ML18093B078
| ML18093B078 | |
| Person / Time | |
|---|---|
| Site: | North Anna  |
| Issue date: | 12/21/2017 |
| From: | Burkardt M Dominion Engineering |
| To: | Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML18093B072 | List: |
| References | |
| 18-048 C-4520-00-03-NP, Rev 1 | |
| Download: ML18093B078 (38) | |
Text
Attachment 3 Serial No.18-048 Docket Nos. 50-339 Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation (Non-proprietary)
North Anna Power Station Unit2 Virginia Electric and Power Company (Dominion Energy Virginia)
CALCULATION
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Title:
CrackGrowth Analyses for NAP~-~~!!_?§tear:0~enerator Outlet N_~~~I~~ ________________ _
Calculation No.: C-4520-00-03-NP Revision No.:
1 Page of 37 RECORD OF REVISIONS Prepared by Checked by Reviewed by Approved by Rev.
Description Date Date Date Date 12/20/201 7 12/20/2017 12/20/2017 12/20/2017 0
Original Issue M. Burkardt G. Lenci G. A. White G. A. White Associate Engineer Engineer Principal Engineer Principal Engineer 1
Added stress intensity factor
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profiles for axial and t/i.1 /z o1 1 1../ 2-1/ 2.r:;IJ' ~*~li\\\\7.0\\i G.. rze>\\9 z-/2. l circumferential crack growth calculation.
M. Burkard!
G. Lenci G. A. White G. /1.. White Engineer Engineer Principal Engineer Principal Engineer The last revision number to reflect any changes for each section of the calculation is shown in the Table of Contents. The last revision mm1bers to reflect any changes for tables and figures are shown in the List of Tables and the List of Figures. Changes made in the latest revision, except for Rev. 0 and revisions which change the calculation in its entirety, are indicated by a double line in the right hand margin as shown here.
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Title:
Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-NP Revision No.:
1 Page 2
of 37 TABLE OF CONTENTS Last Mod.
Section Page Rev.
1 PURPOSE.................................... **************************************........................................................... 5 0
2
SUMMARY
OF RES UL TS................................................................................................................. 5 0
3 INPUT REQUIREMENTS.................................................................................................................. 7 0
4 ASSUMPTIONS.............................................................................................................................. 9 0
5 ANALYSIS................................................................................................................................... 11 0
5.1 Stress Intensity Factor Calculation............................................................................... 12 0
5.1.1 Loads and Stresses....................................................................................... 12 1
5.1.2 Universal Weight Function Method................................................................ 14 0
5.2 Crack Growth Calculation............................................................................................. 19 0
5.2.1 Approach........................................................................................................ 19 0
5.2.2 Results........................................................................................................... 20 1
5.3 Software Usage............................................................................................................ 22 0
6 REFERENCES............................................................................................................................. 22 0
A CONTENTS OF DATA DISK D-4520-00-03..................................................................................... 33 0
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Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-NP Revision No.:
1 Page 3
of 37 LIST OF TABLES Table No.
Table 1.
Crack Growth Results Table A-1.
Software Usage Records LIST OF FIGURES Figure No.
Figure 1.
Annotated Drawing Indicating Wall Thickness and Average Weld Width (Average of Maximum and Minimum Widths)
Figure 2.
Residual Plus Operating Stress Profiles Applied for PWSCC Crack Growth Calculations using 360° 55% Through-Wall ID Weld Repair Figure 3.
Residual Plus Operating Stress Profiles Applied for PWSCC Crack Growth Calculations using 360° 45% Through-Wall ID Weld Repair Figure 4.
Residual Plus Operating Stress Profiles Applied for PWSCC Crack Growth Calculations using No Weld Repair Figure 5.
Axial Crack Depth, alt, as a Function of Time Figure 6.
Circumferential Crack Depth, alt, as a Function of Time Figure 7.
Axial Crack Half-Length on ID, c, as a Function of Time Figure 8.
Circumferential Crack Half-Length on ID, c, as a Function of Time Figure 9.
Axial Crack Aspect Ratio, 2cla, as a Function of Time Figure 10.
Circumferential Crack Aspect Ratio, 2cla, as a Function of Time Figure 11.
Axial Crack Stress Intensity Factor at Deepest Point, Kgo, as a Function of Crack Depth Figure 12.
Circumferential Crack Stress Intensity Factor at Deepest Point, Kgo, as a Last Mod.
Rev.
0 0
Last Mod.
Rev.
0 0
0 0
0 0
0 0
0 0
1 12100 Sunrise Valley Drive, Suite 22.0 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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of 37 Figure No.
Function of Crack Depth Figure 13.
Axial Crack Stress Intensity Factor at Surface Point, Ko, as a Function of Crack Depth Figure 14.
Circumferential Crack Stress Intensity Factor at Surface Point, Ko, as a Function of Crack Depth 12100 Sunrise Valley Drive. Suite 220 Reston, VA 20191 PH 703.657.7300 Last Mod.
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of 37 1
PURPOSE The steam generator outlet nozzles at North Anna Power Station (NAPS) Unit 2 are joined to stainless steel safe ends with Alloy 82/182 double V-groove butt welds [1]. The Alloy 82/182 butt welds in NAPS Unit 2 are covered on the inside surface with an Alloy 52/152 barrier weld. Requirements for periodic examination of Alloy 82/182 butt welds in pressurized water reactor (PWR) primary system piping are currently specified by ASME Code Case N-770-2 [2], which is mandated with conditions by U.S. Nuclear Regulatory Commission (NRC) per IO CFR 50.55a(g)(6)(ii)(F). This code case requires that a volumetric examination be performed of unmitigated cold-leg butt weld locations (Table 1, Inspection Item B of N-770-2) every second inspection period (as defined by ASME Section XI), not to exceed 7 years. As recategorization under Table 1 of N-770-2 has not been authorized by NRC to credit the presence of the Alloy 52/152 barrier weld, the steam generator outlet nozzles at NAPS Unit 2 are treated as unmitigated cold-leg butt weld locations for the purposes of 10 CFR 50.55a(g)(6)(ii)(F) and Code Case N-770-2.
This calculation provides a technical basis for alternative volumetric reexamination intervals for the NAPS Unit 2 steam generator outlet nozzles. This calculation treats these locations as unmitigated butt welds and does not credit the presence of the Alloy 52/152 barrier welds, as crack growth is modeled exclusively on the basis of crack growth rates applicable to Alloy 182 material.
2.
SUMMARY
OF RESULTS Crack growth calculations were performed considering the specific geometry and loads applicable to the NAPS Unit 2 steam generator outlet nozzles, including the weld residual stress (WRS) analysis results documented in C-4520-00-01, Rev. 0 [6]. These calculations applied the common deterministic approach for unmitigated Alloy 82/182 piping butt welds in PW Rs. The results of these crack growth calculations demonstrate the acceptability of the following alternative volumetric reexamination intervals for the NAPS Unit 2 steam generator outlet nozzles:
"Loop l" and "Loop 3" nozzles: Once per Section XI interval (nominally l O years), as specified by ASME Code Cases N-770-3 [3] and N-770-4 [4] per Inspection Item B-2 for unmitigated cold-leg butt weld locations NPS 14 or larger (N-770-3 and N-770-4 are not currently approved by NRC)
"Loop 2" nozzle: Six nominal 18-month fuel cycles (nominally 9 years) 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7:300 FX 703.657.7301
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of 37 The crack growth calculations presented below demonstrate that these alternative volumetric examination frequencies are sufficient to provide reasonable assurance of the structural integrity of the cold-leg piping at NAPS Unit 2. Hence, these alternative frequencies provide an acceptable level of quality and safety.
The key results of the crack growth calculations are as follows:
The crack growth rate for axial cracks was found to be greater than for circumferential cracks, due to the total (residual plus operating) hoop stresses being greater than the total axial stresses.
Thus, the analysis cases for axial cracks are the limiting cases.
The limiting case for the calculated time for a crack to grow from 10% through-wall to the allowable depth is 9.1 years. The limiting case is for an axial crack growing to an allowable depth of 75% through-wall. In this limiting case, an additional 3.1 years is calculated for the axial crack to penetrate through the remaining 25% of the wall thickness. This limiting case is applicable only to the "Loop 2" nozzle, which includes a 55% through-wall localized weld repair.
The limiting case applicable to the "Loop 1" and "Loop 3" nozzles results in a time of 10.3 years for an axial crack to grow from 10% through-wall to 75% through-wall. In this case, an additional 2.8 years is calculated for the axial crack to penetrate through the remaining 25% of the wall thickness.
The relatively large thickness of the subject Alloy 82/182 weld (4.813 inches) compared to other Alloy 82/182 butt welds in U.S. PWRs is a main factor in these calculated crack growth times.
As the wall thickness increases, the distance for the crack to grow increases.
These limiting axial crack growth calculation results reflect some key conservatisms that tend to provide increased assurance of the structural integrity of the cold-leg piping at NAPS Unit 2:
The limiting crack growth result is for axial flaws, which are not a credible concern for becoming unstable and causing rupture of the pressure boundary. This is because the critical flaw length of a through-wall axial flaw for causing unstable rupture in this case is much greater than the axial width of Alloy 82/182 weld metal susceptible to primary water stress corrosion cracking (PWSCC) (see Section 5.2.2). For the limiting case, the calculated time for a flaw detectable via ultrasonic testing (UT), i.e., initial depth of 10% through-wall, to grow though the weld thickness and cause leakage is 12.2 years.
As discussed in Section 5. l.2, a universal weight function method was applied to calculate accurately the stress intensity factor resulting from the through-wall stress distribution. This approach does not fit a polynomial to approximate the stress profile, as is often the case when applying published solutions such as the method of influence coefficients. Fitting the stress profile to a polynomial can introduce a significant source of modeling uncertainty depending on the accuracy of the fit obtained. Conservatism results from assuming that the same through-wall WRS profile is present along the entire length of the modeled axial crack.
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of 37 For modeling axial cracks, the stress intensity factor calculation conservatively does not credit the effect of flaw total-length-to-depth aspect ratios (2cla) below 1. Because of the lack of published solutions for this range of aspect ratios, a conservatism is introduced by assuming 2cla = 1 in the stress intensity factor calculations when 2cla < 1. This results in stress intensity factors at the deepest point on the crack somewhat greater than the true stress intensity factor corresponding to the true aspect ratio with identical crack loading. The end result is a conservatism in the calculated crack growth time since the axial crack growth occurs with 2cla < 1 during most of the time (see Figure 9).
3 INPUT REQUIREMENTS The following inputs were used in support of this calculation:
- 1.
Key dimensions required for the crack growth calculation are as follows:
- a.
Dissimilar metal weld (DMW) region machined ID: 31.03 in. [5, Figure l]
- b.
Wall Thickness: 4.813 in. (at centerline of double-V groove, as shown in Figure I) [5, Figure 1]
- 2.
The DMW for the steam generator outlet nozzle is fabricated using Alloy 182 and/or Alloy 82.
An Alloy 52/152 barrier weld is also present on the nozzle ID, but its presence is not credited in this crack growth calculation. [l]
- 3.
The crack growth rates for Alloy 182 are evaluated per the MRP-115 [7] crack growth rate disposition curve, which is also specified in Nonmandatory Appendix C of ASME Section XI [8]
- 4.
The operating temperature of the steam generator outlet nozzle is: 549°F [9]
- 5.
The operating stress profiles are defined in C-4520-00-01 RO [6]
- a.
Cold-leg hoop stress profile for 55% weld repair
- b.
Cold-leg axial stress profile for 55% weld repair
- c.
Cold-leg hoop stress profile for 45% weld repair
- d.
Cold-leg axial stress profile for 45% weld repair
- e.
Cold-leg hoop stress profile for no weld repair
- f.
Cold-leg !1Xial stress profile for no weld repair
- 6.
Nozzle operating forces are as follows [10, Table 2] (tensile forces are positive):
- Confidential Commercial lnformatio..,
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- 7. [
I Confidential Nozzle operating moments due to normal thermal expansion are as follows [10, Table 2]:
r
~ Confidential Commercial In.formation
- 8.
Nozzle operating moments due to pressure are as follows [10, Table 2]:
r
~ Confidential Commercial Information
- 9.
Nozzle operating moments due to dead weight are as follows [I 0, Table 2]:
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of 37 l 0.
Influence coefficients used in the stress intensity factor calculation were obtained from API 579-1 I ASME FFS-1 [11, Table C.12 and Table C.14]
4 ASSUMPTIONS
- 1.
In accordance with the standard approach of the non mandatory appendices of ASME Section XI
([8], [12]), circumferential and axial surface flaws evaluated in this subcritical growth calculation are modeled to have semi-elliptical shape.
- 2.
The weld material is reported in technical documentation as Alloy 182 or Alloy 82 [l]. The standard deterministic crack growth rate for Alloy 182 per MRP-115 [7] and Nonmandatory Appendix C of ASME Section XI [8] is conservatively applied for the weld material as it is higher than the corresponding crack growth rate for Alloy 82 per these standard references.
Although an Alloy 52/152 barrier weld is also present, the benefit obtained from the PWSCC-resistant Alloy 52/152 weld material is conservatively not credited in this assessment.
- 3.
For the axial crack growth calculation, the double V-groove weld cross-sectional geometry is approximated as a rectangular geometry with a constant width equal to the average width of the double V-groove weld. This width limits the axial extent of the modeled axial crack. This average weld width (average of maximum and minimum weld width as shown in Figure 1) is 1.6 in. [ 5, Figure I].
- 4.
An initial flaw depth of 10% through-wall (alt= 0.1) is applied on the basis that this is the minimum flaw depth covered by the ASME Section XI Appendix Vlll, Supplement 10 qualifications for UT flaw detection [13]. This approach does not rely on performance of eddy current testing to validate a shallower assumed initial flaw.
- 5.
As cracking degradation in piping butt welds is dominated by PWSCC, fatigue crack growth is not modeled in this calculation. Accordingly, the effects of transient loading are not considered to be significant, and are thus not modeled. The dominance of PWSCC growth is illustrated by the crack growth results of Reference [14] for the NAPS Unit 2 steam generator inlet and outlet nozzles.
- 6.
For axial cracks, the maximum length of the flaw is limited to the axial extent of the Alloy 82/182 weld. It is widely accepted that the PWSCC growth mechanism does not have a significant effect in stainless or low-alloy steels for a normal primary water environment relative to PWSCC growth in the Alloy 82/182 weld [15]. The subject DMWs are exposed to flowing primary water and not stagnant conditions where impurity ions or oxygen could concentrate. The experience for the leaking reactor vessel outlet nozzle weld at V.C. Summer Station illustrates 121 00 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Page 10 of 37 the expected behavior. The leak in this weld was caused by an axial crack extending over most of the weld cross section without penetrating a significant distance into the low-alloy steel nozzle or stainless steel pipe materials [16]. For circumferential cracks, the maximum length of the flaw remains less than the inner circumference of the DMW. Thus, the maximum circumferential flaw length does not need to be limited in this analysis.
- 7.
For axial flaws, an initial aspect ratio (2c/a) of 2 is appropriate because the axial flaw growth due to PWSCC is limited to the axial length of the dissimilar metal weld (as indicated in Assumption 6). For circumferential flaws, an initial aspect ratio (2c/a) of 10 is conservatively applied.
- 8.
When calculating the effective bending moment and OD bending stress, circumferential cracks are conservatively assumed to be centered at the point of maximum bending tensile stress.
- 9.
Each component (Mx, My, and M 2) of the effective bending moment is calculated conservatively using the maximum between the absolute value of the total moment contributions for "Loop l,"
"Loop 2," and "Loop 3" (where the term total refers to the sum of the NTE, pressure, and DW load sources) for the same moment component, as in Equation [ 4-1]. The effective bending moment (Men) is then determined as a combination of the bending and torsional moments based on a Von Mises stress approach:
[4-1]
- 10.
Values for Go and G1 influence coefficients are obtained by interpolating or extrapolating from tables in APT Standard 579-I IASME FFS-1 [11, Table C.12 and Table C.14]. For input parameters outside the domains provided in the tables, extrapolation is performed following Assumption 11. For input parameters inside those domains, influence coefficients are determined through log-linear interpolation in tlR; and in ale, and linear interpolation in alt.
- 11.
Solutions for influence coefficients Go and G1 are provided in API Standard 579-llASME FFS-1
[11] only for alt ~ 0.8 and for ale ~ 0.125 (for the tlR; values of interest). In order to predict the time to through-wall growth, the influence coefficients are linearly extrapolated for the range 0.8 <alt < 1.0. Extrapolation of influence coefficients for alt > 0.8 is considered to be standard practice, and has also been applied in probabilistic fracture mechanics codes such as xLPR (E2itremely.L_ow frobability of Rupture) [17]. Furthermore, the time required for a crack to grow from 10% through-wall to through-wall (which is affected by this extrapolation for alt > 0.8) is considered to be a secondary result of this calculation. The time required for a crack to grow from 10% through-wall to the allowable depth (no greater than 75% through-wall), which is the primary result of this calculation, remains unaffected by this assumption. The influence coefficients are log-linearly extrapolated for ale< 0.125 because there are no influence 12100 Sunrise Valley Drive, Suite 220 Reston; VA 20191 PH 703.657.7300
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Page 11 of 37 coefficients available in this range in API Standard 579-1/ASME FFS-1 for the tlR; values of interest. It would be nonconservative to apply influence coefficients for ale= 0.125 when calculating stress intensity factors for ale< 0.125.
- 12.
As recommended by Rudland, et al. [17], the influence coefficients and the flaw shape parameter are evaluated consistently with the available influence functions. For crack aspect ratios ale> 2.0 (2c/a < 1 ), a crack aspect ratio of ale = 2.0 (2c/a = 1) is applied in evaluating the influence coefficients and flaw shape parameter.
- 13.
A plant capacity factor of 0.93 is applied to account for time in which the plant is not operating (e.g., due to refueling outages). This assumption is considered to be conservative.
- 14. The residual stress profile is represented as a piecewise linear stress profile, as defined within C-4520-00-01 RO [6]. Defining a piecewise linear stress profile with a relatively fine spatial resolution of 2.5% through-wall (TW) as done here is considered appropriate for stresses output from finite-element analyses at discrete locations through the thickness of the weld ([12], [18]).
- 15.
The WRS profile applied in the stress intensity factor calculations resulting in the limiting crack growth times assumes the presence of a 360° 55% through-wall weld repair on the inner diameter (ID) surface from plant construction. The weld fabrication records for NAPS Unit 2 [19] identify a 55% through-wall localized repair in the Loop 2 steam generator outlet nozzle. A 360° 45%
through-wall weld repair bounds the weld repairs affecting the other two steam generator outlet nozzles at NAPS Unit 2. Given the availability of the detailed review of weld fabrication records
[19], these weld repair cases were applied instead of the general default assumption of a 50%
through-wall weld repair on the ID surface.
- 16.
A time step of l month is applied for the crack growth calculation. This time step is appropriately refined to yield converged results given the time-scale over which a crack grows through the thickness of the weld (i.e., greater than 9 years).
- 17. Numerical integration for the weight function integral is performed using 10,000 bins, and a value of y = 0.57. These values were selected using sensitivity studies to ensure appropriate numerical convergence of the stress intensity factors resulting from the weight function integrals.
- 18.
The operating pressure for NAPS Unit 2, P, is assumed to be 2235 psig. This is equal to the operating pressure for NAPS Unit 1 [20, Table 4] and is also the standard operating pressure for Westinghouse PWRs.
5 ANALYSIS The purpose of this section is to describe the stress intensity factor calculations (Section 5.1) and crack growth calculations (Section 5.2) performed for the North Anna Unit 2 steam generator outlet nozzle dissimilar metal welds. Deterministic crack growth calculations that are documented in this section are used to determine the time required for axial and circumferential cracks to grow (I) to a depth of 75%
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Page 12 of 37 through-wall (maximum allowable depth when flaw stability is not limiting (8]) or (2) through the thickness of the weld.
5.1 Stress Intensity Factor Calculation
- 5. 1. 1 Loads and Stresses Tensile stresses are one of the key factors influencing PWSCC. For the purposes of crack growth calculations, separate stresses are considered in the hoop direction (which drive axial crack growth) and the axial direction (which drive circumferential crack growth).
This calculation appropriately considers weld residual stresses, operating pressure stresses, operating temperature stresses, and piping loads due to dead weight, pressure, and thermal expansion. The effect of transient stresses is not significant, as discussed in Assumption 5.
Weld residual stresses, operating pressure stresses, and operating temperature stresses were calculated using finite-element analyses that are documented in C-4520-00-01 (6]. In the finite-element model, the final length of the safe end (weld center-line to weld center-line) is 8.31 inches. The through-wall operating stress profile considering these load sources was determined in C-4520-00-01 (6] and is shown in Figure 2 (55%through-wall ID weld repair case), Figure 3 (45% through-wall ID weld repair case), and Figure 4 (no weld repair case). The axial operating stress profile is given as O'op,a(x/t), and the hoop operating stress profile is given as O'op,h(x/t).
Piping loads due to dead weight, pressure, and normal thermal expansion act to create a longitudinal force component, a torsion moment, and two orthogonal bending moments. These loads have a null or negligible effect on the hoop stress. The axial membrane stresses due to dead weight and normal thermal expansion are calculated as follows:
_FDW,x CYow,a-A' 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 II
[5-1]
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Page 13 of 37 FNTE.
a
=--"
NTE,a A
[5-2]
where Fow.x and FNTE,x are the axial forces due to dead weight and normal thermal expansion, respectively, and A is the axial cross-sectional area of the weld. The forces for the bounding loop (most tensile) are applied in the crack growth calculation. Based on the forces specified in Input 6, the net axial force for the bounding loop is -100.37 kips (-446.5 kN). The axial membrane stress due to the end cap pressure loading is included in the axial operating stress profile O'op,a(x/t) from the finite-element analysis.
The axial bending stress is calculated using the bending moment and torsion components of the dead weight, pressure, and normal thermal expansion piping loads. An effective bending moment (Meff) is determined as a combination of the bending and torsional moments based on a Von Mises stress approach:
[5-3]
As discussed in Assumption 9, when calculating the effective bending moment, the inputs describing the Loop I, Loop 2, and Loop 3 values for dead weight, pressure, and normal thermal expansion are used to calculate a conservative effective bending moment according to Equation [4-1]. Based on the moments specified in Inputs 7, 8, and 9, an effective bending moment of 12,960.22 in-kips (1,464.3 kN-m) is calculated. The outer diameter (OD) bending stress at the point of maximum bending is then calculated as:
[5-4]
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l
~--------~-----------'-~--------'---*----------------
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Page 14 of 37 n(R4 - R4)
I=
0 I
4
[5-5]
where R0 is the weld outer radius and I is the moment of inertia of the weld cross-sectional area.
For both axial and circumferential cracks, a membrane stress accounting for the effect of crack face pressure, P, equal to the operating pressure acting on the crack face is also considered.
As the principle of superposition applies for linear-elastic fracture mechanics, the individual membrane stress contributions defined above are superimposed to obtain a total stress profile. The resulting total axial stress profile is defined as:
(jtot,a ( X) = O"op,a ( X) + O" DW,a + O"N"rE,a + p *
[5-6]
For circumferential cracks, the global bending stress, <J"s, is applied separately in the K calculation.
The resulting total hoop stress profile is defined as:
(jtot,h ( X) = (jop,h ( X) + p *
[5-7]
5.1.2 Universal Weight Function Method Given the total hoop and axial stress profiles defined in Section 5. l. l, along with the orientation, depth, and aspect ratio of the crack, stress intensity factors can be calculated. To facilitate flexibility in total stress profile applied to the crack face, instead of fitting a polynomial to the stress profile and applying the influence coefficient method, the universal weight function method is applied. The general form of the mode I stress intensity factor calculation by way of the universal weight function method is given by [ 11]:
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Page 15 of 37 K1 = J: h(x,a)a101,1,(x)dx,
[5-8]
where:
Ki = mode I stress intensity factor (MPa"m)
X = distance from the ID surface (m) a = crack depth (m), and h(x,a) = weight function.
For circumferential cracks, there is an additional contribution to the mode I stress intensity factor due to a global bending moment. With this additional term, the form of the stress intensity factor for circumferential cracks is given by:
where:
K, = rr,G,fi + J: h(x,a)rr""'(x)dx, G5 = influence coefficient for the effect of global bending on a circumferential flaw centered at the point of maximum bending stress Q = flaw shape parameter defined below in Equation [5-18]
[5-9]
In general, the weight function, h(x,a) is a function of the influence coefficients, Go and G,. For the purpose of modeling crack growth under the semi-elliptical crack shape approximation (Assumption 1), the universal weight function method is applied to calculate separate stress intensity factors for the deepest point and the surface point of the semi-elliptical flaw.
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Page 16 of 37 For the deepest point, the influence coefficients Go and G 1 are determined as:
6 G90,i = L-41,i
- n;O
[5-10]
and for the surface point, the influence coefficients Go and G 1 are determined as:
Go. =A..
,I
.L-'(),I
[5-11]
The individual A,,,; and Ao,; fitting coefficients are obtained from linear-elastic finite element analyses.
These fitting coefficients are tabulated in API 579-1 I ASME FFS-1 [11, Table C.12 and Table C.14]
for specific combinations of the ratio of the weld thickness to inner radius (t/R;), the ratio of the crack depth to crack half-length (ale), and the ratio of the crack depth to the weld thickness (alt).
Values from tables of Go and G 1 influence coefficients are interpolated in tlR;, ale, and alt to obtain values of Go and G 1 specific to the crack geometry. This is accomplished by performing interpolation of the influence coefficients (Assumption 10):
- 1.
Log-linear interpolation in t/R;
- 2.
Log-linear interpolation in ale
- a.
If ale > 2.0, evaluate using ale= 2.0 (Assumption 12)
- b.
If ale < 0.125, log-linearly extrapolate in ale (Assumption 11)
- 3.
Linear interpolation in alt
- a.
If alt > 0.8, linearly extrapolate up to alt = 1.0 (Assumption 11 ).
Crack-geometry-specific Go and G 1 influence coefficients are then applied to compute the weight function coefficients, M; (for the deepest point) and N; (for the surface point) [11, Section C.14.2]:
M =_l!:_(3G -G ) - 24 I
.j2Q 90,1 90,0 5
[5-12]
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1 Page 17 of 37 Mi=3
[5-13]
6Jr (
) 8 M3 = Mn G900 -2G90 1 +-
v2Q s
[5-14]
N 1 = gj(2G0,0 -5G0,1)-8
[5-15]
[5-16]
N 3 = gj(3G0,0 -lOG0,1)-8,
[5-17]
where the flaw shape parameter, Q, is applied using the definition in API 579-1 / ASME FFS-1 [11, Section C.3.4.1] modified according to Assumption 12:
( r 65 1.0 + 1.464 :
for a/c::; 1.0 Q=
( r 65 1.0 + 1.464 :
for 2.0 ~ a/c > 1.0.
[5-18]
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Page 18 of 37 For the deepest point of a semi-elliptical surface crack, the weight function, h90, is then defined as [11]:
h,,(x,a)~ ~ 2 [1+M1(1-x) 112
+M2(1-x)+M3(1-x) 312 J.
2.1Z' ( a - x) a a
a
[5-19]
Similarly, for the surface point of the crack, the weight function, ho, is defined as [11]:
[5-20]
The integrals for the stress intensity factors (Equations [5-8] and [5-9]) are numerically evaluated for each individual time step using open extended formulas and using strategies to obtain accurate solutions despite the integrable power-law singularities at their lower or upper limits [21].
The following identity is applied ifthere is a singularity at the lower limit of the integral (as is the case when evaluating Ko):
f f( x)dx =- 1-rb-af' t':r 1(/ r +a}t (b >a).
a 1-r 0
[5-21]
Similarly, the following identity is applied if there is a singularity at the upper limit of the integral (as is the case when evaluating K90):
r f (x)dx = rb-a)'-r / r f (b-t1~r }t (b >a).
a 1-r 0
[5-22]
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Page 19 of 37 The right-hand side integrals in Equations [5-21] and [5-22] are solved by dividing the integration domain into 10,000 intervals, using a value of y = 0.57 (Assumption 17), and applying the open numerical integration expression shown below [21]:
The resulting stress intensity factors are then input into the crack growth calculation, which is detailed in Section 5.2.
5.2 Crack Growth Calculation 5.2.1 Approach The crack growth rates for axial and circumferential cracks in the Alloy 82/182 weld metal are calculated considering the PWSCC growth mechanism. Per Assumption 5, as cracking degradation in the subject weld is dominated by PWSCC, fatigue crack growth is not modeled in this calculation.
Accordingly, the standard PWSCC crack growth rate equation for Alloy 182 ([7], [8]) is applied for the crack growth calculation (see Assumption 2):
where da = exp[- Qg (J_-_l J] aKP dJ R T T
I,90 ref de =exp[-Qg(J_ __ l J]aKP dt R
T T
i,o' ref da/dt = crack growth rate at the deepest point of the crack (m/s) dc/dt = crack growth rate at the surface point of the crack (mis) 12100 Sunrise Valley Drive. Suite 220 Reston, VA 20191 PH 703.657.7300
[5-24]
[5-25]
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Page 20 of 37 Qg = thermal activation energy for crack growth = 130 kJ/mol ([7], [8])
R = universal gas constant= 8.314x 10-3 kJ/mol-K T
Tref (J.
Ki,9o K,,o
/3
=
=
=
=
=
=
absolute operating temperature at crack location = 560.4 K (Input 4) absolute temperature (325°C) used to normalize crack growth data = 598.15 K ([7],
[8])
crack growth rate coefficient= 1.5 x 10-12 at 325°C for m/s and MPa'1m ([7], [8])
stress intensity factor at the deepest point of the crack, calculated per Section 5.1.
(MPa'1m) stress intensity factor at the surface point of the crack, calculated per Section 5.1.
(MPa'1m) crack growth rate exponent = 1.6 ([7], (8])
To model growth of the cracks over time, the crack growth rate is calculated and integrated to determine the new crack length and depth using one-month time steps (Assumption 16). The crack growth rates obtained in Equations [5-24) and (5-25) are multiplied by the plant capacity factor (Assumption 13) to account for calendar time in which the plant is not operating (e.g., due to refueling outages). Using this approach, the times required (1) to produce a flaw with a depth of 75% through-wall (maximum allowable depth when flaw stability is not limiting) and (2) for the flaw to penetrate through-wall (resulting in leakage) are calculated.
Initial conditions applted assume an initial depth of 10% through-wall (Assumption 4), along with an initial aspect ratio (2c/a) of 2 for axial flaws and an initial aspect ratio (2c/a) of 10 for circumferential flaws (Assumption 7). Three WRS analysis cases were considered, assuming either no weld repair, a 360° 45% through-wall weld repair on the ID surface, or a 360° 55% through-wall weld repair on the ID surface (Assumption 15).
5.2.2 Results The results of the crack growth calculations are summarized in Table 1 and shown in Figure 5 through Figure 10. Crack depth as a function of time is shown in Figure 5 and Figure 6 for axial and circumferential cracks, respectively. Figure 7 and Figure 8 show the crack half-length on the ID surface as a function of time for axial and circumferential cracks, respectively. Figure 9 and Figure 10 show the crack aspect ratio (2c/a) as a function of time for axial and circumferential cracks, respectively.
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Page 21 of 37 In addition, plots are provided showing the key intermediate result of the crack-tip stress intensity factors applied in the crack growth equation. Figure 11 and Figure 12 show the crack-tip stress intensity factor at the deepest point (K90) as a function of crack depth (alt), and Figure 13 and Figure 14 show the crack-tip stress intensity factor at the surface point (Ko) as a function of crack depth (alt),
for axial and circumferential cracks, respectively.
Allowable flaw size calculations [14] performed in accordance with ASME Section XI confirm that the allowable flaw depth limit for axial flaws is 75% through-wall. These calculations were performed for the NAPS Unit 2 steam generator inlet and outlet nozzles. Reference [14] reports an allowable depth of 75% through-wall for axial flaws with lengths up to at least 7.4 inches, which as expected bounds the lengths reported below in Figure 7. For circumferential cracks, Reference [14] reports an allowable depth of 75% through-wall for circumferential flaw lengths up to at least 40% of the circumference.
For the circumferential crack growth cases resulting from the present work, the flaw depth and length (Figure 6 and Figure 8) remain within these allowable limits for at least 51.0 years. In the limiting circumferential flaw case, the total flaw length on the ID (2c) reaches 40% of the circumference (i.e.,
40% of 97.5 in., or 39.0 in.) after 53.5 years and 75% through-wall after 51.0 years. After 10 years, the total length for the limiting 55% ID repair circumferential flaw case is calculated to be about 8.8 inches (see Figure 8), which is only about 9% of the circumference at the weld ID, and the corresponding flaw depth is less than 50% through-wall (see Figure 6). Conservatively assuming a constant-depth circumferential flaw geometry, these dimensions after l O years correspond to a flaw size of less than 5% of the weld cross section, which is clearly within the allowable flaw size limit.
The times required for a flaw with an initial depth of 10% through-wall to grow (1) to a depth of 75%
through-wall (maximum allowable depth per ASME Section XI when flaw stability is not limiting [8])
and (2) through-wall are reported in Table 1. The limiting case for the time for a flaw to grow from an initial depth of 10% through-wall to the allowable depth per ASME Section XI is for an axial flaw. In this limiting case, the growth time is 9.1 years, the allowable flaw depth is 75% through-wall, and an additional 3.1 years is calculated for the axial crack to penetrate through the remaining 25% of the wall thickness. This limiting case is applicable only to the "Loop 2" nozzle, which includes a 55% through-wall localized weld repair. The limiting case applicable to the "Loop 1" and "Loop 3" nozzles results in a time of l 0.3 years for an axial crack to grow from 10% through-wall to 75% through-wall. In this case, an additional 2.8 years is calculated for the axial crack to penetrate through the remaining 25% of the wall thickness.
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Page 22 of 37 5.3 Software Usage The following software, controlled in accordance with DEI's quality assurance program for nuclear safety-related work [22], was used in preparing this calculation.
The stress intensity factor and crack growth calculations used in this work were performed using Python 3.5 as a one-time-use engineering analysis computer program on a Dell Precision 5510 with an Intel Core i5-6300HQ processor and running Windows 7 Professional (Service Pack 1). The results from this one-time-use program were checked and reviewed in accordance with DEI's nuclear quality assurance (QA) program manual [22). Each output from the one-time-use Python calculation is individually verified in Memo M-4520-00-02 [23]. The alternate calculation documented in the memo was performed using Excel 2010. Furthermore, the memo compares results obtained using the Python model with axial and circumferential crack growth calculations published in peer-reviewed papers for Alloy 82/182 piping butt welds. Native electronic files for the Software Usage Records associated with the above software use are included in the data disk that accompanies this calculation [24]. These files are listed in Appendix A of this calculation.
6 REFERENCES
- 1.
Westinghouse Letter to Dominion Generation, LTR-SGDA-06-79, Dated June 28, 2006,
Subject:
North Anna Unit 2 Replacement Steam Generator Safe End to Inlet and Outlet Nozzle Welds.
- 2.
ASME Code Case N-770-2, "Alternative Examination Requirements and Acceptance Standards for Class 1 PWR Piping and Vessel Nozzle Butt Welds Fabricated With UNS N06082 or UNS W86182 Weld Filler Material With or Without Application of Listed Mitigation Activities,"
Section XI, Division 1, American Society of Mechanical Engineers, New York, Approval Date:
June 9, 2011.
- 3.
ASME Code Case N-770-3, "Alternative Examination Requirements and Acceptance Standards for Class 1 PWR Piping and Vessel Nozzle Butt Welds Fabricated With UNS N06082 or UNS W86182 Weld Filler Material With or Without Application of Listed Mitigation Activities,"
Section XI, Division 1, American Society of Mechanical Engineers, New York, Approval Date:
April 7, 2013.
- 4.
ASME Code Case N-770-4, "Alternative Examination Requirements and Acceptance Standards for Class 1 PWR Piping and Vessel Nozzle Butt Welds Fabricated With UNS N06082 or UNS W86182 Weld Filler Material With or Without Application of Listed Mitigation Activities,"
Section Xl, Division 1, American Society of Mechanical Engineers, New York, Approval Date:
May 7, 2014.
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Page 23 of 37
- 5.
Letter from E. S. Grecheck (Virginia Electric and Power Company, Dominion) to U.S. NRC, "North Anna Power Station Unit 2, ASME Section XI Inservice Inspection Program Examination Results and Revised Request for Alternative to ASME Code Steam Generator Nozzle-to-Vessel Weld Examination Requirements, Alternative Request N2-I4-LMT-001-Rl." Dated April 22, 2013. [NRC ADAMS Accession No.: ML13114A253]
- 6.
Dominion Engineering, Inc. Calculation C-4520-00-01, Revision 0, December 2017.
- 7.
Materials Reliability Program Crack Growth Rates for Evaluating Primary Water Stress Corrosion Cracking (PWSCC) of Alloy 82, 182, and 132 Welds (MRP-115), EPRI, Palo Alto, CA: 2004. I 006696. (Freely available at www.epri.com]
- 8.
ASME Boiler and Pressure Vessel Code,Section XI, Nonmandatory Appendix C. 2015 Edition.
- 9.
Incoming Correspondence IC-4520-00-02, Rev. 0, "RE: North Anna Unit 2 Crack Growth Results for SG Outlet Nozzles," dated October 25, 2017.
- 10.
Westinghouse Letter to Dominion Generation, VRA-13-26, Dated April 30, 2013,
Subject:
Dominion Generation North Anna Unit 2 Steam Generator Inlet and Outlet Nozzle Loads.
- 11.
API Standard 579-1/ASME FFS-1 Fitness for Service, 2007.
- 12.
ASME Boiler and Pressure Vessel Code,Section XI, Nonmandatory Appendix A. 2015 Edition.
- 13.
ASME Boiler and Pressure Vessel Code,Section XI, Mandatory Appendix VIII. 2015 Edition.
- 14.
"Flaw Tolerance Evaluation of Steam Generator Hot Leg Inlet and Cold Leg Outlet Nozzle Dissimilar Metal Welds, North Anna Power Station, Unit 2," Structural Integrity Associates, Inc.,
Calculation File No. 1300532.315, Rev. 0, May 15, 2013.
- 15.
EPRI Materials Degradation Matrix, Revision 3. EPRI, Palo Alto, CA: 2013. 3002000628.
- 16.
G. Rao, G. Moffatt, a'nd A. McJlree, "Metallurgical Investigation of Cracking in the Reactor Vessel Alpha Loop Hot Leg Nozzle to Pipe Weld at the V.C. Summer Station," Proceedings of the international Symposium, Fontevraud V, September 23-27, 2002.
- 17.
D. Rudland, D.-J. Shim, and S. Xu, "Simulating Natural Axial Crack Growth in Dissimilar Metal Welds due to Primary Water Stress Corrosion Cracking," Proceedings of ASME 2013 Pressure Vessels and Piping Conference, July 14-18, 2013, Paris, France, ASME, 2013. PVP2013-97188.
- 18.
S. Xu, D. Lee, D. Scarth, and R. Cipolla, "Closed-Form Relations for Stress Intensity Factor Influence Coefficients for Axial JD Surface Flaws in Cylinders for Appendix A of ASME Section XI," Proceedings of the ASME 2014 Pressure Vessels & Piping Conference, July 20-24, 2014, Anaheim, California, USA, 2014. PVP2014-28222.
- 19.
"Fabrication and Repair History of the Unit 2 Steam Generator Inlet and Outlet Nozzles,"
Dominion Generation Engineering Technical Evaluation.ETE-NA-2017-04 l, Revision 0, August 2017.
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Page 24 of 37
- 20.
Westinghouse Letter to Dominion Generation, LTR-SGDA-09-32, Dated March 13, 2009,
Subject:
Transmittal of Design Information for North Anna Unit 1 Model 5 lF Steam Generator Channel Head Primary Nozzles.
- 21.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes. The Art of Scientific Computing. Second Edition. Cambridge University Press, Cambridge, UK, 1992.
- 22.
Dominion Engineering, Inc. Quality Assurance Manual for Safety-Related Nuclear Work, DEI-002, Revision 18, November 2010.
- 23. Dominion Engineering, Inc. Memorandum M-4520-00-02, "Verification of One-Time Use Software Outputs for C-4520-00-02 RO and C-4520-00-03 RO." Revision 0, December 2017.
- 24.
Dominion Engineering, Inc. Data Disk D-4520-00-03, Revision 0, December 2017.
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Page 25 of 37 Table 1.
Crack Growth Results Crack Weld Residual Stress j Growth Time to I Growth Time to Orientation Profile jWeld Material 75% TW (yr) I TW (yr)
Axial 55% ID Repair Cold Leg I Alloy 182 I
9.1 I
12.2 Axia l 1 45% 16Repair Cold LegJ All;y 182 f
- 10.3 ****
I 13:i
- ci~~~~~:]~~~i-~*-i**ss~
0 1~~ef:~:~~~l ~et~
= ~ ~:~+:-~
'---~~:~ --.. }--... -~~~-
- __ -
Cir~umf~rential
- 45%_1D RE:paJr Cold Leg Alloy 18~--
87.7
.... *******-l*-
108 Circumferential No Repair Cold Leg Alloy 182 125 I
137 Maximum weld width Wall thickness Minimum weld width Figure 1.
Annotated Drawing Indicating Wall Thickness and Average Weld Width (Average of Maximum and Minimum Widths) 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191
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Page 26 of 37 Figure 2.
Figure 3.
400 i
~ 200 ci5 bl)
- a f
0
~
0
~ -200 "Cl "ii a: -400
...._._.. _.._._.......-,+-+-**
~
-+-Hoop Stress
- Axial Stress 0%
I 0%
20%
30%
40%
50%
60%
70%
80%
90%
I 00%
Percent Through-Wall (x/t)
Residual Plus Operating Stress Profiles Applied for PWSCC Crack Growth Calculations using 360° 55% Through-Wall ID Weld Repair
~ 400 i
~ 200 ci5 bl)
C.: f 0
~
0
~-200 "Cl 'ij a: -400
-+-Hoop Stress
- *Axial Stress 0%
I 0%
20%
30%
40%
50%
60%
70%
80%
90%
1 00%
Percent Through-Wall (x/t)
Residual Plus Operating Stress Profiles Applied for PWSCC Crack Growth Calculations using 360° 45% Through-Wall ID Weld Repair 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Page 27 of 37 Figure 4.
400 i
~ 200 V)
.5 f 0
Q, 0., =
~-200
" =
- E t a: -400
-+-Hoop Stress
- ***Axial Stress 0%
I 0%
20%
30%
40%
50%
60%
70%
80%
90%
I 00%
Percent Through-Wall (x/t)
Residual Plus Operating Stress Profiles Applied for PWSCC Crack Growth Calculations using No Weld Repair 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Page 28 of 37 Figure 5.
Figure 6.
0.9 0.8 0.7
~0.6
..c:
Q, 0 05
...... e o.4 u
OJ 0.2 0.1
,/
I I
I I
I I
I I
- 55% Repair
-****45% Repair
- - - No Repair 0 +-'-~-"--+~~-+--'~~1-'-~-'-l-~~+-'-~
-'--+~~-+--'~~l-'-~..L....!
0 2
4 6
8 10 Time (Years)
Axial Crack Depth, alt, as a Function of Time 0.1 12 14
/
I 16
- - 55% Repair
- 45% Repair
- - - No Repair 18 0 +-'-~~t-'-~~l-"-~........,r-'--~..L-t~~-'-+~~.....,.~~..,...~~'"-1 0
20 40 60 80 Time (Years) 100 Circumferential Crack Depth, alt, as a Function of Time 120 140 160 12100 Sunrise Valley Drive. Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Page 29 of 37 Figure 7.
Figure 8.
0.9 0.8
,.....0.7
- §,
-: 0 6
"" =
., ! 05
- i:
,:,: 0.4 f!
U 0.3 0.2 0.1 r-----*------------------------ ------.
/
- - 55% Repair
45% Repair
- - - - No Repair 0 +-'--'-'--'-+--'-'--'-'-+-'--'-'--'-+--'-'--'-'-4-'--'-'--'--+--'-'--'-'-+--'--'-'--'--+--'-'--'-'-+-'--'-'-...L.-l 0
2 4
6 8
10 12 Time (Years)
Axial Crack Half -Length on ID, c, as a Function of Time 35 30 10 5
14 16
- - 55% Repair
45% Repair
- - - No Repair 18 0 +-'-............. ~l-'-~--'-+~'--'--'---+-.............. --'--'--+-'--'-~-+-'-............. ~l-'-.............. -'-1~~.......,
0 20 40 60 80 100 120 140 160 Time (Years)
Circumferential Crack Half-Length on ID, c, as a Function of Time 1----------------------------------------------f 12*100 Sunrise Valley Drive. Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Page 30 of 37 Figure 9.
2.5 ------------------------
C. < I
......... u 0.5
- - 55% Repair
45% Repair
. - - - No Repair 0 +--'-~.......... ~~.........,_,__,_._._,_,_.._._.,_,__.,_,__+-'-~.......... ~~
......... _._,_,_._._,_,_.L...i 0
2 4
6 8
10 12 14 16 18 Time (Years)
Axial Crack Aspect Ratio, 2c/a, as a Function of Time 20 -----------------------~
18 16
]
12 IX ti 10 C. < 8 '
......... u 6 4
2
- - 55% Repair
-****45% Repair
- - - No Repair 0.J-..-.,.'-'-~+-'-~-'-+-'-~'-'-i--'-~--"-f-'-..............L-f-'-'-~-'--+~-'-"-+~--'-'---1 0
20 40 60 80 Time (Years) 100 120 140 160 Figure 10.
Circumferential Crack Aspect Ratio, 2c/a, as a Function of Time 12100 Sunrise Valley Drive. Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Page 31 of 37 140.------,-----,----------------,
120 100 40 20
- - 55% Repair
- 45% Repair
- - - No Repair 0 +--'---"-'---'--1~~~~-~~~~+--'---"-'---'--I~~~~_,
0 0.2 0.4 0.6 0.8 Crack Depth (a/t)
Figure 11.
Axial Crack Stress Intensity Factor at Deepest Point, Kgo, as a Function of Crack Depth 140.-------------------------,
120 100 40 20
--55% Reµair
- 45% Repair
- - - No Repair
' 11
,f1
'It I'
,: I
,'/1 I/ /
/it
//,
,'/,
, /I
\\
\\
\\
,'//
\\
\\
///
\\
\\
\\
I,, I
\\
\\
\\
,///
\\\\
\\
\\
~',/ /
\\
\\ *** - -
- -- - - - _.. "'.>~.. :.. -.... -..~:~-~.:::,..,
0 -+---'----'---'---'--1~~~~-~~~~-+--'----'---'---'--l~~~~---i 0
0.2 0.4 0.6 0.8 Crack Depth (a/t)
Figure 12.
Circumferential Crack Stress Intensity Factor at Deepest Point, #{go, as a Function of Crack Depth 12100 Sunrise Valley Drive. Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
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Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-NP Revision No.:
Page 32 of 37 200
~150 e
'T' c..
~
~ 100 50
- - 55% Repair
45% Repair
- - - No Repair 0 +---~'---'~---+--'---'--'---........... _..__~.___.__.__.....__._~
........... ~_..__~.___.__.____,
0 0.2 0.4 0.6 0.8 Crack Depth (a/t)
Figure 13.
Axial Crack Stress Intensity Factor at Surface Point, Ko, as a Function of Crack Depth 100 90
- - 55% Repair 80 70
[
60 E
'T'.. 50 c.. 6
= 40 30 20 10 0
0 0.2 0.4 0.6 0.8 Crack Depth (a/t)
Figure 14.
Circumferential Crack Stress Intensity Factor at Surface Point, Ko, as a Function of Crack Depth 12100 Sunrise Valley Drive. Suite 220 Reston; VA 20191 PH 703.657.7300 FX 703.657.7301
Dominion [n~ineerin~, Inc.
NON-PROPRIETARY V ERSION
Title:
Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-NP Revision No.:
Page 33 of 37 A
CONTENTS OF DATA DISK D-4520-00-03 The following tables list the contents of Data Disk D-4520-00-03. The contents include Software Usage Records in their native electronic formats.
12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
Dominion [n~ineerin~, Inc N ON-PROPRIETARY V ERSION
Title:
Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-NP Revision No.:
1 Page 34 of 37 Table A-1.
Software Usage Records Software Usage Records Folder File name Description C ra c kgrowth_ co Id leg__noinl a y _ o. py Python script that generates the output files CL_O_axial.csv Axial stress profile from FEA (MPa)
CL_O_hoop.csv Hoop stress profile from FEA (MPa)
TableC12_axial.txt API 579-1/ASME FFS-1 Table C.12 input data - axial TableC14_circ.txt API 579-1/AMSE FFS-1 Table C.14 input data - circ out_2c_over _a_ax.txt Output - 2c/a axial solution out_2c_over _a_ho. txt Output - 2c/a hoop solution out_a_over _t_ax.txt Output - a/t axial solution out_a_over_t_ho.txt Output - a/t hoop solution Case_O out_kO_ax. txt Output - KO axial solution out_kO_ho.txt Output
- KO hoop solution out_k90_ax.txt Output* K90 axial solution out_k90_ho.txt Output
- K90 hoop solution out_time_ax.txt Output
- time axial solution (years) out_time_ho.txt Output
- time hoop solution (years) out_timethroughwall_ax.txt Output* time for through-wall crack in axial solution (years) out_timethroughwall_ho.txt Output* time for through-wall crack in hoop solution (years) out_timeto75_ax.txt Output
- time for 75% through-wall crack in axial solution (years) out_timeto75_ho.txt Output
- time for 75% through-wall crack in hoop solution (years)
Crackgrowth_coldleg__noinlay_ 45.py Python script that generates the output files CL_ 45_axial.csv Axial stress profile from FEA (MPa)
CL_ 45_hoop.csv Hoop stress profile from FEA (MPa)
TableC12_axial.txt API 579-1/ASME FFS-1 Table C.12 input data* axial TableC14_circ.txt API 579*1/AMSE FFS-1 Table C.14 input data* circ out_2c_over _a _ax. txt Output
- 2c/a axial solution out_2c_over _a_ho. txt Output
- 2c/a hoop solution out_a_over_t_ax.txt Output* a/t axial solution out_a_over_t_ho.txt Output
- a/t hoop *solution Case_ 45 out_kO_ax. txt Output* KO axial solution out_kO_ho.txt Output
- KO hoop solution out_k90_ax.txt Output* K90 axial solution out_k90_ho.txt Output
- K90 hoop solution out_time_ax.txt Output
- time axial solution (years) out_time_ho.txt Output* time hoop solution (years) out_timethroughwall_ax.txt Output
- time for through-wall crack in axial solution (years) out_timethroughwall_ho.txt Output* time for through-wall crack in hoop solution (years) out_timeto75_ax.txt Output
- time for 75% through-wall crack in axial solution (years) out_timeto75_ho.txt Output
- time for 75% through-wall crack in hoop solution (years) 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
Dominion [n~ineerin~, Inc.
N ON-PROPRIETARY V ERSION
Title:
Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-N P Revision No.:
1 Page 35 of 37 Table A-1.
Software Usage Records (Continued)
Software Usage Records Folder File name Description Cra c kgrowth _ co Idle&_ no inlay _55. py Python script that generates the output files CL_55_axial.csv Axial stress profile from FEA (MPa)
CL_55_hoop.csv Hoop stress profile from FEA (MPa)
TableC12_axial.txt API 579-1/ASME FF5-1 Table C.12 input data - axial TableC14_circ.txt API 579-1/AM5E FFS-1 Table C.14 input data - circ out_2c_over _a_ax. txt Output - 2c/a axial solution out_2c_over_a_ho. txt Output - 2c/a hoop solution out_a_over _t_ax. txt Output - a/t axial solution out_a_over_t_ho.txt Output - a/t hoop solution Case_55 out_kO_ax. txt Output - KO axial solution out_kO_ho.txt Output - KO hoop solution out_k90_ax.txt Output - K90 axial solution out_k90_ho. txt Output - K90 hoop solution out_time_ax.txt Output - time axial solution (years) out_time_ho. txt Output - time hoop solution (years) out_timethroughwall_ax.txt Output - time for through-wall crack in axial solution (years) out_timethroughwall_ho.txt Output - time for through-wall crack in hoop solution (years) out_timeto75_ax.txt Output - time for 75% through-wall crack in axial solution (years) out_timeto75_ho.txt Output - time for 75% through-wall crack in hoop solution (years)
Cr ackgro wth _ co Id le&_ no inlay_ O. py Python script that generates the output files CL_O_axial.csv Axial stress profile from FEA (MPa)
CL_O_hoop.csv Hoop stress profile from FEA (MPa)
TableC12_axial.txt API 579-1/ASME FF5-1 Table C.12 input data - axial TableC14_circ.txt API 579-1/AMSE FF5-1 Table C.14 input data - circ out_2c_over _a_ax. txt Output - 2c/a axial solution out_2c_over _a_ho. txt Output - 2c/a hoop solution out_a_over _t_ax. txt Output - a/t axial solution out_a_over_t_ho. txt Output - a/t hoop solution Python_Closed_Form_Case_O out_kO_ax. txt Output - KO axial solution out_kO_ho.txt Output - KO hoop solution out_k90_ax.txt Output - K90 axial solution out_k90_ho. txt Output - K90 hoop solution out_time_ax.txt Output - time axial solution (years) out_time_ho. txt Output - time hoop solution (years) out_timethroughwall_ax.txt Output - time for through-wall crack in axial solution (years) out_timethroughwall_ho.txt Output - time for through-wall crack in hoop solution (years) out_timeto75_ax.txt Output - time for 75% through-wall crack in axial solution (years) out_timeto75_ho.txt Output - time for 75% through-wall crack in hoop solution (years) 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301
~-------- ---- - - - - - -
Dominion [n~ineerin~, Inc.
NON-PROPRIETARY VERSION
Title:
Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-N P Revision No.:
1 Page 36 of 37 Table A-1.
Software Usage Records (Continued)
Software Usage Records Folder File name Description Crackgrowth_coldleg_noinlay _ 45. py Python script that generates the output files CL_ 45_axial.csv Axial stress profile from FEA (MPa)
CL_ 45_hoop.csv Hoop stress profile from FEA (MPa)
TableC12_axial.txt API 579-1/ASME FFS-1 Table C.12 input data - axial TableC14_circ.txt API 579-1/AMSE FFS-1 Table C.14 input data - circ out_2c_over _a_ax. txt Output - 2c/a axial solution out_2c_over_a_ho. txt Output - 2c/a hoop solution out_a_over _t_ax. txt Output - a/t axial solution out_a_over_t_ho.txt Output - a/t hoop solution Python_Closed_Form_Case_ 45 out_kO_ax. txt Output - KO axial solution out_kO_ho.txt Output - KO hoop solution out_k90_ax.txt Output - K90 axial solution out_k90_ho. txt Output - K90 hoop solution out_time_ax.txt Output - time axial solution (years) out_time_ho.txt Out put - time hoop solution (years) out_timethroughwall_ax.txt Output - time for through-wall crack in axial solution (years) out_timethroughwa ll_ho.txt Output - time for through-wall crack in hoop solution (years) out_timeto75_ax.txt Output - time for 75% through-wall crack in axial solut ion (years) out_timeto75_ho.txt Output - time fo r 75% through-wall crack in hoop solution (years)
Crackgrowth_coldleg_noinlay _5 5. py Python script that generates the output files CL_SS_axial.csv Axial stress profile from FEA (MPa)
CL_SS_hoop.csv Hoop stress profile fro m FEA (MPa)
TableC12_axial.txt API 579-1/ASME FFS-1 Ta ble C.12 input data - axial TableC14_circ.txt API 579-1/AMSE FFS-1 Table C.14 input data - circ out_2c_over _a _ax. txt Output - 2c/a axial solution out_2c_over _a_ho. txt Output - 2c/a hoop solution out_a_over _t_ax. txt Output - a/t axial solution out_a_over_t_ho.txt Output - a/t hoop solution Python_ Closed_Form_ Case_ss out_kO_ax.txt Output - KO axial solution out_kO_ho.txt Output - KO hoop solution out_k90_ax.txt Output - K90 axial solution out_k90_ho. txt Output - K90 hoop solution out_time_ax. txt Output - time axial solution (years) out_t ime_ho. txt Output - time hoop solution (years) out_t imet hro ughwa ll_ax. txt Output - time fo r through-wall crack in axial solution (years) out_timethroughwall_ho.txt Output - time for through-wall crack in hoop solution (years) out_timeto 75_ax. txt Output - time fo r 75% through-wall crack in axia l solution (years) out_timeto75_ho.txt Output - time for 75% through-wall crack in hoop solution (years) 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191
- PH 703.657.7300 FX 703.657.7301
Dominion [n~ineerin~, Inc.
NON-PROPRIETARY VERSION
Title:
Crack Growth Analyses for NAPS Unit 2 Steam Generator Outlet Nozzles Calculation No.: C-4520-00-03-NP Revision No.:
1 Page 37 of 37 Table A-1.
Software Usage Records (Continued)
Software Usage Records Folder File name Description C ra c kgrowth _ co Id leg__ no inlay_ O. py Python script that generates the output files CL_O_axial.csv Axial stress profile from paper (MPa)
TableC12_axial.txt API 579-1/ASME FFS-1 Table C.12 input data - axial TableC14_circ.txt API 579-1/AMSE FFS-1 Table C.14 input data - circ out_2c_over _a_ho. txt Output - 2c/a hoop solution J_PVP _Tech_Circ out_a_over_t_ho. txt Output - a/ t hoop solution out_kO_ho.txt Output - KO hoop solution out_k90_ho.txt Output - K90 hoop solution out_time_ho.txt Output - time hoop solution (years) out_timethroughwall_ho.txt Output - time for through-wall crack in hoop solution (years) out_timeto75_ho.txt Output - time for 75% through-wall crack in hoop solution (years)
Cra c kgrowt h_ co Id leg__noinl ay _ O. py Python script that generates the output files CL_O_hoop.csv Hoop stress profile from paper (MPa)
TableC12_axial.txt API 579-1/ASME FFS-1 Table C.12 input data - axi al TableC14_circ.txt API 579-1/AMSE FFS-1 Table C.14 input data - circ out_2c_over _a_ax. txt Output - 2c/a axial solution PVP2009-77855_Axial out_a_over _t_ax. txt Output - a/t axial solution out_kO_ax. txt Output - KO axial solution out_k90_ax.txt Output - K90 axial solution out_time_ax.txt Output - time axial solution (years) out_timethroughwall_a x. txt Output - time for through-wall crack in axi al solution (years) o ut_timeto 75_ax. txt Output - time for 75% through-wall crack in axial solution (years)
M-4520-00-02_RO M-4520-00-02 RO.pdf Memo documenting alternate calculation for one-time use engineering analysis computer program.
NA Unit 2 (Axial 55%).xlsm Alternate calculation for axial crack 55% ID weld repair case NA Unit 2 (Axial 45%).xlsm Alternate calculation for axial crack 45% ID weld repa ir case Excel_Closed_Form NA Unit 2 (Axial 0%).xlsm Alternate calculation for axial crack no weld repair case NA Unit 2 (Circ 55%).xlsm Alternate calculation for circ. crack 55% ID weld repair case NA Unit 2 (Circ 45%).xlsm Alternate calculation for circ. crack 45% ID weld repair case NA Unit 2 (Circ 0%).xlsm Alternate calculation for circ. crack no weld repair case 12100 Sunrise Valley Drive, Suite 220 Reston, VA 20191 PH 703.657.7300 FX 703.657.7301