ML093360331
| ML093360331 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 07/20/2009 |
| From: | Jing P FirstEnergy Nuclear Operating Co, Structural Integrity Associates |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| L-09-268, TAC ME0477, TAC ME0478 0800368.326, Rev. 0 | |
| Download: ML093360331 (33) | |
Text
Structural Integrity Associates, Inc. File No.: 0800368.326 CALCULATION PACKAGE Project No.: 0800368 Quality Program: Z Nuclear I] Commercial PROJECT NAME: Davis Besse Phase 2 Alloy 600 CONTRACT NO.: 49151, Rev. 1 CLIENT: PLANT: Welding Services Inc. (WSI) Davis-Besse Nuclear Power Station, Unit 1 CALCULATION TITLE: Crack Growth Evaluation of Reactor Coolant Pump Discharge Nozzle with Weld Overlay Repair Document Affected Project Manager Preparer(s)
&Revision Pages Revision Description Approval Checker(s)
Signature
& Date Signatures
& Date 01 -30 Initial Issue Preparers:
A-1 -A-3 Stan S. Tang Peihua Jing 07/20/09 07/20/09 Checker: Jim Wu 07/20/09 Page 1 of 30 F0306-01RO Structural Integrity Associates, Inc.Table of Contents 1.0 PURPOSE ......................................................................................................................
4 2.0 M ETHODOLOGY
....................................................................................................
4 3.0 DESIGN INPUTS .....................................................................................................
4 3.1 Geom etry ......................................................................................................
4 3.2 Fracture M echanics M odels ...........................................................................
5 3.3 Loads ..........................................................................................................
6 3.4 Crack Growth Laws ......................................................................................
9 3.4.1 Alloy 82/182 Fatigue Crack Growth Law ...................................................
9 3.4.2 Alloy 82/182 PWSCC Growth Law ................................................................
9 3.4.3 Treatment of Negative Stress Intensity Factors ...........................................
10 4.0 ASSUM PTION S ......................................................................................................
10 5.0 CALCULATION S ..................................................................................................
11
6.0 CONCLUSION
S AND DISCUSSION S ...............................................................
12
7.0 REFERENCES
........................................................................................................
14 APPENDIX A COMPUTER FILE DESCRIPTIONS
...................................................
A-1 File No.: 0800368.326 File No.: 0800368.326 Revision:
0 F0306-O1RO Page 2 of 30 V Structural Integrity Associates, Inc.List of Tables Table 1: Stress Coefficients for Various Loadings at the DMW ........................................
15 Table 2: Discharge Nozzle Bounding Piping Interface Loads ..........................................
16 Table 3: Bounding Thermal Transients for the Discharge Nozzle ...................................
16 Table 4: Sequence of Events and Cycles for Fatigue Crack Growth .................................
17 Table 5: Crack Growth Results for PATHs 1, 2, and 3 .....................................................
17 List of Figures Figure 1: Sections Used For Crack Growth ......................................................................
18 Figure 2: Stress Path Definitions for Maximum Weld Overlay for Thermal Transient Analyses at 0, 90 and 180 Degree Locations
......................................
19 Figure 3: Stress Path Definitions for Minimum Weld Overlay for Mechanical Load Analyses (pressure, axial force, and moment loads)0, 90 and 180 D egree Locations
........................................................................
20 Figure 4: Critical Paths Used for Through-wall Mapped Stresses of Minimum Weld Overlay for Residual Stress Analyses .....................................................
21 Figure 5: Time Histories of Linearized Membrane-plus-Bending Stress at the Inside Surface for Reactor Trip 8A Transient
....................................................
22 Figure 6: Through-wall Residual Stress Distribution at 70'F and Curve Fits at the D M W .................................................................................................
23 Figure 7: K-vs-a Plots for Paths 1, 2, and 3 Residual Stresses at 70'F ............................
24 Figure 8: Circumferential Flaw Model, Non-Moment Loading ........................................
25 Figure 9: Circumferential Flaw Model, Moment Loading ...............................................
26 Figure 10: A xial Flaw M odel ............................................................................................
27 Figure 11: K-vs-a at Normal Steady State Operating Conditions for PATH 1 .................
28 Figure 12: K-vs-a at Normal Steady State Operating Conditions for PATH 2 .................
29 Figure 13: K-vs-a at Normal Steady State Operating Conditions for PATH 3 .................
30 File No.: 0800368.326 Page 3 of 30 Revision:
0 F0306-O1RO V Structural Integrity Associates, Inc.1.0 PURPOSE The purpose of this calculation package is to calculate crack growth in the dissimilar metal weld (DMW)for the reactor coolant pump discharge nozzle with optimized weld overlay (OWOL) repair. Loads considered are external piping loads, internal pressure, thermal transients, and residual stress. Both fatigue crack growth (FCG) and Primary Water Stress Corrosion Cracking (PWSCC) are considered.
FCG is due to cyclic loading and PWSCC is due to sustained loading at steady state normal operating conditions.
2.0 METHODOLOGY
Representative fracture mechanics models (see Section 3.2) are used to determine stress intensity factors (K). The stress intensity factors for each type of load are computed as a function of crack depth in the original weld (DMW) and superimposed for the various operating states. Stresses that contribute to fatigue crack growth are compiled from previous calculations (References 4 and 6). These stresses result from primary loads such as internal pressure and external piping loads, and secondary loads such thermal gradient stresses (due to thermal transient events), and residual stresses.
The through-wall stresses are extracted and fitted to a third order polynomial.
FCG (or combined FCG and PWSCC growth if PWSCC is active) is computed using linear elastic fracture mechanics (LEFM) techniques.
PWSCC is determined by computing the stress intensity factor versus flaw depth curve (K-vs-a) at steady state normal operating conditions.
A crack growth law for Alloy 600 weld metals (Alloy 82/Alloy 182), with a multiplier to account for crack growth in a pressurized water reactor (PWR)environment, is used at the DMW.Cases for both optimized weld overlay (OWOL) and full structural weld overlay (FSWOL) will be considered.
For circumferential flaws, a postulated initial flaw of 50% (75%) of the original base metal thickness is assumed for computing crack growth in the nozzle with an OWOL (FSWOL). This assumption is based on the fact that for circumferential flaws, the depth of the inspection volume of the nozzle with an overlay is limited to the outer 50% of the original base metal thickness.
Thus the time it takes for a postulated initial circumferential flaw of 50% (75%) of the original base metal thickness with an OWOL (FSWOL) to reach 75% (100%) of the original base metal thickness is computed and reported herein.For axial flaws, the depth of the inspection volume of the nozzle with an overlay is limited to the outer 25% of the original base metal thickness.
Therefore, an initial axial flaw of 75% of the original base metal thickness is considered for nozzles with both an OWOL and FSWOL.3.0 DESIGN INPUTS 3.1 Geometry Details of the discharge nozzle geometry are provided in the finite element model calculation package[1]. Three sections are selected to evaluate for crack growth, as shown in Figure 1. Note that in the figure, the minimum and maximum dimensions of each section (due to the use of minimum or OWOL File No.: 0800368.326 Page 4 of 30 Revision:
0 F0306-O1RO V Structural Integrity Associates, Inc.design and maximum, or FSWOL design in the finite element models [1]) are shown. The thinner sections are used for pressure, piping interface loads and residual stresses.
The thicker sections are used for all local thermal gradient stresses.
This approach assures that the actual applied overlay and resulting stresses are bounded. See Section 3.3 for descriptions of the different loads applied to the nozzle.The typical approach for computing crack growth is to select the sections that give highest stresses for each loading condition and map the corresponding stress on one representative section, which is then used for crack growth. However, an initial analysis for this particular nozzle showed that using all the bounding stresses on one section lead to overly conservative results. This conservatism occurs with (1)residual stress distributions (see Section 3.3 under "Residual Stress" for details) and (2) moment load (see Section 3.3 under "pipe interface loads" for details), both of which show significant variation depending on the position within the DMW. To remove this conservatism, the three sections shown in Figure 1 are selected for computing crack growth using a residual stress and moment stress distribution that is representative for that section. For all other load types (internal pressure, piping loads excluding moment, and thermal transients) the bounding stresses are used on each path (see Section 3.3 for details).3.2 Fracture Mechanics Models Three crack models are utilized to compute the stress intensity factors, two from the EPRI Ductile Fracture Handbook [2] and the third from Tada-Paris-Irwin
[3], are shown in Figures 8 through 10. The three models are described below: o Circumferential flaw, all the loading type except the moment loading (EPRI Ductile Fracture Handbook model): This model is applied to the axial loading due to piping loads and transients conditions.
Full 3600 flaw in a cylinder with the actual Ri/t ratio is used, where 1 < Ri/t < 10. Ri is the inside radius and t is the thickness of the selected section for analysis.
The Ri/t ratios are calculated as follows (geometric dimensions obtained from Figure 1): for PATH 1: o DMW min-WOL: Ri/t= (14.0)/(3.99)
= 3.48 o DMW max-WOL: Ri/t= (14.0)/(4.40)
= 3.20 for PATH 2: o DMW min-WOL: Ri/t= (14.0)/(3.82)
= 3.66 o DMW max-WOL: Ri/t-- (14.0)/(4.21) 3.33 for PATH 3: o DMW min-WOL: Ri/t= (14.0)/(4.09) 3.42 o DMW max-WOL: Ri/t= (14.0)/(4.49)
= 3.12 It is determined in Reference 12 that the influence coefficients for calculating K must be computed using the plots provided in the reference as opposed to using the provided equation.o Circumferential flaw, moment loading only(Tada-Paris-Irwin model): This model applied to moment loads from various piping loading and transient conditions.
Full 3600 flaw in a cylinder File No.: 0800368.326 Page 5 of 30 Revision:
0 F0306-O1RO V Structural Integrity Associates, Inc.with the actual inside radius-to-outside radius ratio Ri/Ro is used. Ri is the inside radius and Ro is the outside radius with overlay thickness at the thinnest section. The Ri/Ro ratios are calculated as follows (geometric dimensions obtained from Figure 1): for PATH 1: o DMW min-WOL: o DMW max-WOL: for PATH 2: o DMW min-WOL: o DMW max-WOL: for PATH 3: o DMW min-WOL: o DMW max-WOL: Ri/Ro = (14.0)/(17.99)
= 0.778 Ri/Ro = (14.0)/(18.40)
= 0.761 Ri/Ro = (14.0)/(17.82)
= 0.786 R/R= (14.0)/(18.21)
= 0.769 RiiFo = (14.0)/(18.09)
= 0.774 Ri/Ro = (14.0)/(18.49)
= 0.757 o Axial flaw (EPRI Ductile Fracture Handbook model): a semi-elliptical inside surface flaw with an aspect (depth-to-length) ratio of 0.167 in a cylinder is used for FCG and PWSCC per ASME Code Section XI [9].Stress intensity factors using the above flaw models for all loads (see Section 3.3) are all calculated via a Microsoft Excel Visual Basic for. Applications (VBA) macro in spreadsheets"StressIntensityFactors*.xls." (where * =1,2,3) at the DMW. The macro is verified to ensure the equations from the EPRI Ductile Fracture Handbook [2] and the Paris-Tada-Irwin solution [3] are correctly used.3.3 Loads Loads considered (described in detail in the following subsections) are internal pressure, interface piping loads, local thermal gradient stresses due to thermal transients, and residual stresses.
Through-wall stresses are curve fitted with a third order polynomial in the form shown below: 2 C 3 o)= CO + CIX+/-+C 2 x2 +C 3 x (1)where:= stress (axial or hoop)x = normalized distance from the inside surface, 0<x<1, x equals distance divided by the path length Through-wall stresses were obtained for through-wall paths in the DMW (Figure 2 and 3). These paths are defined in the thermal and mechanical stress analysis calculation package [4]. It is important to note that the mechanical stresses and thermal stresses are extracted from models with the minimum and maximum overlays, respectively (see Section 3.1). The intent for this approach is to characterize the stresses for each of the different loading conditions for three regions within the DMW: a path near the File No.: 0800368.326 Revision:
0 Page 6 of 30 F0306-01RO V Structural Integrity Associates, Inc.nozzle interface within the weld butter, a path in the approximate center of the susceptible material (which includes the weld butter, the postulated ID weld repair, and the weld), and a path near the elbow side of the weld. As long as the correct stresses are extracted from the correct model (minimum or maximum overlay model depending on the load type), the resulting stress intensity factors are conservative for the sections shown in Figure 1. As explained in Section 3.1, residual stresses and unit moment load that are representative of each section are used for crack growth.Curve fits for residual stresses are calculated in spreadsheet "normalized RESfactors.xls", based on the spreadsheet "DB-0800368_324_RES.xls" obtained from the residual stress analysis [6]. Linearized stresses and curve fits for local thermal gradient stresses (and stresses due to mechanical loads) are compiled in spreadsheet "ThermStressCoeff(DMW)Normalized.xlsm".
The curve fit coefficients are used to calculate the K-vs-a values using a K-solution from Paris-Tada-Irwin
[3] for circumferential flaw moment loading (see Figure 9) or input into the EPRI Ductile Fracture Handbook models [2] for the circumferential (non-moment loading) and axial flaws (see Figures 8 and 10). These spreadsheets are included in the computer files. Table 1 shows the polynomial coefficients for all loads at the DMW. Details of how the Table 1 coefficients are obtained are explained in the following subsections.
This set of coefficients are stored in spreadsheet "TableOfCoeffcients.xls", which is used in conjunction with spreadsheet"StresslntensityFactors.xls".
Internal Pressure In the thermal and mechanical stress analysis calculation package [4], a unit internal pressure load (1000 psi) was applied to the discharge nozzle finite element model. The resulting through-wall stress distributions within the DMW and weld butter interface were extracted and given a third order polynomial curve fit. Files "DB-PRES P* MAP.OUT" (* =7-15), listed in Appendix A in the table labeled "Stress Output," contain the through-wall stress distributions.
These output files are obtained from Reference
- 4. The CSV file versions of these files contain the resulting stress coefficients for the unit pressure loading condition.
The resulting stress coefficients are shown in Table 1. Stress intensity factors resulting from the stresses in Table 1 are scaled by actual pressure values during the transient.
Note that a constant through-wall stress of 1000 psi is added to the Co coefficient of the "Unit Pressure" stresses to account for the internal pressure acting on the crack face.Piping Interface Loads The bounding piping interface loads were determined in the design loads calculation package [5] and shown in Table 2. Finite element analyses for an applied unit axial force (1000 lbs) and unit moment (1000 in-lb) at the free end of the piping interface were performed in [4]. Through-wall stress distributions within the DMW were extracted from the analyses in [4] and included in this calculation package. See files "DB-AXIAL P* -MAP.OUT" (* =7-15), and "DB-MOMENTP*"NMAP.OUT" (*=7-15)" in Appendix A in the table labeled "Stress Output." These files are included in the computer files. For the axial stresses due to the unit moment load, only the maximum stress in the section is used because a constant stress is required in the fracture mechanics model that is used for moment loading (see Figure 9). Stress intensity factors using the fracture mechanics models described in Section 3.2 File No.: 0800368.326 Page 7 of 30 Revision:
0 F0306-01RO V Structural Integrity Associates, Inc.were determined from these stresses.
Because a unit force and unit moments were performed in Reference 4, the resulting stress intensity factors are scaled to actual values by the axial force values (Fz)in Table 2 for the force Ks or by the square root sum of the squares (SRSS) of the transverse moment values (Mx and My) in Table 2 for the moment Ks. Then according to Reference 4, because the thermal piping interface loads shown in Table 2 are assumed to be at the normal operating temperature of 556°F, thermal piping loads for other temperatures are scaled by (T -70)/(556 -70), where T is the fluid temperature during the transient.
These temperature factors are shown in the "T factor" column in Table 3.The resulting stress coefficients for the unit axial and unit moment cases are shown in Table 1.Local Thermal Gradient Stresses Bounding thermal transients for crack growth analysis are shown in Table 3, which were developed in the design loads calculation package [5]. Determining the thermal gradient stresses due to these transients is a two-step process. First, a bounding path in the DMW is selected by comparing the thermal gradient stresses at the nine representative paths in the DMW (Paths 7-15 in Figures 2 and 3) for the transients.
Second, the times at which the maximum and minimum inside surface membrane-plus-bending axial and hoop stresses during each transient listed in Table 3 are determined so that the worst through-wall thermal gradient stresses may be extracted.
To select the bounding path in the DMW, the time histories of the inside surface linearized membrane-plus-bending stresses for each transient are plotted for axial and hoop stresses.
A typical plot is shown in Figure 5 for axial and hoop stresses for the Reactor Trip 8A transient.
The linearized membrane-plus-bending stresses and corresponding mapped stresses, fit with a third order polynomial, are contained in files "DB-SR**J P* MAP.csv" (where **=1-6, * = 7-15). Figure 5 shows, for example, that Path 12 is used for the maximum axial stress and Path 7 for the minimum axial stress for the Reactor Trip 8A transient.
Table 1 shows the bounding paths used at the DMW. Note that it is possible that a transient has more than one maximum-minimum pair, in other words more than one peak-valley pair. The number of cycles for this kind of transient is multiplied by the number of peak-valley pairs for that particular transient.
Table 4 shows the number of peak valley pairs for each transient.
Once the bounding path for the DMW is determined, the times at which the maximum and minimum membrane-plus-bending axial and hoop stresses during each transient can be determined.
Note that although the inside surface linearized membrane-plus-bending axial and hoop stresses were used in selecting the critical times, the stress coefficients resulting from the through-wall mapped stresses at the critical times are based on total stresses.
The resulting bounding thermal gradient stress coefficients due to the thermal transients at the times of maximum and minimum inside surface linearized membrane-plus-bending stresses are shown in Table 1.Residual Stresses Residual axial and hoop stresses were extracted from the residual stress analysis [6] for three paths within the DMW. These paths from Reference 6 are Paths 1, 2, and 3, and correspond (roughly) to Paths 9-12-15, 8-11-14, and 7-10-13 in Figure 2 and Figure 3. Stresses were obtained from file File No.: 0800368.326 Page 8 of 30 Revision:
0 F0306-OIRO V Structural Integrity Associates, Inc."normalizedRESfactors.xls" of Reference
- 6. The resulting stresses were curve fit with a third order polynomial in this spreadsheet in worksheet "Path Data." The residual stress curve fits were determined for all three paths of the DMW and used for the crack growth analyses.
Residual stresses at 70'F are shown in Figure 6 and the resulting K distributions are shown in Figure 7.The resulting residual stress coefficients at 70'F and at steady state pressure (2255 psig) and temperature (556'F) are shown in Table 1 at the DMW.3.4 Crack Growth Laws 3.4.1 Alloy 82/182 Fatigue Crack Growth Law NUREG/CR-6907
[7] indicates that "The CGRs of Alloy 82/182 in the PWR environment are a factor 5 higher than those of Alloy 600 in air under the same loading conditions." Thus the fatigue crack growth rate for the DMW (made of Alloy 82/182 filler metal) used in this analysis is that for Alloy 600 in air (Equation (2) below) multiplied by 5. The fatigue crack growth rate for air obtained from NUREG/CR-6721
[8] is given by: (da/dN)air
= CA600 (1-0.82R)-
2 2 (AK)4" 1 , units of m/cycle (2)where: CA600 = 4.835x10-14
+ 1.622x10-1 6 T- 1.49 x10-18T2 +4.355 x10-21T3 T = temperature inside pipe, 'C (taken as the maximum during the transient)
R = R-ratio = (Kmin/Kmax)
AK = Kmax -Kmin = range of stress intensity factor, Mpa-m°5 Note that Equation (2) in accordance with NUREG/CR-6907 is independent of rise time.3.4.2 Alloy 82/182 PWSCC Growth Law When appropriate PWSCC growth in the DMW is computed using Equation (3) below. This is for Alloy 182 weld metal and is obtained from Eq. 4.5 of MRP-1 15 [11, pgs 4-4 to 4-5 for US customary units].d = exp[- T -I , j]a(K)i< (3)where:_ crack growth rate at temperature T in in/hr.Qg= thermal activation energy for crack growth (31 kcal/mole)
R= universal gas constant = 1.103 x 10 kcal/mole-R File No.: 0800368.326 Page 9 of 30 Revision:
0 F0306-O1RO Structural Integrity Associates, Inc.T= absolute operating temperature at location of crack, K = 556°F (1015.67 R)Tref= absolute reference temperature used to normalize data = 617'F (1076.67 R)a= power-law constant =2.47 x 10-7 at 617°F K= crack tip stress intensity factor, ksi (in.)0 5 3= 1.6 3.4.3 Treatment of Negative Stress Intensity Factors Because of the beneficial compressive residual stresses produced by the weld overlay, the stress intensity factors for many load cases are negative.
This condition is handled as follows in the FCG analyses: 1. For Alloy 600 and its weld metals (Alloy 82/Alloy 182), the crack growth law in Equation (2) above includes an R-ratio correction (1-0.82R)-2.
2 that applies to both positive and negative R-ratios [7, 8]. For negative R-ratios, the factor is less than 1, yielding a corresponding decrease in crack growth rate when Km. is negative.
Therefore, Equation (2)is used directly for crack growth in the DMW when Kmax is greater than zero, for both positive and negative Kmin. As noted, a factor of 5 [7] is applied for PWR environmental effects.2. If both Kmax and Kmin in a load cycle are negative, zero fatigue crack growth is assumed. This is a reasonable assumption based on the work on compression fatigue crack growth (FCG for which Kmax and Kmin, are negative) in Reference 10, in which it was shown that although FCG is present, the values of FCG are several orders of magnitude smaller than for FCG for which Kmx and Kmmi are not negative.4.0 ASSUMPTIONS Basic assumptions for the analysis are listed below: o Through-wall stresses are curve fitted with a third order polynomial.
o See Section 3.2 for assumed flaw models o See Section 3.4 for the crack growth laws and related assumptions.
o For FSWOL, a postulated initial circumferential flaw 75% of base material thickness is assumed;a postulated initial axial flaw 75% of base material thickness is assumed o For OWOL design, a postulated initial circumferential flaw 50% of base material thickness is assumed; a postulated initial axial flaw 75% of base material thickness is assumed For FCG, there is no requirement to bound the load pairing between transients per the ASME Code,Section XI [9]. Each thermal transient that was analyzed in the thermal and mechanical stress analysis File No.: 0800368.326 Page 10 of 30 Revision:
0 F0306-O1RO V Structural Integrity Associates, Inc.calculation package [4] is analyzed sequentially per Table 4, and the cumulative effect of all transients is summed. In addition, incremental growth due to PWSCC (if active) is computed and added to incremental growth due to FCG. This approach is consistent with the ASME Code,Section XI, C-3200.5.0 CALCULATIONS A Microsoft Excel VBA routine is implemented to calculate combined FCG and PWSCC growth. This combined FCG and PWSCC calculation is based on a yearly basis: one year of PWSCC (if present)followed by one year of FCG. Note that for more accuracy, crack growth may also be based on a monthly basis. Combined FCG and PWSCC growth is calculated until the flaw depth reaches the 75%of the base material.
The number of cycles and sequence of events for FCG are shown in Table 4.Crack growth is calculated based on 60 years of operation.
Thus, the number of cycles/year shown in Table 4 are multiplied by 1.5 for 60-year operation and divided by 60 years. The PWSCC portion of the crack growth is only active if, during the growth of the flaw, the stress intensity factor at steady state normal operating conditions (NOC) is a positive value, which is in accordance with MRP- 115 [11, page 4-2], which states that "there is insufficient data to justify a stress intensity factor threshold other than zero." The Ks from spreadsheets "StresslntensityFactors*.xls" (where *=1,2,3) are imported into spreadsheets "CGDischargeNozzleDMW*.xls"(where
- =1,2,3) to compute crack growth at the DMW.The FCG and PWSCC calculations are described below.FCG For FCG, the individual terms that constitute nominal Kmax and Kmin for the calculation of AK in Equations (2) are summarized in the tabulations below. The individual Ks for nominal Kmax are combined (summed) with all appropriate scale factors applied. Similarly, the individual Ks for nominal Kmfi are combined (summed) with all appropriate scale factors applied. AK is computed by taking the difference of the resulting summed Kmax and Kmin. Note that Kresidual and Kdead weight are constant loads and do not contribute to the AK range.Kresidual Uresidual Kpressure,state 1 Kpressure,state2 Kdead weight Kdead weight Kthermal piping load-state 1 Kthermal piping state 2 Kthermal state 1 Kthermal state 2 OBE is treated as a separate event that the OBE combines with the highest K value for the Kmax side and the OBE combines the lowest K value for the Knin side. Table 4 indicates how OBE is combined with the transients.
File No.: 0800368.326 Page 11 of 30 Revision:
0 F0306-O1RO V Structural Integrity Associates, Inc.PWSCC The K-vs-a curves for both circumferential and axial flaws at steady state normal operating conditions (NOC) are calculated in the PWSCC worksheets of spreadsheets "CGDischargeNozzleDMW*.xls" (where *=1,2,3) and shown in Figure 11 through 13 for section Path 1 through 3, respectively, in Figure 1. The stresses at steady state NOC include internal pressure stresses (P = 2255 psig), residual stresses (at 70'F), steady state thermal stresses at 556°F, and stresses due to the non-cyclic piping loads (including deadweight).
Note that an additional 2255 psig was added to the Co coefficients for the stresses labeled "Resid @ 2255psig+556F" in Table 1 to account for crack face pressure.
This crack face pressure is applicable for both the FCG and PWSCC evaluation.
For both axial and circumferential flaws, the models described in Section 3.2 were used to calculate the stress intensity factors.PWSCC is a time dependent phenomenon and occurs at a sustained loading condition.
Given that the great majority of plant operation is at normal steady state operating conditions (NOC), PWSCC is defined by stress conditions at NOC. The 50% (or 75%) initial crack is grown using the cyclical loadings described previously.
At steps in the evaluation, the value of the crack tip K is continuously checked. If the K is less than zero, then no PWSCC is assumed for the next step of fatigue crack growth. If the crack tip K becomes greater than zero, then the PWSCC crack growth rate in Section 3.4.2 is used to calculate an incremental PWSCC crack growth, which is added to the total crack growth.In this case the Ks at normal operating conditions are positive for PATH 1 through PATH 3 at a flaw depth of 50% of the original base metal thickness for the circumferential flaws.
6.0 CONCLUSION
S AND DISCUSSIONS The crack growth results are shown in Table 5.For PATH 1: For an initial circumferential flaw of 50% of the original base metal thickness at the analyzed section it takes approximately 23 years to reach 75%. Whereas, for an initial circumferential flaw 75% of the original base metal thickness, it takes approximately 31 years to reach the overlay. An initial axial flaw of 75% of the original base metal thickness at the analyzed section remains 75% after 30 years.For PWSCC, this analysis showed that PWSCC is active at NOC at a flaw depth of 50% and 75% of the original base metal thickness at the DMW analyzed section for the circumferential flaw.For PATH 2: For an initial circumferential flaw of 50% of the original base metal thickness at the analyzed section it takes approximately 13 years to reach 75%. Whereas, for an initial circumferential flaw 75% of the original base metal thickness, it takes approximately 26 years to reach the overlay. An initial axial flaw of 75% of the original base metal thickness at the analyzed section remains 75% after 30 years.For PWSCC, this analysis showed that PWSCC is active at NOC at a flaw depth of 50% and 75% of the original base metal thickness at the DMW analyzed section for the circumferential flaw.File No.: 0800368.326 Page 12 of 30 Revision:
0 F0306-O1RO V Structural Integrity Associates, Inc.For PATH 3: For an initial circumferential flaw of 50% of the original base metal thickness at the analyzed section it takes approximately 12 years to reach 75%. Whereas, for an initial circumferential flaw 75% of the original base metal thickness, it takes approximately 33 years to reach the overlay. An initial axial flaw of 75% of the original base metal thickness at the analyzed section remains 75% after 30 years.For PWSCC, this analysis showed that PWSCC is active at NOC at a flaw depth of 50% and 75% of the original base metal thickness at the DMW analyzed section for the circumferential flaw.File No.: 0800368.326 Revision:
0 Page 13 of 30 F0306-O1RO Structural Integrity Associates, Inc.
7.0 REFERENCES
- 1. SI Calculation Package No. 0800368.322, "Finite Element Models of the Reactor Coolant Pump Discharge Nozzle with Weld Overlay Repair," (for revision refer to SI Project Revision Log, Latest Revision).
- 2. Zahoor, A., EPRI Report No. NP-6301-D, Ductile Fracture Handbook, Volumes 1, 2, and 3, (N14-1), Research Project 1757-69, June 1989.3. Hiroshi Tada, Paul C. Paris, and George R. Irwin, "The Stress Analysis of Cracks Handbook," Third Edition, ASME Press, 2000.4. SI Calculation Package 0800368.323, "Thermal and Unit Mechanical Stress Analyses for Reactor Coolant Pump Discharge Nozzle with Weld Overlay Repair," (for revision refer to SI Project Revision Log, Latest Revision)5. SI Calculation Package 0800368.311, "Design Loads for the 28" I.D. Reactor Coolant Pump (RCP) Suction and DischargeNozzles," (for revision refer to SI Project Revision Log, Latest Revision)6. SI Calculation Package 0800368.324, "Residual Stress Analysis of Reactor Coolant Pump Discharge Nozzle with Weld Overlay Repair," (for revision refer to SI Project Revision Log, Latest Revision)7. NUREG/CR-6907, "Crack Growth Rates of Nickel Alloy Welds in a PWR Environment," U.S. Nuclear Regulatory Commission (Argonne National Laboratory), May 2006.8. NUREG/CR-6721, "Effects of Alloy Chemistry, Cold Work, and Water Chemistry on Corrosion Fatigue and Stress Corrosion Cracking of Nickel Alloys and Welds," U.S. Nuclear Regulatory Commission (Argonne National Laboratory), April 2001.9. ASME Boiler & Pressure Vessel Code,Section XI, , 2001 Edition with Addenda through 2003.10. Lenets, Y. N., "Compression Fatigue Crack Growth Behavior of Metallic Alloys: Effect of Environment," Engineering Fracture Mechanics, Vol. 52, No. 5, 1997.11. Materials Reliability Program Report MRP- 115, "Materials Reliability Program: Crack Growth Rates for Evaluating Primary Water Stress Corrosion Cracking (PWSCC) of Alloy 82, 182, and 132 Welds," September 2004.12. SI Calculation 0800554.301, "Computation of Influence Coefficients for Two Stress Intensity Factor Solutions From EPRI Ductile Fracture Handbook," Rev. 0.File No.: 0800368.326 Page 14 of 30 Revision:
0 F0306-O1RO Structural Integrity Associates, Inc.Table 1: Stress Coefficients for Various Loadings at the DMW Transient Name Nozzle-to-Safe End Weld Time Path Used Axial Stress Coefficients, psi Time Path Used Hoop Stress Coefficients, psi (sec) Co C1 C2 C3 (sec) Co C1 C2 C3 Unit Pressure (1) 9 3855.6 -2568.9 1003.9 -582.7 -13 6526.8 -2604 875.9 -314.4 Unit Axial 7 3.4 -1.4 -0.4 0.3 -13 0.8 -1.2 0.3 -0.1 Unit Moment 15 Max Stress at Each Path (4) 10 0 0.2 -0.1 0.1 Plant Heatup, HIGH 0 7 0 0 0 0 28080 13 5659.4 72131.2 -160326 90461.2 Plant Heatup, LOW 17532 7 -20440 116250.6 -178198 95618.1 4383 9 -4400 34065 -61992.1 32294.1 Plant Cooldown, HIGH 10800 9 -8794.3 87792.5 -171203 87412.6 2700 13 9685.1 52486.8 -140980 83249.8 Plant Cooldown,LOW 0 7 -16129.4 98232.2 -164943 97411 46800 12 329.4 10446.4 -22692 10483.1 ReactorTrip 8A, HIGH 150 12 -22750.6 183600.9 -332320 165379.3 150 13 7247.4 61974.6 -145278 83600.2 ReactorTrip 8A, LOW 16.5 7 -18190.8 112135.9 -189477 110485.9 16.5 9 -1612.4 78295.8 -170149 91055 ReactorTrip 8C, HIGH 280 12 -22937.6 184745.2 -334298 166444.1 280 13 6997.1 63191 -146908 84403.8 Reactor Trip 8C, LOW 35 7 -23146.2 143406.7 -241819 137197 40 12 -5801.3 95335.9 -177402 86201.2 Change of Flow, HIGH 50 12 -22242.2 179403.3 -324242 160991.6 70 13 7325 61011.9 -143139 82369 Change of Flow, LOW 360 7 -16581.9 100847.4 -168942 99356.4 360 9 174.8 66094.8 -148097 79063.8 Hydrotest, HIGH 1 9 -1476.3 13147.2 -24874.1 12647.9 2 13 3899.5 51188.6 -114829 63967.5 Hydrotest, LOW 2 13 -14485.9 94739.9 -169225 94931.5 1 12 157.4 4616 -10126.1 4648.8 Resid70, Path 1(3) 63643.61 -544931.84 802965.9 -250409 54940.44 -792286.6 1618604 -768639.7 Resid70, Path 2 (3) 73150.29 -539081.67 686144.5 -135506 27962.384
-730746.59 1612025 -813639.7 Resid70, Path 3 13) 66760.06 -448070.23 499272.2 -45438.2 -1532.997
-486664.43 1147729 -570109.8 Resid @ 2255psig+556F, Path 1(2)(3) 46564.44 -342188.42 455442.9 -99947.1 68916.725
-701647.38 1428069 -687401 Resid @ 2255psig+556F, Path 2 (2)(3) 51811.33 -331455.44 351421.6 3946.245 42707.041
-619933.73 1392511 -718379.8 Resid @ 2255psig+556F, Path 3(2)(3) 41816.55 -221064.86 93768.03 169346 16508.952
-380771.23 941740.3 -477377.4 Notes: 1. 1000 psi was added to the Co coefficient term of the Unit Pressure case to account for crack face pressure.2. 2255 psi was conservatively added to the Co coefficient term of the residual stresses at normal operating pressure and temperature cases to account for crack face pressure.
This is needed for calculating stress intensity factors at normal steady state operating conditions.
- 3. Residual paths, for actual path correlations see Figure 4. Pathl corresponds to Paths 9-12-15, Path 2 to Paths 8-11-14, Path3 to Paths 7-10-13 in Figures 2 and 3.4. The Maximum Axial Stress used for Unit Moment Load is 0.533psi for Path 1, 0.4533psi for Path 2 and 0.376psi for Path 3.File No.: 0800368.326 Revision:
0 Page 15 of 30 F0306-01R0 Structural Integrity Associates, Inc.Table 2: Discharge Nozzle Bounding Piping Interface Loads Load Case Deadweight Thermal OBE Notes: Fx 6512 109334 44160 Forces, lbsO 1)Fy 14600 50100 59600 Fz 8768 192378 77946 Mx 150071 774158 718501 Moments, in-lbsO 1)My 4 500583 81 3 13082884 58 6 4905840 45 Mz 39695 13321 87384 1. Bounding loads between joints 83 and 138, listed as absolute values.2. z is axial to the nozzle.Table 3: Bounding Thermal Transients for the Discharge Nozzle Description Time, sec T, 'F P, psia Cycles T factor Plant Heatup 0 70 15 240 0.000 1A 17532 557 1050 1.002 23400 557 2250 1.002 24480 579 2250 1.047 Plant Cooldown 0 550 2250 240 1.008 lB 10800 300 350 0.473 21600 280 250 0.432 43200 140 15 0.144 Reactor Trip 0 556.5 2250 590 1.001 8A 12 570 2500 1.028 30 550 2200 0.987 25200 550 2250 0.987 Reactor Trip 0 556.5 2200 188 1.001 8C 2 560 2240 1.008 10 565 2400 1.018 15 562 2500 1.012 20 585 2620 1.059 30 590 2500 1.070 40 580 2200 1.049 60 565 2100 1.018 100 552 2025 0.991 Change of Flow 0 556.5 2190 21060 1.001 10 30 546.5 2130 0.980 150 557.5 2250 1.003 180 559.5 2200 1.007 Hydrotest t 1) 100 15 20 0.062 12 400 3125 0.679 100 15 0.062 Notes: 1. Data from a similar plant.File No.: 0800368.326 Revision:
0 Page 16 of 30 F0306-01 V Structural Integrity Associates, Inc.Table 4: Sequence of Events and Cycles for Fatigue Crack Growth Events Event ID 40-yr Cycles (60-yr Cycles) Peak-Valley Pair Transient 1 (Plant Heatup)Transient 2 (Plant Cooldown)Transient 3 ( Reactor Trip 8A)Transient 3 (Reactor Trip 8A)+ OBE Transient 4 (Reactor Trip 8C)+OBE Transient 5 (Change of Flow)Transient 6 (Hydrotest) 1 2 3 4 5 6 7 240(360)240 (360)128(192)462 (693)188(282)21060(31590) 20(30)2 2 1 1 1 1 1 Table 5: Crack Growth Results for PATHs 1, 2, and 3 Circumferential Flaw in Circumferential Flaw in Axial Flaw in PATH 1 PATH 1 PATH 1 _Time for an initial flaw 50% Time for an initial flaw Flaw Depth as % of Base Metal of the Base Material 75% of the Base Material Thickness for an Initial Flaw Thickness to Reach 75% of Thickness to Reach the with 75% of the Base Material the Base Material Thickness Interface Thickness After 30 years-[23 years J--31 years ]75 Circumferential Flaw in Circumferential Flaw in Axial Flaw in PATH 2 PATH 2 PATH 2 Time for an initial flaw 50% Time for an initial flaw Flaw Depth as % of Base Metal of the Base Material 75% of the Base Material Thickness for an Initial Flaw Thickness to Reach 75% of Thickness to Reach the with 75% of the Base Material the Base Material Thickness Interface Thickness After 30 years-13 years --I 26 years 75 Circumferential Flaw in Circumferential Flaw in Axial Flaw in PATH 3 PATH 3 PATH 3 Time for an initial flaw 50% Time for an initial flaw Flaw Depth as % of Base Metal of the Base Material 75% of the Base Material Thickness for an Initial Flaw Thickness to Reach 75% of Thickness to Reach the with 75% of the Base Material the Base Material Thickness Interface Thickness After 30 years-12 years --33 years 75 File No.: 0800368.326 Revision:
0 Page 17 of 30 F0306-0t1 V Structural Integrity Associates, Inc.PATH1 PATH3 PATH2 DMW R=14 Figure 1: Sections Used For Crack Growth File No.: 0800368.326 Page 18 of 30 Revision:
0 F0306-01 V Structural Integrity Associates, Inc.Figure 2: Stress Path Definitions for Maximum Weld Overlay for Thermal Transient Analyses at 0, 90 and 180 Degree Locations (Note: Paths 7 through 15 are for Crack Growth. The inside node is located on the inside face of the nozzle/weld/elbow for all paths.)File No.: 0800368.326 Revision:
0 Page 19 of 30 F0306-O1 V Structural Integrity Associates, Inc.Figure 3: Stress Path Definitions for Minimum Weld Overlay for Mechanical Load Analyses (pressure, axial force, and moment loads) 0, 90 and 180 Degree Locations (Note: Paths 7 through 15 are for Crack Growth. The inside node is located on the inside face of the nozzle/weld/elbow for all paths.)File No.: 0800368.326 Revision:
0 Page 20 of 30 F0306-01 V Structural Integrity Associates, Inc.Residual stress analysis Figure 4: Critical Paths Used for Through-wall Mapped Stresses of Minimum Weld Overlay for Residual Stress Analyses File No.: 0800368.326 Revision:
0 Page 21 of 30 F0306-O V V Structural Integrity Associates, Inc.Axial Stress.J E 500-500-1500-2500-3500-4500-5500-6500-7500-8500 UUU(MWM--"--- Path7--N-- Path8 Path9 Path 10--- Path 11 Path 12 Path 13-Path 14 Path 1V rimels]Hoop Stress 1bUUU 15000 14000 -13000 S12000 ~D11OUUU 9000 8000 0 5000 10000 15000 Time [s]________________
--Path7-s- PathR-*- Path9 Path 10 Path 11-Path 12 P---Path 13 Path 14 Path 15 20000 25000 30000 Figure 5: Time Histories of Linearized Membrane-plus-Bending Stress at the Inside Surface for Reactor Trip 8A Transient File No.: 0800368.326 Revision:
0 Page 22 of 30 F0306-01 V Structural Integrity Associates, Inc.Path 1 Through-Wall Residual Stress y = -250409x 3 + 802966x 2 -544932x -t- 63644 y = -768640x 2 + 2E+06x 2 -792287x + 54940 140 120 100_ 60 g; 40 N 20 0~-20 0 2-40 --Axioal 70'F-60 -,--F-Hoop70*P
-80 Poly. (Axial 70*P)___Poly. (Hoop 701F)Normalized Distance from ID Strae U-y=y =120 100 80 60 40 20 0-20-40-60-80 Path 2 Through-Wall Residual Stress-1 35506x 3 + 686145x 2 -539082x + 73150-813640x 3 + 2E+06x 2 -730747x + 27962-N- Axial 70°F--R- Hoop 70°F-- P oly. (Axial 70 °F)--Puly. (Houp 70-F)IL J Normalized Distance from ID Surface Path 3 Through-Wall Residual Stress y = -45438x 3 + 499272x 2 -448070x + 66760 y = -570110x 3+ 1 E+06x 2-486664x -1533 C 100 80 60 40 20 0-20-40-60-80 KJ 0. 0.4 1 1.2 i~~I -J ~--Hoop 70OF-- Poly. 0-Poly.(Hoop 70"F)Normalized Distance from ID Surface Figure 6: Through-wall Residual Stress Distribution at 70'F and Curve Fits at the DMW Note: Pathl corresponds to Paths 9-12-15, Path 2 to Paths 8-11-14, Path3 to Paths 7-10-13 in Figures 2 and 3.File No.: 0800368.326 Revision:
0 Page 23 of 30 F0306-01*
V Structural Integrity Associates, Inc.Axial Flaw 0'U LA.20 0-20-40-60-80-100-120-140-160 3.5 Flaw Depth [in]Circumferential Flaw 0 U Li.4-.C 1A 4-j 80 60 40 20 0-20-40-60-80-100 Flaw Depth [in]Figure 7: K-vs-a Plots for Paths 1, 2, and 3 Residual Stresses at 701F Note: Pathl corresponds to Paths 9-12-15, Path 2 to Paths 8-11-14, Path3 to Paths 7-10-13 in Figures 2 and 3.File No.: 0800368.326 Revision:
0 Page 24 of 30 F0306-01 V Structural Integrity Associates, Inc.I , R, Source: Reference 2 (Zahoor model, 1 <_ R/t < 10)Figure 8: Circumferential Flaw Model, Non-Moment Loading File No.: 0800368.326 Revision:
0 Page 25 of 30 F0306-011 V Structural Integrity Associates, Inc.Mt 4Mro KiD = KA ios 0 Source: Reference 3"F" is defined below (also from Reference 3)/ 1'I-S 1.0 7 Figure 9: Circumferential Flaw Model, Moment Loading File No.: 0800368.326 Revision:
0 Page 26 of 30 F0306-Ot V Structural Integrity Associates, Inc.T a I 2c Source: Reference 2 (Zahoor model, 1 <-I/t <- 10)Figure 10: Axial Flaw Model File No.: 0800368.326 Page 27 of 30 Revision:
0 F0306-01' V Structural Integrity Associates, Inc.Axial Flaw 50 .T...0'0 0-50: r 4-100 -Circumferential Flaw 60 -LQ C>~40-0 LL 20 3---------0 Figure 11: K-vs-a at Normal Steady State Operating Conditions for PATH I Note: Initial flaw depth =50% of original base metal thickness at the analyzed DMW section = 1.45", 75% of original base metal thickness
=2.175" File No.: 0800368.326 Revision:
0 Page 28 of 30 F0306-01 V Structural Integrity Associates, Inc.Axial Flaw IL, 0 C 0 0 ()0 LL 0 C 4)C 0 0 0 4-Ci)30 20 10 0-10-20-30-40-50-60-70-80---------------------------------------------- ---------_ _4-Flaw Depth, Inches Circumferential Flaw 60 40 (0 X 40 0 I.)(/)U-020 t-o2 (0 0)LLn C: rl-0 0 1 1 2 Flaw Depth, Inches 3 4 Figure 12: K-vs-a at Normal Steady State Operating Conditions for PATH 2 Note: Initial flaw depth = 50% of original base metal thickness at the analyzed DMW section = 1.45", 75% of original base metal thickness
=2.175" File No.: 0800368.326 Revision:
0 Page 29 of 30 F0306-01 V Structural Integrity Associates, Inc.Axial Flaw 0Q 40 4-a 40 P-co 50 40 30 20 10 0-10-20-30-40-50-60-70-80------------------
. .----------
--- ------ ) ---------------
A-----------------
L -----------------
Flaw Depth, Circumferential Flaw 60 ID 40 0 20 CI 0 0 1 2 3 4 Flaw Depth, Inches Figure 13: K-vs-a at Normal Steady State Operating Conditions for PATH 3 Note: Initial flaw depth = 50% of original base metal thickness at the analyzed DMW section = 1.45", 75% of original base metal thickness
=2.175" File No.: 0800368.326 Revision:
0 Page 30 of 30 F0306-01 V Structural Integrity Associates, Inc.APPENDIX A COMPUTER FILE DESCRIPTIONS File No.: 0800368.326 Revision:
0 F0306-O1RO Page A- I of A-3 VStructural Integrity Associates, Inc.Stress Output Filename Description DB-$$ P** MAP.OUT Mapped stress output file for thermal transient analyses (CSV file version also included)($$
= SR1, SR2, SR3, SR4,SR5,SR6) for path **where ** = 7-15 for Paths 7 through 15, shown in Figure 3 DB-AXIALP**_MAP.OUT Through-wall stresses for unit axial load run for path **(CSV file version also included) where ** 7-15 for Paths 7 through 15, shown in Figure 2 DB-PRES_P**_MAP.OUT Through-wall stresses for unit pressure run for path **(CSV file version also included) where ** = 7-15 for Paths 7 through 15, shown in Figure 2 DB-MOMENT*
P** MAP.OUT Through-wall stresses for unit moment run for path **where *=X,Z (CSV file version also included)
- =7-15 for Paths 7 through 15, shown in Figure 2 File No.: 0800368.326 Revision:
0 Page A-2 of A-3 F0306-OIRO V Structural Integrity Associates, Inc.Spreadsheets Filename Description Spreadsheets that contains Microsoft Visual Basic macro StresslntensityFactors*.xls for calculating stress intensity factors at the DMW.(*=1,2,3, corresponds to PATHS 1,2,3)ThermStressCoeff(DMW)
Spreadsheets that contains extraction of linearized Normalized.xlsm stresses; source of Table 1 , Spreadsheet that contains stress coefficients for thermal TableOfCoefficients.xls transient stresses at the DMW; used as input to StressIntensityFactors spreadsheets.
Spreadsheet that contains a copy of through-wall residual stresses from Spreadsheet N dt"DB-0800368 324 RES.xls" of Reference 6 and the coefficients for a third order polynomial fit.Spreadsheets calculation of crack growth at the DMW for the circumferential and axial flaws.CGDischargeNozzleDMW*_%.xls
(*=1,2,3, corresponds to PATHS 1,2,3%=FWOL, OWOL corresponds to FWOL crack growth and OWOL crack growth File No.: 0800368.326 Revision:
0 Page A-3 of A-3 F0306-O1RO