(Y,SlG1 ,3) ODRG2 regress(Y,SIG 2 ,3)

ODRG 3 regress(Y,SIG 3 ,3) ODRG4 regress(Y,SIG 4 ,3)

ODRG 5 regress(Y,SIG5,3) ODRG6 regress(Y,SIG 6 ,3)

ODRG 7 regress(Y, SIG 7 ,3) ODRG 8 regress( Y, SIG 8 , 3)

ODRG 9 regress(Y,SIG 9 ,3) ODRG 1 0 := regress(Y, SIG 1 0 ,3)

ODRGl regress(Y,SIG 1 1 ,3) ODRG 12 regress(Y,SIG 1 2 ,3)

ODRG 13 regress(Y,SIGl 3 ,3) ODRG 1 4 regress( Y,SIG 1 4 ,3)

ODRG 1 5 regress( Y,SIG 15 ,3) ODRG 1 6 regress(Y,SIG 1 6 ,3)

ODRG 17 regress(Y, SIG 1 7 ,3) ODRG 1 8 regress(Y, SIG 18 ,3)

ODRGI 9 regress(Y,SIG 1 9 ,3) ODRG2 0 regress( Y, SIG 2 0 ,3)

Appendix IX Page 10 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Stress Distribution in the tube Stress influence coefficients obtained from thirdorderpolynomial curve fit to the through wall stress distribution ProPLength := ULStrs.Dist - FLCntr - co - 0.5 ProPkength = 0.825 Flaw Propagation of top tip to above J-Weld top Data Files for Flaw Shape Factors from NASA (NASA-TM-111707-SC04 Model)

{NO INPUT Required)

Mt tau RajuNes Eeak fwoma Far flanws fo OeP eirtrce wIa Flawe 2 nde Mettu Raju Newman Sivakumar Forman Solution of OD Part through wall Flaw in Cylinder Jsb := The Table on the left "Jsb"consists of the cylinder and flaw mechanical 0 1 2 0 1.000 0.200 0.000 p'arametersas follows:

1 1.000 0.200 0.200 Column "0" :- Containsthe mean-radius to thickness ratio (Rm /t) of the Cylinder 2 1.000 0.200 0.500 Column "1":- Contains the Flaw Aspect Ratio (4/c) 3 1.000 0.200 0.800 Column "2":-Contains the Flaw Depth-to- Tube- Thickness ratio (a/t) 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 Appendix IX Page 11 of 31

0.000 ion of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Appendix 15 2.000 0.200 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 0.800 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 43 4.000 1.000 0.800 44 4.000 1.000 1.000 45 10.000 0.200 0.000 46 10.000 0.200 0.200 47 10.000 0.200 0.500 48 10.000 0.200 0.800 49 10.000 0.200 1.000 50 10.000 0.400 0.000 Appendix IX Page 12 of 31

Appendix 51 10.000 0.400 0.200 [on of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007--006 52 10.000 0.400 0.500 53 10.000 0.400 0.800 54 10.000 0.400 1.000 55 10.000 1.000 0.000 56 10.000 1.000 0.200 57 10.000 1.000 0.500 58 10.000 1.000 0.800 59 10.000 1.000 1.000 60 300.000 0.200 0.000 61 300.000 0.200 0.200 62 300.000 0.200 0.500 63 300.000 0.200 0.800 64 300.000 0.200 1.000 65 300.000 0.400 0.000 66 300.000 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 0.500 731 300.000 1.000 0.800 741 300.000 1.000 1.000 The Table below "Sambi"contains the FlawInfluence coefficients as follows:

Column "0":-Contains the influence coefficients for Uniform Loading at the depth-tip ("a"-tip)

Column "1" :- Containsthe influence coefficients for LinearLoading at the depth-tip ("a"-tip)

Column "2":-Contains the influence coefficients for QuadraticLoading at the depth-tip (a'"-tip)

Column "3" :- Containsthe influence coefficients for Cubic Loading at the depth-tip (a'"-tip)

Column "4":- Contains the influence coefficients for Uniform Loading at the length-tip ("c" tip)

Column "5" :- Contains the influence coefficients for Linear Loadingat the length-tip ("c'"-tip)

Column "6" :- Contains the influence coefficients for QuadraticLoading at the length-tip ("c"-tip)

Column "7" :- Contains the influence coefficients for Cubic Loading at the length-tip ("c'"-tip)

Appendix IX Page 13 of 31

AM-2007-006 Appendi Sam~bi . =

0 1 2 3 4 5 6 7 0 1.244 0.754 0.564 0.454 0.755 0.153 0.06 0.032 1 1.237 0.719 0.536 0.435 0.594 0.076 0.021 0.009 2 1.641 0.867 0.615 0.486 0.648 0.089 0.026 0.011 3 2.965 1.336 0.858 0.635 1.293 0.271 0.109 0.058 4 4.498 1.839 1.107 0.783 2.129 0.481 0.202 0.11 5 1.146 0.716 0.546 0.448 0.889 0.17 0.064 0.032 6 1.175 0.709 0.539 0.444 0.809 0.132 0.046 0.023 7 1.452 0.806 0.589 0.474 0.934 0.17 0.064 0.033 8 2.119 1.046 0.714 0.55 1.492 0.329 0.136 0.073 9 2.8 1.279 0.833 0.621 2.143 0.497 0.21 0.114 10 1.03 0.715 0.577 0.49 1.148 0.202 0.076 0.039 11 1,054 0.725 0.586 0.499 1.202 0.214 0.081 0.042 12 1.146 0.76 0.606 0.513 1.354 0.256 0.1 0.053 13 1.305 0.817 0.634 0.527 1.594 0.327 0.133 0.071 14 1.412 0.866 0.657 0.537 1.796 0.387 0.161 0.087 15 1.111 0.688 0.522 0.426 0.72 0.121 0.041 0.02 16 1.193 0.7 0.524 0.427 0.611 0.079 0.022 0.01 17 1.655 0.868 0.614 0.484 0.693 0.105 0.035 0.017 18 2.732 1.255 0.817 0.609 1.207 .0.245 0.097 0.051 19 3.842 1.634 1.009 0.726 1.826 0.395 0.162 0.086 20 1.077 0.685 0.528 0.436 0.817 0.14 0.049 0.023 21 1.136 0.692 0.528 0.436 0.796 0.13 0.046 0.022 22 1.403 0.785 0.576 0.465 0.959 0.182 0.071 0.037 23 1.942 0.984 0.682 0.53 1.425 0.315 0.131 0.071 24 2.454 1.168 0.78 0.591 1.915 0.443 0.188 0 102 25 1.02 0.72 0.585 0.498 1.152 0.196 0.072 0.036 26 1.044 0.722 0.584 0.498 1.185 0.209 0.079 0.041 27 1.117 0.746 0.597 0.505 1.318 0.25 0.098 0.052 28 1.236 0.797 0.625 0.523 1.56 0.315 0.127 0.068 29 1.335 0.844 0.652 0.538 1.775 0.37 0.151 0.08 30 1.009 0.65 0.507 0.427 0.589 0.073 0.018 0.006 31 1.162 0.691 0.524 0.434 0.612 0.08 0.023 0.01 32 1.64 0.861 0.613 0.488 0.786 0.134 0.049 0.025 33 2.51 1.178 0.782 0.596 1.16 0.242 0.097 0.051 Appendix IX Page 14 of 31

Appendi 34 3.313 1.464 0.932 0.693 1.517 0.339 0.139 0.073i AM-2007-006 35 1 0.655 0.518 0.44 0.754 0.118 0.036 0.017 36 1.109 0.685 0.53 0.445 0.793 0.13 0.045 0.022 37 1.36 0.773 0.575 0.472 0.994 0.195 0.078 0.041 38 1.727 0.914 0.653 0.523 1.4 0.318 0.134 0.073 39 2.025 1.032 0.72 0.568 1.781 0.427 0.181 0.1 40 0.986 0.711 0.589 0.513 1.127 0.189 0.068 0.034 41 1.03 0.72 0.591 0.513 1.163 0.204 0.077 0.04 42 1.094 0.743 0.603 0.52 1.286 0.243 0.096 0.051 43 1.156 0.777 0.625 0.536 1.498 0.302 0.122 0.064 44 1.194 0.804 0.644 0.551 1.681 0.35 0.142 0.073 45 0.981 0.636 0.501 0.422 0.598 0.078 0.02 0.007 46 1.147 0.685 0.521 0.432 0.612 0.08 0.023 0.01 47 1.584 0.839 0.6 0.48 0.806 0.142 0.053 0.028 48 2.298 1.099 0.739 0.568 1.262 0.277 0.114 0.062 49 2.921 1.323 0.859 0.645 1.715 0.402 0.169 0.092 50 0.975 0.645 0.516 0.439 0.75 0.114 0.036 0.017 51 1-096 0.68 0.528 0.444 0.788 0.128 0.045 0.022 52 1.31 0.755 0.565 0.466 0.984 0.192 0.076 0.04 53 1.565 0.858 0.625 0.505 1.378 0.309 0.129 0.07 54 1.749 0.938 0.675 0.539 1.747 0.411 0.174 0.095 55 0.982 0.709 0.588 0.515 1.123 0.188 0.068 0.034 56 1.025 0.718 0.59 0.513 1.156 0.202 0.076 0.039 57 1.078 0.738 0.6 0.518 1.266 0.236 0.092 0.048 58 1.118 0.765 0.619 0.533 1.453 0.286 0.113 0.059 59 1.137 0.786 0.636 0.548 1.613 0.326 0.129 0.067 60 0.936 0.62 0.486 0.405 0.582 0.068 0.015 0.005 61 1.145 0.681 0.514 0.42 0.613 0.081 0.024 0.011 62 1.459 0.79 0.569 0.454 0.79 0.138 0.051 0.026 63 1.774 0.917 0.641 0.501 1.148 0.239 0.096 0.051 64 1.974 1.008 0.696 0.537 1.482 0.328 0.134 0.07 65 0.982 0.651 0.512 0.427 0.721 0.103 0.031 0.013 66 1.095 0.677 0.52 0.431 0.782 0.127 0.045 0.022 67 1.244 0.727 0.546 0.446 0.946 0.18 0.071 0.037 68 1.37 0.791 0.585 0.473 1.201 0.253 0.102 0.054 69 1.438 0.838 0.618 0.496 1.413 0.31 0.126 0.066 Appendix IX Page 15 of 31

Appendix IX Evaluation of PWSCC Crack Growth of Postulated Flaw in CRDM AM-2007-006 In the declarationsbelow dummy variablesare defined in order to develop a continuousfunction for the various influence coefficients. A continuous function can then be readilyused inside the calculation to obtain the requiredinfluence coefficient in an efficient manner. The functions are developed using regressionanalysis with a thirdorderpolynomial for Rm /t less than 4.0 anda secondorderpolynomial for the higher ratios.

The dummy arrays W, X, and Y contain the cylinder and flaw mechanical parameters k /t ratio, a/c aspect ratio and a/t ratio respectively. Thus W=Jsb ,0> is a column array containing the Rm /t ratio, which is also Column "0" in the Jsb matrix. In a similar manner the other column arrays for the influence coefficients are defined.

W := Jsb(o) X :=Jsb~') Y :=Jsb (2) au Sambi(O0 aL Sambi~') aQ Sainbi(2) ac Saxnbi (3 cu Sambi W~ cL Samnbi(5) cQ Sambi(6 cc Samnbi(7) n: 3 if Rt < 4.0 Order of polynomial selected based on R m/t ratio 2 otherwise The regression analysis below develops the continuous functions for the six influence coefficient arrays using the declarations above. For example the continuous function defining the influence coefficients for the Uniform Loading at the "a" or depth tip is defined as:

Fau (W,X,Y) which is the standard nomenclature is Fau (k m, , a/c, a/t)

Once these functions are defined they are used in the iterative calculation loop as functions whose values are dependent on the three variables (Po

/t, a/c, a/t) that are defined within the loop based on the results from the previous iteration.

Appendix IX Page 16 of 31

Appendix IX Evaluation of PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 "a-Tip" Coefficients "a-Tip" Uniform Term MaU:= augment(W,X,Y) VaU:= aU RaU:- regress(MaUVaU~n) faU(,X,):=interp{RaUMaUVaU{ X1 "a-Tip" Linear Term MaL:= augment(W,X,Y) VaL:= aL RaL :=regress( MaL,VaL,n) faL(W,X,Y) := interp RaLMaLVaL,{X a-Tip" Quadratic Term (w)_~

MaQ:= augment(W,X,Y) VaQ:= aQ RaQ := regress(MaQ ,VaQ,n) faQ(WXY)= ,MaQ, VaQ jxH

ý,Y)j "a-Tip" Cubic Term MaC := augment(W,X,Y) VaC := aC Rac:- regress(MaC, VaC,n) faC(W,X,Y) := interp RaC,MaC,VaC X "c" Tip Coefficients "c-tip" Uniform Term McU:= augment(W,X,Y) vu=Cu RCU : regress(McU ,VCU n) f UW,,Y:=interp{RC5 CcU, fC~~xY UVcU{'j C

Appendix IX Page 17 of 31

Appendix MX Evaluation of PWSCC Crack Growth of PostulatedFlawin CRDM AM-2007-006 "c-tip" Linear Term McL:= augment(W,X,Y) VcL : CL RcL :=regress( McL, VcL,n) fcL(W, X,Y) : nepRL cVL "c-tip" Quadratic Term McQ := augment(W, X, Y) VcQ := CQ RCQ :=regress(MCQ ,VCQ, n) fcQ(W,X,Y) :=interp RcQMcQVCQ, X Cubic Term McC:= augment(W,X,Y) VcC:= cC R~CC: regress(MCC,V~C,n) fcC(W,X,Y): nepRCMVX Appendix IX Page 18 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Calculations : Recursive calculations to estimate flaw growth.

Recursive Loop for Calculation of PWSCC Crack Growth as a function of Hot Operating Time CGRsambi j <-a0 Co Co a-NCB0 +- Cblk while j _ Ilim a00- ODRG1 3 ifcj_*co ODRG2 3 if co < cj _<co + IncStrs.avg ODRG3 3 if co + Incstrs.avg < Cj _ CO + 2.lnCStrs.avg ODRG4 33 if co + 3-Incstrs.avg < cj _<Co + 3"IncStrs.avg ODRG5 3 if co + 3-Incstrs.avg < cj _ Co + 4.lncstrs.avg ODRG 6 3 if co + S-Incstrs.avg < cj _-co + 5-IncStrs.avg ODRG 7 3 if co + 5-nCStrs.avg < cj _*CO + 6.fnCstr~s.avg ODRG 8 3 if co + 6"lncstrs.avg < Cj _5co + 7"fIncStrs.avg ODRG9 3 if co + 7Ilncstrs.avg < cj

• co + 8-Incstrs.avg ODRG1 0 3 if Co + 8llncstrs.avg < cj _ co + 9"InCStrs.avg ODRG 1 if co + 9.Incstrs.avg < cj _ co + io.Incstrs.avg 3

ODRG 1 2 1 if co + Io-Incstrs.avg < cj _ co + I I-lncStrs.avg Appendix IX Page 19 of 31

App AM-2007-006 ODRG1 3 if co + I I-Incstrs.avg < Cj Cco + 12 IncStrs.avg ODRG14 3 if CO + 12" Incstrs.avg < ci co + 13.Incstrs-avg ODRG 1 53 if co + 13-1nCStrs.avg < cj < co + 14Ilncstrs.avg ODRG16 3 if Co + 14"Incstrs.avg < cj <_co + 15-lIncstrs.avg ODRG 1 73 if Co + 15-IncStrs.avg < cj _ Co + 16.IncStrs.avg ODRG 1 83 if CO + 16"Incstrs.avg < Cj C + 17.IncStrs.avg Co ODRG 1 93 if CO + 17-Incstrs.avg < cj < Co + 18.lncstrs.avg ODRG20 3 otherwise ODRG1 4 if cj <ýco ODRG2 4 if co < cj <5 co + Incstrs.avg ODRG34 if co + IncStrs.avg < cj _< Co+ 2. IncStrs.avg ODRG4 4 if Co + 2"Incstrs.avg < cj <5 co + 3-Incstrs.avg ODRG51 if co + 3."Incstrs.avg < Cj< Co+4 IlncStrs. avg ODRG6 4 if co + 4' Incstrs.avg < cj <5 co + 5-Incstrs.avg ODRG7 4 if co + 5."Incstrs.avg < cj <5 co + 6" Incstrs.avg ODRG84 if CO he+ 6.Incstrs.avg < c co + 7-Incstrs.avg ODRG94 if CO + 7-Incstrs.avg < cj co + 8+Incstrs.avg ODRG10" if Co + 8-IncStrs.avg < cj <Co + 9"Incstrs.avg Appendix IX Page 20 of 31

App AM-2007-006 ODRG1 14 if Co + 9-Incstrs.avg < cj < Co + lo'Incstrs.avg 4

ODRG 1 24 if Co + Io-IncStrs.avg < cj _<CO + ll-IncStrs.avg ODRG13 4 if co + IIl'Incstrs. avg, < cj <5 co + 12"Incstrs.avg ODRG14 4 if Co + 12-IncStrs.avg < cj _ Co + 13- IncStrs.avg ODRG 15 4 if co+ 13-IncStrs.avg < Cj < co + 14- IncStrs.avg ODRG 16 4 if Co + 14-Incstrs.avg < cj < CO + 15- IncStrs.avg ODRG 17 if Co + 15-Incstrs.avg < cj < CO + 16-IncStrs.avg 4

ODRG 18 4 if co + 16-lncstrs.avg < cj < co + 17- IncStrs.avg ODRG 19 4 if Co + 17"Incstrs.avg < cj < CO + I8dlncstrs.avg ODRG2 0 4 otherwise cr2 <- ODRGI5 if cj

• co ODRG2 5 if Co < cj < Co + lncstrs.avg ODRG3 5 if co + Incstrs.avg < cj < Co + 2.Incstrs.avg ODRG4 5 if Co + 2"IncStrs.avg < cj < CO + 3"Incstrs.avg ODRG5 5 if Co + 3-Incstrs.avg < Cj < Co + 4-Incstrs.avg ODRG6 5 if Co + 4"Incstrs.avg < cj < Co + 5-Incstrs.avg ODRG7 5 if CO + 5-lncstrs.avg < cj < Co + 6-Incstrs.avg ODRG8s if CO + 6-IncStrs.avg < Cj _<Co + 7IlncStrs.avg Appendix IX Page 21 of 31

AM-2007-006 App ODRG 9 5 if cO + 7- ncStrs.avg < *j<_CO + S .nCStrs.avg ODRG 1 0 5 if Co + 8-Incstrs.avg < cj CO + 9-lncstrs.avg ODRG 11 5 if co + 9-Incstrs.avg < cj: Co + io.lncstrs.avg ODRG 12 5 if co + io.Incstrs.avg < cj co + I i-Incstrs.avg ODRG 13 5 if Co + ii.Incstrs.avg < cj Co + 12-lncstrs.avg ODRG 14 5 if co + 12-Incstrs.avg < cj CO + 13-lncstrs.avg ODRG 1 5 5 if co + 13-IncStrs.avg < cj CO + 14-lncstrs.avg ODRG 1 6 5 if CO + 14"Incstrs.avg < cj K Co + 15.InCstrs.avg ODRG 1 75 if Co + 15-Incstrs.avg < cj CO + 16-Incstrs.avg ODRG 1 8 5 if c 0 + 16.Incstrs.avg < cj Co + 17-Incstrs.avg ODRG 19 5 if CO + 17"Incstrs.avg < cj <Co + 18-Incstrs.avg ODRG 2 0 5 otherwise ODRG1 6 if cj < co ODRG 2 6 if co < cj < co + Incstrs.avg ODRG 3 6 if co + Incstrs.avg < Cj < Co + 2-IncStrs.avg ODRG4 6 if CO + 2.IncStrs.avg < cj co +

C 3.IncStrs.avg ODRG5 6 if co + 3-lncstrs.avg < cj _co + 4.Incstrs.avg ODRG, if cn + 4-Inc... < c; < cn + 5Incc .. .

.. . . I Appendix IX Page 22 of 31

App a AM-2007-006 ODRG 7 6 if Co + 5*IlncStrs.avg < Cj < Co + 6.Incstrs.avg ODRG8 6 if Co + 6-Incstrs.avg < Cj _<Co + 7.Incstrs.avg ODRG9 6 if co + 7.Incstrs.avg < cj < co + 8.Incstrs.avg ODRG 10 6 if co + 8Ifncstrs.avg < cj < co + 9-IncStrs.avg ODRG 11 6 if co + 9- Incstrs.avg < cj co + io.Incstrs.avg ODRG12 6 if co + So-Incstrs.avg < cj < co + l'Incstrs.avg S

ODRG13 6 if co + i I.-Incstrs.avg < cj <5 Co + 12"lncstrs.avg ODRG 1 46 if Co + 12"IlncStrs.avg < cj < C0 + 13-Incstrs.avg ODRG15 6 if Co + 13- Incstrs.avg < cj _<ý Co + 14.Incstrs.avg ODRG 1 66 if CO+ 14.Incstrs.avg < cj < Co+ 15.Incstrs.avg ODRG 1 76 if Co + 15-Incstrs.avg < cj < Co + 16"lncstrs.avg ODRG 1 86 if co + 16-Incstrs.avg < cj < co + 17-lncstrs.avg ODRG 196 if co + 17-Incstrs.avg < cj < co + 18-Incstrs.avg ODRG2 0 6 otherwise

ý0 <- CF 0

< roa 0 - +

sIaji 2O +

aT2 -

L2.5*aj )

t +a3

( - 323o1aj

• ° '5Pajag2

_Append+1.(

Appendix IX Page, 23 of 31

App AM-2007-006 (0.75.aj (-1*a 2 (L71 .aj3 030+ t )+ (YT-- t + -

73 t (1.0 ,aj Ll.o~aj) ao Cr (I.Oaj 44+- +02*' t +03* t x0 +- 0.0 Xi <-- 0.25 X24- 0.5 x3 <- 0.75 X -- stack(x 0 ,xl ,x 2 ,x 3 ,x 4 )

ST +- stack(ý 0 ,j 1,'*2,'3,4)

RG <- regress(X, ST,3) o004 -- RG 3 + Pint 0 10 - RG 4 c20 +- RG 5 030 - RG6 aj ARj <--

cj ATj +--aj t

Gauj 4- faU(Rt,ARjATj)

Gali <- faL( Rt,ARjATj)

Appendix IX Page 24 of 31

App AM-2007-006 Gaqj +- £aQ(RtARjATj)

Gac <-- faC(Rt,ARj,ATj)

Gcu - fcU (Rt,ARj, ATj)

J Gclqi fcL(RtARjATj)

Gcj --fcQ (Rt,,A*j, ATJ)

Gcc ,- fcC (Rt,,*j ,ATJ)

Qj +-- 1+ 1.464. 6 i f cj > aj I £c 1+1.464"( otherwise jc K -(taj O'.j 00*.Gauj + T10. Gal.i+ cy20. Gaqj + y3 0"Gacj)

Kcj 4-- .(7a00.GcuG + 1+.ioGc + 20-Gcqj + 30"Gccj)

K. -Ka.-1.099 J J SKYj +-Kc *1.099 Ka< - 9.0 if KaX 9.0 Ka otherwise Ky -- 9.0 if Kyj 9.0 K,. otherwise Appendix IX Page 25 of 31

App I IJ AM-2007-006 Da <- C 0.(Kaj - 9.0)1.16 Dagj DajCFinf-Cblk if < 80.0 4 0 .CFihr*-Cblk otherwise DcC+- Co."(K~j - 9.0)1.16 Dcgj -- Dcj.CFinhr.Cblk if Kgj < 80.0 4-10.- -CFinh-Cblk otherwise outputj, 0 J outputj, I- aj OUtPUtj , 2 - Cj - Co OutpUtj, 3 4- Dagj outputj , 4 4- Dcgj OutpUtj, 5 -Ka.

j outputj, 6 -Kcj NCBj 365-24 outputj, 8 -Gauj outputj, 9 4- Gal.

J outputj, 10 - Gaqj outputj, II +- Gac.

J Appendix IX Page 26 of 31

App *-- Gcu.

oUtPUtj, 12App AM-2007-006 J

OUtPUtj, 13 <-- Gcl J

OUtPUtj, 14 - Gcqj outputj, 15 '-Gcc NCBj 365.24 OUtPUtj, 16 --*1.5 .98 aj -- aj_1 + Dagj_,

Cj <-- CIj + Dcgj_

aj4- It if aj>t aj otherwise NCBj <- NCBjl + Cblk output k 0.. Ilim ProPLength = 0.825 Appendix IX Page 27 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Flaw Growth in Length Direction .855 0.8

-C U

C 0.6 C

0) 0.4 0

Cu 0.2 0

0 I 2 3 4 5 6 7 8 Operating Time (fuel cycles)

Flaw growth in the length direction, as a function of fuel cycles. The extension of the "c-tip" or OD surface point is shown. The available propagation length to the top of the weld (J-groove weld root) is 0.855 inch. The time available for the flaw growth by PWSCC is about 6.67 fuel cycles and is limited by the instability of K I . When the upper tip of the flaw reaches the weld root, a leakage path to the annulus can be established. Thus this calculation estimates the operating time to first leak.

Appendix IX Page 28 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Flaw Growth in Depth Direction 0.6 0.5 U

0.4

0. 0.3 0.2 0.1 0

0 I 2 3 4 5 6 7 8 Operating Time {fuel cycles}

Flaw growth in the depth direction, as a function of Hot Operating Years. The extension of the "a-Tip" or is shown. The available propagation depth to the ID surface is about 0.55 inch. The flaw depth at the calculated Hot Operating Time of 6.67 fuel cycles (time for upper flaw tip to reach J-groove weld root) is 0.297 inch. Hence the flaw is not expected to propagate to the ID surface when the upper tip of the flaw reaches the J-groove weld root.

Appendix IX Page 29 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Stress Intensity Factors 72.42 I I I III U . .. . .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0~

3-0 U

C U) 0 1 2 3 4 5 6 7 8 Operating Time {fuel cycles}

Depth Point

.... Surface Point The behavior of Stress Intensity Factor at the two flaw tips as a function of operating time is shown. The initial flaw had a semicircular geometry, which results in a higher "K value at the surface point. The geometry of this initial flaw causes the Appendix IX Page 30 of 31

Appendix IX Evaluationof PWSCC Crack Growth of PostulatedFlaw in CRDM AM-2007-006 Influence Coefficients - Flaw 1.4 6.67 1.2 U.,

0

.E 0.8 The influence coefficients as a function of operating time is shown. The behavior for 4q" the "a-tip" shows the effect of the flaw 0 0.6 aspect ration for the initial flaw and early growth. No erratic behavior of the influence W = 0.4 coefficients is observed. When the flaw depth reaches 80% of wall thickness the coefficients show a departure from normal (expected) trends.

0 0 2 4 6 8 Operating time {fuel cycles}

"a" - Tip -- Uniform

.............. a" - Tip -- Linear

---

"a" - Tip -- Quadratic

........... a" - Tip -- Cubic "c" - Tip -- Uniform Sc' - Tip -- Linear

....... "c" - Tip -- Quadratic c" - Tip -- Cubic Appendix IX Page 31 of 31