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{{#Wiki_filter:NMPC Project 03-9425 M PM-USE-293216 FINAL REPORT entitled ELASTIC-PLASTIC FRACTURE MECHANICS ASSESSMENT OF NINE MILE POINT UNIT 1 BELTLINE PLATES FOR SERVICE LEVEL C AND D LOADINGS MPM Research dr ConsuIting wi<~~~'//j~j~~Zp/>>
{{#Wiki_filter:NMPC Project 03-9425 MPM-USE-293216 FINAL REPORT entitled ELASTIC-PLASTIC FRACTURE MECHANICS ASSESSMENT OF NINE MILE POINT UNIT 1 BELTLINE PLATES FOR SERVICE LEVEL C AND D LOADINGS MPM Research               dr ConsuIting wi<~~~'//j~j~~Zp/>>
February 22, 1993 9303040ih7
February 22, 1993 PDR P  'DR 9303040ih7 '730226
'730226 PDR.ADQCK.05000220 P'DR
    .ADQCK.05000220


3 Table of Contents 1.0 Introduction
3 Table of Contents 1.0   Introduction                                                                   ~   \   ~ ~ ~ ~ ~ ~
~\~~~~~~2.0 Material Model.3.0 Transient Selection 3.1 Level C Transient Selection....3.2 Level D Transient Selection....3.3 Screening Analysis 3.3.1 Model Description..........
2.0     Material Model   .
3.3.2 Level C Transient Analysis 3.3.3 Level D Transient Analysis 3.3.4 Summary of Candidate Transients 7 7 7 8 8 9 9 10 4.0 Finite Element Analysis..........,.......
3.0   Transient Selection                                                                                 7 3.1   Level C Transient Selection ....                                                           7 3.2     Level D Transient Selection ....                                                           7 3.3   Screening Analysis                                                                           8 3.3.1 Model Description..........                                                           8 3.3.2 Level C Transient Analysis                                                             9 3.3.3 Level D Transient Analysis                                                             9 3.3.4 Summary of Candidate Transients                                                       10 4.0   Finite Element Analysis   ..........,.......                                                       26 4.1     Model Description ..                                                                       26 4.2     Finite Element Analysis Results                                                             26 4.3     Limiting Transients ............                                                           27
4.1 Model Description
'lastic-Plastic             Fracture Mechanics Assessment   .....                                               39 5.1     Model Description....                                                                       39 5.1.1 Vessel Geometry............                                                           39 5.1.2 Applied Loads                                                                         39 5.1.3 Limits for Small Scale Yielding Analysis                                             40 5.1.4 Fracture Mechanics   Model........                                                   40 5.2     Calculations for A302B Material Model......                                                 43 5.2.1 Level C Loading......                                                                 43 5.2.2 Level D Loading   Analysis,.........                                                 43 5,2.3 Tensile Instability Analysis                                                         43 6.0   Summary and Conclusions t
..4.2 Finite Element Analysis Results 4.3 Limiting Transients
                                        ...................                                                     52
............
    '.0 References ...................                                                                           54 Acknowledgement .........                                                                                 56 Appendtces ...................
26 26 26 27'lastic-Plastic Fracture Mechanics Assessment
            +0 57 Appendix A                                                                                         58 Appendix B                                   ~   ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~   ~   ~             83
.....5.1 Model Description....
 
5.1.1 Vessel Geometry............
1.0    Introduction Nuclear reactor pressure vessel materials must be tested and evaluated to ensure that they are safe in terms of both brittle and ductile fracture under normal operation and during design basis transients. With regard to ductile fracture protection, Appendix G to 10 CFR 50 prescribes a screening criterion of 50 ft-lbs. If any beltline materials are expected to exhibit Charpy Upper Shelf Energy (USE) (T-L orientation) lev'els below 50 ft-lbs, then additional analyses must be performed to ensure continued safe operation. The Draft ASME Appendix X [ASME92] was developed to assist licensees in performing elastic-plastic fracture mechanics evaluations for beltline materials with low upper shelf energies. This report documents application of the draft Appendix X calculative procedures and criteria to two Nine Mile Point Unit 1 (NMP-1) beltline plates for Service Level C and D loadings.
5.1.2 Applied Loads 5.1.3 Limits for Small Scale Yielding Analysis 5.1.4 Fracture Mechanics Model........
The NMP-1 beltline materials were evaluated to determine whether any materials would exceed the 50 ft-lb screening criterion. The results of these evaluations are summarized in Reference
5.2 Calculations for A302B Material Model......
[MA93] and were presented in the response to NRC Generic Letter 92-01 [MA92]. As a result of these evaluations, NMPC concluded that an Appendix X analysis must be performed for beltline plates G-8-1 and 6-307-4. The results of the Appendix X analysis for Service Level A and B loadings were reported in Reference [MA93]. This report presents the results of the Service Level C and D loading analysis.
5.2.1 Level C Loading......
5.2.2 Level D Loading Analysis,.........
5,2.3 Tensile Instability Analysis 39 39 39 39 40 40 43 43 43 43 6.0 Summary and Conclusions
...................
t'.0 References
...................
52 54 Acknowledgement
.........56 A+0 ppendtces...................
Appendix A Appendix B~~~~~~~~~~~~~~~~~~57 58 83  


1.0 Introduction Nuclear reactor pressure vessel materials must be tested and evaluated to ensure that they are safe in terms of both brittle and ductile fracture under normal operation and during design basis transients.
With regard to ductile fracture protection, Appendix G to 10 CFR 50 prescribes a screening criterion of 50 ft-lbs.If any beltline materials are expected to exhibit Charpy Upper Shelf Energy (USE)(T-L orientation) lev'els below 50 ft-lbs, then additional analyses must be performed to ensure continued safe operation.
The Draft ASME Appendix X[ASME92]was developed to assist licensees in performing elastic-plastic fracture mechanics evaluations for beltline materials with low upper shelf energies.This report documents application of the draft Appendix X calculative procedures and criteria to two Nine Mile Point Unit 1 (NMP-1)beltline plates for Service Level C and D loadings.The NMP-1 beltline materials were evaluated to determine whether any materials would exceed the 50 ft-lb screening criterion.
The results of these evaluations are summarized in Reference[MA93]and were presented in the response to NRC Generic Letter 92-01[MA92].As a result of these evaluations, NMPC concluded that an Appendix X analysis must be performed for beltline plates G-8-1 and 6-307-4.The results of the Appendix X analysis for Service Level A and B loadings were reported in Reference[MA93].This report presents the results of the Service Level C and D loading analysis.
/
/
2.0 Material Model The NMP-1 beltline plates were fabricated using A302B modified (A302M)steel.At present, sufficient J-R data are not available to construct an A302M model.As discussed in Reference[MA93], the NMP-1 plates are best modelled using an A302B J-R material model.The A302B material model is fully described in Reference[MA93].For Service Level C loadings, the J-R curve inputs are two sigma lower bound curves which are the same as for Service Levels A and B.However, for Service Level D analysis, Reference[ASME92]allows the use of J-R curves which are a best estimate representation for the vessel material being analyzed.Therefore, the best estimate, or mean, J-R curves, as a function of USE level, were determined.
2.0     Material Model The NMP-1 beltline plates were fabricated using A302B modified (A302M) steel. At present, sufficient J-R data are not available to construct an A302M model. As discussed in Reference
The J,c versus USE model reported in Reference[MA93]was used to calculate the mean J,c data given in Table 2-1.The 6T JD-ha data reported in Reference[HI89]were used to determine the J-R curves at the USE levels shown in Table 2-1.The 6T JD-ha data were reduced or increased by the difference between the 6T test J<<value (525 in-lb/in')
[MA93], the NMP-1 plates are best modelled using an A302B J-R material model. The A302B material model is fully described in Reference [MA93]. For Service Level C loadings, the J-R curve inputs are two sigma lower bound curves which are the same as for Service Levels A and B. However, for Service Level D analysis, Reference [ASME92] allows the use of J-R curves which are a best estimate representation for the vessel material being analyzed. Therefore, the best estimate, or mean, J-R curves, as a function of USE level, were determined. The J,c versus USE model reported in Reference [MA93] was used to calculate the mean J,c data given in Table 2-1. The 6T JD-ha data reported in Reference [HI89] were used to determine the J-R curves at the USE levels shown in Table 2-1. The 6T JD-ha data were reduced or increased by the difference between the 6T test J<<value (525 in-lb/in') and the J,c data listed in Table 2-1. The yield stress, modulus, and Poisson ratio used in the analysis are identical to the Reference
and the J,c data listed in Table 2-1.The yield stress, modulus, and Poisson ratio used in the analysis are identical to the Reference[MA93]data.  
[MA93] data.


Table 2-1 Mean J,c Data as a Function of USE Level USE-LBS 10~J-LB 79.2 20 158.3 30 237.5 40 316.6 50 395.8 60'0 474.9 554.1 80 90 100 633.2 712.4 791.5  
Table 2-1 Mean J,c Data as a Function of USE Level USE     -LBS               ~J   -LB 10                          79.2 20                           158.3 30                         237.5 40                         316.6 50                         395.8 60                         474.9
>p 3.0 Transient Selection The ASME draft Appendix X does not specify procedures for calculating Level C and D service loadings since the combinations of loadings and material properties encountered in practice are too diverse.Therefore, the most limiting transients for Levels C and D, from a ductile fracture perspective, were identified as follows: The NMP-1 and NMP-2 plant documentation was carefully examined to identify potential limiting transients.
    '0                            554.1 80                         633.2 90                          712.4 100                          791.5
 
>p 3.0     Transient Selection The ASME draft Appendix X does not specify procedures for calculating Level C and D service loadings since the combinations of loadings and material properties encountered in practice are too diverse. Therefore, the most limiting transients for Levels C and D, from a ductile fracture perspective, were identified as follows:
The NMP-1 and NMP-2 plant documentation was carefully examined to identify potential limiting transients.
A screening calculation was then performed to reduce the spectrum of transients to a few most likely candidates.
A screening calculation was then performed to reduce the spectrum of transients to a few most likely candidates.
Finite element calculations were performed on the reduced set of transients to determine the most limiting Level C transient and the most limiting Level D transient and the resultant loading.3.1.Level C Transient Selection The NMP-1 and NMP-2 updated FSARs and thermal cycle diagrams were reviewed to determine a spectrum of candidate Level C transients for further analysis.Prior to performing the screening calculations, it was not clear whether the rapid pressure loss transients or the slow depressurization transients would provide the largest combined pressure and,thermal gradient loads.Therefore, the transients shown in Figure 3-1 were chosen for analysis since they bound all Level C transients in terms of cooldown rate.Table 3-1 lists the temperature/pressure variation at various times during the transient.
Finite element calculations were performed on the reduced set of transients to determine the most limiting Level C transient and the most limiting Level D transient and the resultant loading.
3.1 . Level C Transient Selection The NMP-1 and NMP-2 updated FSARs and thermal cycle diagrams were reviewed to determine a spectrum of candidate Level C transients for further analysis. Prior to performing the screening calculations, it was not clear whether the rapid pressure loss transients or the slow depressurization transients would provide the largest combined pressure and,thermal gradient loads. Therefore, the transients shown in Figure 3-1 were chosen for analysis since they bound all Level C transients in terms of cooldown rate.
Table 3-1 lists the temperature/pressure variation at various times during the transient.
The classification of the automatic blowdown transient and emergency cooldown transient as Level'C events is consistent with the definition of the emergency condition transients.
The classification of the automatic blowdown transient and emergency cooldown transient as Level'C events is consistent with the definition of the emergency condition transients.
, Figure 3-1 includes two events described in the Unit 1 updated FSAR (References
    , Figure 3-1 includes two events described in the Unit 1 updated FSAR (References
[FSAR]and[CENC])and the Unit 2 (References
[FSAR] and [CENC]) and the Unit 2 (References [STRS] and [TCD]) emergency condition automatic blowdown.
[STRS]and[TCD])emergency condition automatic blowdown.3.2 Level D Transient Selection As with the Level C transient selection, the Level D transients were selected after careful examination of the NMP-1 and NMP-2 plant documentation.
3.2     Level D Transient Selection As with the Level C transient selection, the Level D transients were selected after careful examination of the NMP-1 and NMP-2 plant documentation. A set of transients were chosen which bound all Level D events in terms of cooldown rate. Plots of the selected transients are shown in Figures 3-2 through 3-5 (pressure/temperature profile data are also given in Tables 3-2 and 3-3.) The NMP-2 faulted condition events are specified based on the Reference [NEDC] analysis. The events included for consideration include the break spectrum for the recirculation line breaks, the steam line break, core spray line break, and the feedwater line break.
A set of transients were chosen which bound all Level D events in terms of cooldown rate.Plots of the selected transients are shown in Figures 3-2 through 3-5 (pressure/temperature profile data are also given in Tables 3-2 and 3-3.)The NMP-2 faulted condition events are specified based on the Reference[NEDC]analysis.The events included for consideration include the break spectrum for the recirculation line breaks, the steam line break, core spray line break, and the feedwater line break.
 
tp 3.3 Screening Analysis 3.3.1 Model Description The transients described earlier were analyzed using a simple linear elastic fracture mechanics model to determine those transients which require a detailed finite element analysis to determine the limiting loads.The temperature difference across the vessel wall for the Level C transients was calculated using the TRUMP/MPM code[TRUMP].The NMP-1 vessel was modelled using cylindrical coordinates, The vessel is 7.281 in.thick with an inner radius of 106.5 inches.The 0.1563 in.stainless steel liner was modelled as having the physical properties of 316 SS, and the rest of the vessel thickness was modelled as A302B ferritic steel.A total of 17 radial nodes, each of approximately OA4 in.thickness, were used to discretize the vessel thickness.
tp 3.3 Screening Analysis 3.3.1   Model Description The transients described earlier were analyzed using a simple linear elastic fracture mechanics model to determine those transients which require a detailed finite element analysis to determine the limiting loads. The temperature difference across the vessel wall for the Level C transients was calculated using the TRUMP/MPM code [TRUMP]. The NMP-1 vessel was modelled using cylindrical coordinates, The vessel is 7.281 in. thick with an inner radius of 106.5 inches. The 0.1563 in. stainless steel liner was modelled as having the physical properties of 316 SS, and the rest of the vessel thickness was modelled as A302B ferritic steel. A total of 17 radial nodes, each of approximately OA4 in. thickness, were used to discretize the vessel thickness. A nodel temperature boundary condition was applied at the ID surface of the vessel. The surface node was modelled as being in thermal equilibrium with the downcomer fluid temperature.
A nodel temperature boundary condition was applied at the ID surface of the vessel.The surface node was modelled as being in thermal equilibrium with the downcomer fluid temperature.
This assumption leads to conservative through wall gradient estimates, particularly for the Level D transients during which phase change occurs. Therefore, the initial temperature of all vessel nodes were set to 500'F.
This assumption leads to conservative through wall gradient estimates, particularly for the Level D transients during which phase change occurs.Therefore, the initial temperature of all vessel nodes were set to 500'F.Once the temperature difference across the wall was calculated, the relative contribution of the pressure loading and the thermal loading was approximated using the linear elastic fracture mechanics model given in Appendix G to the ASME code.It should be emphasized that these equations are based on linear elastic fracture mechanics principles and are strictly applicable for thermal ramps of up to 100'F/hr.Nevertheless, for screening purposes, these equations are adequate for assessing the relative contributions of the pressure and thermal loads to the total crack tip stress intensity for the various Level C and D events.Appendix G uses the following equations to calculate the stress intensities:
Once the temperature difference across the wall was calculated, the relative contribution of the pressure loading and the thermal loading was approximated using the linear elastic fracture mechanics model given in Appendix G to the ASME code. It should be emphasized that these equations are based on linear elastic fracture mechanics principles and are strictly applicable for thermal ramps of up to 100'F/hr. Nevertheless, for screening purposes, these equations are adequate for assessing the relative contributions of the pressure and thermal loads to the total crack tip stress intensity for the various Level C and D events.
I K=K~+K~where, K~=Ma=membrane stress intensity factor (ksi V in)K~=MT bT=stress intensity factor due to thermal gradient (ksi 0 in)M=ASME membrane factor (0 in)MT=ASME thermal factor (ksi 0 in/'F) lp e
Appendix G uses the following equations to calculate the stress intensities:
!bT=temperature difference across vessel wall ('F)o=stress (ksi)(A~+B~)(B~-A2)(3-2)A=vessel inner radius (in.)B=vessel outer radius (in.)P=internal pressure (psig)Since the Appendix X flaw growth criterion is more severe at deep crack depths under Level C and D event loads, the screening calculations were performed assuming a one-quarter thickness flaw.This flaw exceeds the deepest postulated flaw analyzed under the Level C and D analysis.3.3.2 Level C Transient Analysis The blowdown transients are terminated when the pressure reaches 35 psig to account for the containment pressure level at that time in the transient.
I K = K~ + K~
In the TRUMP/MPM calculations, these transients were extended to longer times, conservatively assuming a 300'F/hr cooldown to a 212'F vessel ID temperature.
where, K~ = Ma = membrane         stress intensity factor (ksi V in)
The thermal gradient and pressure data for the Level C transients are summarized in Table 3-4.Based on the data in Table 3-4, the 250'F/7.5 min.Blowdown and the Thermal Transient Blowdown are limiting in terms of ductile fracture.Therefore, detailed finite element calculations were performed for both of these transients to determine the most limiting vessel wall stress distribution.
K~ = MT bT =     stress intensity factor due to thermal gradient (ksi 0 in)
3.39 Level D Transient Analysis Since the Level D transient depressurization occurs over a relatively short time period, and it has been assumed that the downcomer fluid temperature equals the wall surface temperature for the purpose of performing a screening analysis, it was not necessary to perform a thermal transient heat transfer analysis for the Level D transients.
M= ASME membrane           factor (0 in)
Based on the Level C analysis results, the vessel wall bT is approximately equal to 528'F minus the current downcomer fluid temperature for the initial five minutes of the transient.
MT = ASME thermal factor (ksi 0 in/'F)
Therefore, the crack tip stress intensities can be calculated directly.It should be recognized that these assumptions are increasingly over-conservative after the initial five minutes of the transient.
 
The results of the stress intensity factor calculations for the Service Level D  
lpe
                                      !
bT = temperature difference across vessel wall ('F) o=   stress (ksi)
(A~ + B~)
(3-2)
(B~ A2)
A = vessel inner radius (in.)
B = vessel outer radius (in.)
P = internal pressure (psig)
Since the Appendix X flaw growth criterion is more severe at deep crack depths under Level C and D event loads, the screening calculations were performed assuming a one-quarter thickness flaw. This flaw exceeds the deepest postulated flaw analyzed under the Level C and D analysis.
3.3.2   Level C Transient Analysis The blowdown transients are terminated when the pressure reaches 35 psig to account for the containment pressure level at that time in the transient. In the TRUMP/MPM calculations, these transients were extended to longer times, conservatively assuming a 300'F/hr cooldown to a 212'F vessel ID temperature.
The thermal gradient and pressure data for the Level C transients are summarized in Table 3-4. Based on the data in Table 3-4, the 250'F/7.5 min. Blowdown and the Thermal Transient Blowdown are limiting in terms of ductile fracture.
Therefore, detailed finite element calculations were performed for both of these transients to determine the most limiting vessel wall stress distribution.
3.39     Level D Transient Analysis Since the Level D transient depressurization occurs over a relatively short time period, and it has been assumed that the downcomer fluid temperature equals the wall surface temperature for the purpose of performing a screening analysis, it was not necessary to perform a thermal transient heat transfer analysis for the Level D transients. Based on the Level C analysis results, the vessel wall bT is approximately equal to 528'F minus the current downcomer fluid temperature for the initial five minutes of the transient. Therefore, the crack tip stress intensities can be calculated directly. It should be recognized that these assumptions are increasingly over-conservative after the initial five minutes of the transient.
The results of the stress intensity factor calculations for the Service Level D
 
10 transients are shown in Tables 3-5 and 3-6. Based on these calculations, the Steam Line Break Transient, NMP-2 Recirculation Line Break Transient, and the NMP-1 Recirculation Line Break Transient were analyzed in further detail using the finite element method. The other transients yield lower peak stress intensities.
In addition, the stress intensity factor estimates for the other transients are very conservative since a significant portion of the transient is spent in a steam forced convection and/or subcooled free convection heat transfer regime.
3.3.4  Summary of Candidate Transients A simplified model was developed to determine the limiting Service Level C and D transients. Perfect heat transfer between the downcomer fluid and the vessel wall surface was assumed to provide conservative estimates of the through wall thermal gradient. A quarter thickness flaw was assumed and the ASME Appendix G linear elastic model was used to estimate the crack tip stress intensities. Based on the simplified model for screening calculations, the most limiting transients, from a ductile fracture perspective, are summarized in Tables 3-7 and 3-8.
 
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Table 3-1 Level C Transient Temperature/Pressure Variation as a Function of Time Measured From the Initiation of the Event Emergency Condition Level C Transients Unit    1 Design Basis    Unit 2 Design Basis          Unit    1 Emergency Unit 1 SB-LOCA 250'F/7.5 min          Thermal Transient              Cooldown                    ADS Blowdown Blowdown                  Blowdown                    300'F/br
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              $ 1$            3.3              37$        10        $$ 6      478                  730  $ 08 196    zoo g0            121  342        20        344        430      7.7          110  33$
87    JJo g5              87  318        30        191 7.$        48      pro 20              62  29$        40        103        330 25              $0  281      $0          $0        281 60        20        228
          *Nominal Subcooling 100% Power Rated Feedwater Temperature
 
0 12 Table 3-2 Level D Steam Line Break Temperature/Pressure Variation as a Function of Time Measured From the Initiation of the Event Steam Line Break Oyster Creek Analysis Reference (1)                              Reference (2)
Time        Pressure          Temp          Time        Pressure        Temp (sec)        (PSIA)            OF            (sec)      (PSIA)          oF 0          1045        528*                0          1050          552 20              660            497          70              120        350'12 40              310            420          300                  0 60              200            381          450              35          281 80              130            347 100              90            320 120              60          .292 140              40            267 160              31            252 180              25            240 300                15          212 Reference  1 - NMP1 SAFER/CORECOOL/GESTR-LOCA Analysis NEDC-31456P, 1987, NMP1, Figure A017 Reference 2 - Oyster Creek Report GENE-523-70-0692 August '92 "Oyster Creek Vessel Fracture Mechanics Analysis" for upper shelf energy requirement. Figure 5-6 Page 5-13
*Nominal Subcooling 100% Power Rated Feedwater Temperature
 
+c
  ~p 0
 
13 Table 3-3 Level D Recirculation Line Break Spectrum Temperature/Pressure Variation as a Function of Time Measured From Initiation of the Event Recirculation Line Break Spectrum DBA              40% DBA                                                                              .05 ft ~
Tiae  Prrn Trap Tiae    Prnr    Teap  Tlae  Prrss  Tear  Tlae  Prrsr  leap  Ti ae Prrn    Teap  IINIr  Prrrs  Teap (eee) PS(A (sh  (e eel  I'SIA  (rh    (eeet PS(A  (eh    (eee)  PSIA    (eh    (eeei PS!A    reh    (srr)  I'SIA 1045          0    104S              0 104$              0  104$              0 IO4$                  1045 lo  760 S12            ddo    521      20  920  $3$      50            $ 39        960    S40    240          S32
  '20      417            660    491      $0  doo  Sld    100            Sld    Ido  d60    S21    2do          Sld 30    80 312    40      430    452          600          1$ 0    520    411          790    $ 11          130 40    40 261    50      260    404      90  400          Ido    2do    411    300    4do    463            $ 60  419
  $0  20 22d    60      150    3$d    100    320  423    200            Sdl    340                  440    400  44$
IS 212    70            32d    130    110          300      80    312                  411            320  423 90      60    293    1$ 0  120  341    400      40    261    410    220    390            210  3ds 320        IS    212    200                                                                    110 300    40  261                                                        80  312 Iodo      40  261
 
tc 4/
 
Table 3-4 Stress Intensity Factor Estimates  for Service Level C Transients'50'F/7.5 Min. Blowdown                Thermal Transient Blowdown                              Emergency Cooldown 300'F/hr.
Time (Min.)    P      hT      K~      Krr    K        P      hT                K~      K                        P    hT    K~
1030      57      40      18    58    1030      91      40      29      68                    1030    10    40            43 500      101      19      32    51      500    137      19      43      62                    1030    15    40            45 500      146      19      46      65      169    155                49      55                    1030    20    40            46 181    206      7        65    72      169    162                51      57                    1030    30    40            49 33    244        1      77      78      169    167                53      59                    1030    39    40      12    52 10      33    245        1      77      78      169    168                53    59                      541      48    21      15    36 20                                                                                                          329      81    13    .25    38 30                                                                                                          176    107    7      34    40 40                                                                                                          88    120    3      38    41 50                                                                                                          35    130    1    41    42 60                                                                                                            5    140    0    44    44
'nits-        P=psig; AT=max temp diff. ('F); K,=membrane stress intensity (ksi din);
K~thermal  stress intensity (ksi din); K=total stress intensity (ksi din)
'eak    wall thermal gradient
 
tC 15 Table 3-5A Stress. Intensity Factor Estimates    for Service Level D Transients'lnle Steam                  Feed water                  Core Spray              Recirc. Line Break                Recirc. Line Break        Recirc. Line Brcak Line Break                Line Break                  Line Break                    NMP-2                                DBA                    4&#xb9; DBA (Sec.) P  hT                                                  P  hT                K  P                                    P  AT                K P    6T 10 2$ $    I 615 Sl            IO 35 33        33
                                                                                                                                $5  214    3            QS    Sl            10  35
                                                                                                                                                        $ 15  74 115 117 135  $ 70          $3 75                                    10 115 Ill                                                                                                                    SN    0 71  N 75                45 45                    N Ia 715                    S3
'nits-        P=psig; hT=max temp diff. ('F); KtM=membrane stress intensity (ksi din);
Kn -thermal stress intensity (ksi din); K=total stress intensity (ksi din)
 
+c
  ~ f
 
16 Table 3-5B Stress Intensity Factor Estimates      for Service Level D Transients'rme Steam                    Feedwater                  Core Spray              Recirc. Line Break                  Recirc. Line Break  Recirc. Line Break Line Break                Line Break                  Line Break                    NMP-2                                  DBA              40% DBA (Sec.)                        P    dT                K  P                            P    dT                              K P                    P  dT 270 715  2l    2l
                        ~I 15 Sr 5    0                                                                                          27 SIl    0
                                                        <<71 205                      51 210
                                                    <<75 <<75 115                57 247
                                                                                <<7l 217
                                                    <<lt <<tt SIl
                                                                                <<tt  <<tt SI 5
'nits-      P=psig; AT=max temp diff. ( F); Km=membrane stress intensity (ksi din);
Kn -thermal stress intensity (ksi din); K=total stress intensity (ksi din)


10 transients are shown in Tables 3-5 and 3-6.Based on these calculations, the Steam Line Break Transient, NMP-2 Recirculation Line Break Transient, and the NMP-1 Recirculation Line Break Transient were analyzed in further detail using the finite element method.The other transients yield lower peak stress intensities.
J
In addition, the stress intensity factor estimates for the other transients are very conservative since a significant portion of the transient is spent in a steam forced convection and/or subcooled free convection heat transfer regime.3.3.4 Summary of Candidate Transients A simplified model was developed to determine the limiting Service Level C and D transients.
                                                                                                                                            '17
Perfect heat transfer between the downcomer fluid and the vessel wall surface was assumed to provide conservative estimates of the through wall thermal gradient.A quarter thickness flaw was assumed and the ASME Appendix G linear elastic model was used to estimate the crack tip stress intensities.
                                                                . Table 3-6A Stress Intensity Factor Estimates   for Service Level D Recirc. Line Break 1
Based on the simplified model for screening calculations, the most limiting transients, from a ductile fracture perspective, are summarized in Tables 3-7 and 3-8.
ft'~                               0.5 ft'ecirc.
/<x Table 3-1 Level C Transient Temperature/Pressure Variation as a Function of Time Measured From the Initiation of the Event Emergency Condition Level C Transients Unit 1 Design Basis Unit 2 Design Basis 250'F/7.5 min Thermal Transient Blow down Blowdown Unit 1 Emergency Cooldown 300'F/br Unit 1 SB-LOCA ADS Blowdown ((Ioo (IOlOoOOI(SIoooooo (SS(SP ((Ioo (IOONOOO(SIooooIo (SS (S((lIII~(oIkIIloo(SIoo ooI~(pS(o)(IIop (SJ ((Io o (oIooO o I(SIooooI@SoSlA)JOS5 0 JOSS JJdo JOSS$1$3.3 37$10$$6 478 730$08 196 zoo g0 121 342 20 344 430 7.7 110 33$87 JJo g5 87 318 30 191 7.$48 pro 20 62 29$40 103 330 25$0 281$0$0 281 60 20 228*Nominal Subcooling 100%Power Rated Feedwater Temperature 0
Recirc. Line Break Transients'lmc 0.1 Line Break ft'M Recirc. Line Break 0.05 ft sec.                            K                                                                                K~  P hT     KM 10 15 35     2     37 30 50   785 10     30     3     33       885   11                     37 70   585 42             13     36 75 90   385 83     15     26     41 305  105    12     33     45       785   10     30             33     945   12           36             4 120 130  155  160            50    56 140 145 150 105 187           59     63       505   57       19     18     37
12 Table 3-2 Level D Steam Line Break Temperature/Pressure Variation as a Function of Time Measured From the Initiation of the Event Steam Line Break Time (sec)Reference (1)Pressure (PSIA)Temp OF Time (sec)Oyster Creek Analysis Reference (2)Pressure (PSIA)Temp oF 0 20 40 60 80 100 120 140 160 180 300 1045 660 310 200 130 90 60 40 31 25 15 528*497 420 381 347 320.292 267 252 240 212 0 70 300 450 1050 120 0 35 552 350'12 281 Reference 1-NMP1 SAFER/CORECOOL/GESTR-LOCA Analysis NEDC-31456P, 1987, NMP1, Figure A017 Reference 2-Oyster Creek Report GENE-523-70-0692 August'92"Oyster Creek Vessel Fracture Mechanics Analysis" for upper shelf energy requirement.
'nits-     P=psig; AT=max temp diff. ('F); K~=membrane stress intensity (ksi din);
Figure 5-6 Page 5-13*Nominal Subcooling 100%Power Rated Feedwater Temperature
Krr=thermal stress intensity (ksi din); K=total stress intensity (ksi din)
+c~p 0 13 Table 3-3 Level D Recirculation Line Break Spectrum Temperature/Pressure Variation as a Function of Time Measured From Initiation of the Event Recirculation Line Break Spectrum DBA 40%DBA.05 ft~Tiae (eee)Prrn PS(A Trap (sh Tiae (e eel Prnr I'SIA Teap (rh Tlae (eeet Prrss PS(A Tear (eh Tlae (eee)Prrsr PSIA leap (eh Ti ae (eeei Prrn PS!A Teap reh IINI r (srr)Prrrs I'SIA Teap 1045 0 104S 0 104$0 104$0 IO4$1045 lo 760 S12 ddo 521 20 920$3$50$39 960 S40 240 S32'20 417 660 491$0 doo Sld 100 Sld Ido d60 S21 2do Sld 30 80 312 40 430 452 600 1$0 520 411 790$11 130 40 40 261 50 260 404 90 400 Ido 2do 411 300 4do 463$60 419$0 20 22d 60 150 3$d 100 320 423 200 Sdl 340 440 400 44$IS 212 70 32d 130 110 300 80 312 411 320 423 90 60 293 1$0 120 341 400 40 261 410 220 390 210 3ds 320 IS 212 200 110 300 40 261 80 312 Iodo 40 261 tc 4/
Table 3-4 Stress Intensity Factor Estimates for Service Level C Transients'50'F/7.5 Min.Blowdown Thermal Transient Blowdown Emergency Cooldown 300'F/hr.Time (Min.)P hT K~Krr 1030 57 40 18 K P hT 58 1030 91 40 K~K 29 68 P hT K~1030 10 40 43 500 101 19 32 51 500 137 19 43 62 1030 15 40 45 10 20 30 40 50 60 500 146 19 46 181 206 7 65 33 244 1 77 33 245 1 77 65 169 155 72 169 162 78 169 167 78 169 168 49 55 51 57 53 59 53 59 1030 20 40 1030 30 40 1030 39 40 541 48 21 329 81 13 176 107 7 88 120 3 35 130 1 5 140 0 12 15.25 34 38 41 44 46 49 52 36 38 40 41 42 44'nits-P=psig;AT=max temp diff.('F);K,=membrane stress intensity (ksi din);K~thermal stress intensity (ksi din);K=total stress intensity (ksi din)'eak wall thermal gradient tC 15 Table 3-5A Stress.Intensity Factor Estimates for Service Level D Transients'lnle (Sec.)P hT Steam Line Break Feed water Line Break Core Spray Line Break P hT K P Recirc.Line Break NMP-2 Recirc.Line Break DBA P AT Recirc.Line Brcak 4&#xb9;DBA K P 6T 10 615 Sl IO 35 2$$I$5 214 3 QS Sl$15 74 33 10 33 35 115 117 135$70$3 75 115 Ill 75 45 45 N 10 SN 0 71 N Ia 715 S3'nits-P=psig;hT=max temp diff.('F);KtM=membrane stress intensity (ksi din);Kn--thermal stress intensity (ksi din);K=total stress intensity (ksi din)
+c~f 16 Table 3-5B Stress Intensity Factor Estimates for Service Level D Transients'rme (Sec.)Steam Line Break P dT Feedwater Line Break K P Core Spray Line Break Recirc.Line Break NMP-2 P dT K P Recirc.Line Break DBA P Recirc.Line Break 40%DBA dT 270~I 715 2l 2l Sr 5 0 15 27 SIl 0 210<<71 205 51 247<<75<<75 115 57 SIl<<lt<<tt 217 SI 5<<7l<<tt<<tt'nits-P=psig;AT=max temp diff.(F);Km=membrane stress intensity (ksi din);Kn--thermal stress intensity (ksi din);K=total stress intensity (ksi din)
J  
'17.Table 3-6A Stress Intensity Factor Estimates for Service Level D Transients'lmc sec.10 15 Recirc.Line Break 1 ft'~K Recirc.Line Break 0.5 ft'ecirc.Line Break 0.1 ft'M K~Recirc.Line Break 0.05 ft P hT KM 30 35 2 37 50 785 10 30 3 33 885 11 37 70 585 75 42 13 36 90 385 305 120 130 155 140 145 83 105 160 15 26 41 12 33 45 50 56 785 10 30 33 945 12 36 4 150 105 187 59 63 505 57 19 18 37'nits-P=psig;AT=max temp diff.('F);K~=membrane stress intensity (ksi din);Krr=thermal stress intensity (ksi din);K=total stress intensity (ksi din)  


18 Table 3-6B Stress Intensity Factor Estimates for Service Level D Transients'llllC sec.160 175 Recirc.Line Break 1 ft'ecirc.Line Break 0.5 ft'~K~K P Recirc.Line Break 0.1 ft'ecirc.Line Break 0.05 ft'T KlM K~K 180 280 55 225 2 71 73 265 185 117 147 10 37 47 845 46 53 775 33 30 33 33 785 10.30 3 33 320 261 1 82 83 65 216 3 68 71 465 65 18 38 715 20 28 6 34 440 470<316 0 261 82 83 385 205 111 15 138 8 35 43 50 51 385 83 15 26 41<316<99<99 305 105 12 33 45 630 195 143 8 45 53 95 193 4 61 65 930 1080 1420 mts-<316 0=pstg;=max temp 1.;,=mern rane stress tntenstty st m;K~thermal stress intensity (ksi din);K=total stress intensity (ksi din)65<216 3 25<216 1<316 0<68<82<83<99<99 It 0 19 Table 3-7 Level C Transients for Finite Element Analysis NMP-1 Design Basis 250'F/7.5 Min, Blowdown'MP-2 Design Basis Thermal Transient Blowdown~Time (Min.)7.5 20.7 Pressure (psig)1030 500 181 72 33 Temp.528 470 380 318 278 212 Heat Transfer Coefficient h=BTU/(hr ft'F)10,000 10,000 10,000 10,000 10,000 500 Time (Min.)3.3 10 15 20 25 38.8 Pressure (psig)1030 169 106 72 47 35 Temp.P)528 375 342 318 295 281 212 Heat Transfer Coefficient h=BTU/I hr fPF)10,000 10,000 10,000 10,000 10,000 10,000 500'MP-1 Updated FSAR~Reference[STRS]
18 Table 3-6B ft'ecirc.
ec I t Table 3-8 Level D Transients for Finite Element Analysis 20 Steam Line Break'ecirculation Line Break'NMP-2 Recirculation Line Break'NMP-1 DBA Time (Sec.)pressure Temp (psig)('F)Heat Transfer Coefficient h=BTU/(hr ft F)Time (Sec.)Pressure (psig)Temp.('F)Heat Transfer Coefficient h=BTU/(hr ft F)Time (Sec.)Pressure (psig)Temp ('F)Heat Transfer Coefficient h=BTU/(hr ft F)20 40 1030 295 528 497-420 10,000 10,000 10,000 15 20 , 1030 35 23 528 281 264 69,188 164 164 10 15 1030 474 528 512 464 10,000 10,000 164 60 80 185 381 115 347 10,000 10,000 60 100 23 18 264 256 164 164 20 30 285 417 312 164 164 100 120 140 160 180 300 380 400 75 45 25 16 10 320 292 267 252 240 212 212 212 10,000 10,000 10,000 10,000 10,000 10,000 164 500 200 300 1300 3.5 235 222 212 164 164 500 40 50 80 25 267 228 212 164 164 500 Reference[NEDC]References
Stress Intensity Factor Estimates   for Service Level D Recirc. Line Break 1
[NMP2TC],[STRS], and[NMP1DP]
Line Break 0.5 ft'~
Recirc. Line Break 0.1 Transients'llllC ft'ecirc.       0.05 Line Break ft'T sec.                                                          K~    K      P                                                    KlM     K~ K 160 175 180                                     265    117    10      37    47    845            33                      33 55 225   2     71   73       185     147           46   53     775           30                     33 280                                                                                                                  785 10     30
                                                                                                                                .         3   33 261     1     82     83     65     216     3       68   71     465   65     18                     38 715 20     28       6   34 320 261             82   83     385   111     15                   35 50 440        <316  0                                                                                                  385 83     15       26 41 470                                                                        205    138    8                    43 51
                                              <316           <99   <99                                             305 105     12       33 45 195 143     8       45 53 630 95 193     4       61 65 65  <216    3        <68 930                                                                               <316    0 1080                                                                                                                 25  <216    1        <82 <83 1420                                                                                                                     <316   0       <99 <99 mts-    =pstg;     =max temp 1   .;,=mern         rane stress tntenstty     st m; K~thermal stress intensity (ksi din); K=total stress intensity (ksi din)


Emergency Condition Level C Transients 600 528'F 500 400--300--~~281'F@35 slg 200 100-0-Data  
It 0 19 Table 3-7 Level C Transients for Finite Element Analysis 250'F/7.5 Min,  Blowdown'MP-2 NMP-1 Design Basis                                                Design Basis Thermal Transient Blowdown~
Heat Transfer                                                Heat Transfer Time      Pressure        Temp.        Coefficient      Time        Pressure        Temp.        Coefficient (Min.)      (psig)                    h=BTU/(hr ft'F)    (Min.)        (psig)            P)        h=BTU/Ihr fPF) 1030            528        10,000                        1030            528          10,000 500              470        10,000          3.3            169            375          10,000 181            380        10,000          10            106            342          10,000 72              318        10,000          15            72              318          10,000 7.5          33              278        10,000          20            47              295          10,000 20.7                          212          500            25            35              281          10,000 38.8                            212            500
'MP-1 Updated      FSAR
~
Reference [STRS]
 
ec tI
 
20 Table 3-8 Level D Transients for Finite Element Analysis Steam Line Break
                              'ecirculation              Break' Line NMP-2 Recirculation Line Break' NMP-1 DBA Heat Transfer                                Heat Transfer                            Heat Transfer Time      pressure  Temp        Coefficient  Time    Pressure    Temp.      Coefficient  Time  Pressure  Temp      Coefficient (psig)  ('F)      h=BTU/(hr  (Sec.)      (psig)    ('F)      h=BTU/(hr  (Sec.)  (psig)      ('F)    h=BTU/(hr (Sec.)
ft F)                                              ft F)                                    ft F) 1030    528          10,000              ,  1030      528        69,188            1030      528        10,000 20                497-        10,000      15        35      281          164        10              512        10,000 40        295    420          10,000      20          23      264          164        15    474      464          164 60          185    381          10,000      60          23      264          164        20    285      417          164 80        115    347          10,000      100        18      256          164        30              312          164 100          75    320          10,000    200                  235          164        40      25      267          164 120          45    292          10,000    300          3.5      222          164        50              228          164 140          25    267          10,000    1300                  212          500        80              212          500 160          16    252          10,000 180          10    240          10,000 300                212          10,000 380                212          164 400                212          500 Reference [NEDC]
References [NMP2TC], [STRS], and [NMP1DP]
 
Emergency Condition Level C Transients 600 528'F 500 400 -
300--                                                                                     ~ ~ 281'F @ 35 slg Data  


==References:==
==References:==


%300'F/hr Emergency+Unit 2 Design Basis Cooldown Unit 1 FSAR Thermal Transient Blowdown from 762E673~'250'F/7.5'min
200
'.'vent 23 NMP2.Vessel.
            % 300'F/hr   Emergency Cooldown Unit 1 FSAR
'ooldown Unit 1 FSAR Stress Analysis (Six ERV's open)STRS 16.010-5039A
                                          + Thermal Unit 2 Design Basis Transient
-Relief valves reset at 50 psia (35 psig), cooldown assumed at 300'F/hr to 0 psig-..".0 5 10 IS 20 25 30 35 40 45 50 55 60 Time (minutes)Unit 1 Design Basis%Unit 2 Design Basis A Unit I Emer Cool~Nom.ADS BD 3 ERVs open Figure 3-1 Level C Transients Analyzed to Determine the Most Limiting Transient for NMP-1  
                                                                              - Relief valves reset at 50 psia (35 psig),
+c t Steam Break 22 600 500 TAFU-Uncover380 sec TAFR-Recover Q 400 sec-Oyster Creek GENE-523-70-0692 Steamllne Break profile 400 300 TAFU TAFR I I I I 281'F+35 psfg 200 212'F Q 0 psig 100 DATA REFERENCE Assume boiling HTC=NEOC4N56P, tg87, NMPt (0000 gTUthl.ft).oF.Safei/CoreooofLGESTR-LOCA
Blowdown from 762E673             cooldown assumed at 100-    ~ '250'F/7.5'min     '.         'vent 23 NMP2.Vessel.                300'F/hr to 0 psig- .. " .
....until.TAFR analysis, Figure A-17 Subcooled Boiling HTC thereafter from ECCS flow HTC=500 BTR/hr-ft2-'F 0 50 100 150 200 250 300 350 400 450 500 550 600" Nominal Subcooling 100%power rated feedwater temperature Figure 3-2 Level D Steam Line Break Transient Pressure Profile ec t Feedvater Line reak 23 600 528'F 500 400 300''TAFU TAFR TAFU-Uncover145 sec TAFR-Recover I 265 sec 281'F Q 85 psig 200 100 DATA  
Unit 1 FSAR         Stress Analysis     'ooldown (Six ERV's open)               STRS 16.010-5039A 0-0       5     10       IS     20     25     30       35         40   45       50       55     60 Time (minutes)
Unit 1 Design Basis % Unit 2   Design Basis   A Unit I Emer Cool ~Nom.ADS BD 3 ERVs open Figure 3-1 Level C Transients Analyzed to Determine the Most Limiting Transient for NMP-1
 
+c t
 
Steam               Break 22 600 TAFU - Uncover  380 sec TAFR - Recover Q 400 sec Oyster Creek GENE-523-70-0692 Steamllne Break profile 500 400 TAFU TAFR I
I I
300                                                                      I         281'F+35   psfg 212'F Q 0 psig 200 DATA REFERENCE                   Assume boiling HTC =     Subcooled Boiling HTC thereafter NEOC4N56P, tg87, NMPt           (0000 gTUthl.ft).oF     from ECCS flow HTC=500 BTR/hr-ft2-'F
      .Safei/CoreooofLGESTR-LOCA ....until.TAFR 100 analysis, Figure A-17 0       50       100   150       200   250       300   350     400   450     500   550   600
                      " Nominal Subcooling   100% power rated feedwater temperature Figure 3-2 Level D Steam Line Break Transient Pressure Profile
 
ec t
 
Feedvater Line             reak 23 600 528'F 500 400 TAFU - Uncover TAFR - Recover   I   145 sec 265 sec
                                      '
TAFU 300'                                                              281'F Q 85 psig TAFR 200 Assume Boiling HTC 10,000 DATA  


==REFERENCE:==
==REFERENCE:==
BTU/hr-ft2-'F until TAFR NEDC-31446P 1 987,              Subcooled HTC thereafter...
100          'NMP1 Safer/Corecool/            from ECCS flow HTC = 500 GESTR-LOCA. Fig. A-19          - BTU/hr-ft2-'F 0  50  100 150 200 250 300 350 400 450 500 550 600 650 700 Time (sec)                          10        75      100      200      300        400      500 Pressure (I'SIR)          1,045    960      800      720      400      140          80      50 Saturaled Temp ('F) W      528~    528"      518      506        444      353        312      281
* Nominal Subcooling 100% power rated feedwater temperature Figure 3-3 Level D Feedwater Line Break Transient Pressure Profile


NEDC-31446P 1 987,'NMP1 Safer/Corecool/
C
GESTR-LOCA.
                                                                                                                '4 Core Spray Line Break 600 TAFU - Uncover Q 245 sec 528'F i                                          TAFR - Recover      320 sec 500 400 I       I I
Fig.A-19 Assume Boiling HTC 10,000 BTU/hr-ft2-'F until TAFR Subcooled HTC thereafter...
TAFU TA R                                 281'F O 35 psig 300 200                                             -Assume Bolting HTC 10,000-    --
from ECCS flow HTC=500-BTU/hr-ft2-'F 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 Time (sec)Pressure (I'SIR)1,045 10 960 75 100 200 800 720 400 140 80 50 300 400 500 Saturaled Temp ('F)W 528~528" 518 506 444 353 312 281*Nominal Subcooling 100%power rated feedwater temperature Figure 3-3 Level D Feedwater Line Break Transient Pressure Profile C
DATA  
Core Spray Line Break'4 600 528'F i 500 TAFU-Uncover Q 245 sec TAFR-Recover320 sec 400 300 I I I TAFU TA R 281'F O 35 psig 200 100 DATA  


==REFERENCE:==
==REFERENCE:==


NEDC-31446P, 1987,"NMP1 Safer/Corecool/G ESTR-LOCA Figure A-16-Assume Bolting HTC 10,000---BTU/hr-ft2-'F until TAFR Subcooled HTC thereafter from ECCS flow HTC=500 BTU/hr-f t2-'F 0 0 100 200 300 400 500 600 700 800 Time (sec)Pressure (I'SIA 1,045 145 800 175 730 400 400 220 500 130 630 50*Saturated Temp ('F)W 528~518 507 444 390 347 281'ominal Subcoollng 100%power rated feedwater temperature Figure 3-4 Level D Core Spray Line Break Pressure Profile Jc C Recirculation Line Break Spectrum25 528 F 600-$00-IAfV 4 I I t I IAfV~---..300.F/hr--AKISASIICKS.
BTU/hr-ft2-'F until TAFR NEDC-31446P, 1987, "NMP1 Subcooled HTC thereafter Safer/Corecool/G ESTR-LOCA from ECCS flow HTC = 500 Figure A-16 100                                                BTU/hr-ft2-'F 0
ll AA IIHtOI HHWIV Clltlb4lv Isa>>45OCSllif4, I&Sf'NVAI SAfe4co4ecoovoes'lll.locA'5e II Vvff.fffef f5.l4fvoe voooN IIIOIAIAI CICloA 400 28t oF@35 psig+IAf4 I IAf ll+IAfll I prAIR.I.I I 200 100-Reference 2 In'a'll cases, level is at TAF prior to complete depressurization.
0         100       200     300       400       500       600       700       800 Time (sec)                               145        175                  400          500        630 Pressure (I'SIA             1,045       800       730       400       220         130         50
Downcomer Level is assumed to follow core level.Therefore,.assurpe.saturated steam.conditions.
* Saturated Temp ('F) W       528 ~       518       507       444       390         347         281
in,cfowncomqr.during,...
                            'ominal   Subcoollng 100% power rated feedwater temperature Figure 3-4 Level D Core Spray Line Break Pressure Profile
depressurization until TAF is recover by ECCS.Then assume free convection to subcooled ECCS.0 100 200 300 400$00 600 700 800 900 1,000 1,100 Time (Seconds)~DBA+40%DBA I Ft 2+.$Ft 2 Hj.l Fl 2+.0$Ft 2 Figure 3-5 Level D Recirculation Line Break Spectrum Pressure Profile Jf 4 Finite Element Analysis 26 The candidate transients listed in Tables 3-7 and 3-8 were analyzed using the finite element method to determine the most severe Level C and Level D loadings.The WELD3 finite element code package IWELD3]was used to perform the calculations.
 
4.1 Model Description The WELD3 model assumes axisymmetric behavior.A single column of elements was used, thus making the solution essentially one dimensional (i.e., temperatures and stresses only depend on the radial position within the vessel wall).The finite element grid is shown in Figure 4-1.Elements 1 and 2 represent the cladding.The cladding inner surface radius is 106.344 inches, the base metaVclad interface is at 106.5 inches, and the vessel outer radius is 113.781 inches.The axial dimension of the model is 0.15 inches.For thermal modeling, the outer vessel surface was treated as perfectly insulated.
Jc C
The inner surface has a prescribed heat transfer coefficient and fluid temperature (both functions of time).All heat flow is radial.Temperature dependent properties were used in the thermal analysis.The mechanical model is constrained to'ave a uniform axial strain so that plane sections remain plane.The average axial stress and the internal pressure are input to the model based on the pressure transient input.Thermal transients are input via element temperatures.
 
Temperature dependent properties are also used for the stress calculations.
Recirculation Line Break Spectrum                                                                    25 600- IAfV                                                                                   AKISASIICKS.
The WELD3 calculations assumed linear elastic behavior for both the cladding and base metal so as to be consistent with the use of the small scale yielding assumption (linear elastic fracture mechanics with plastic zone corrections) in the subsequent fracture mechanics analyses.4.2 Finite Element Analysis Results Two Level C cases and three Level D cases were analyzed.The transient thermal and pressure boundary conditions are described in Tables 3-7 and 3-8.Although the pressure and thermal loadings could be analyzed separately due to the use of linear elasticity, it was judged more expedient to combine the loadings.The cladding has a different coefficient of thermal expansion than the base metal.This impacted the analysis in several ways..First, there will be some residual stress even when the vessel is at a uniform temperature.
I                                                                     ll AA IIHtOI HHWIV Clltlb4lv IAfV                                                                   Isa>> 45OCSllif4, I&Sf 'NVAI 4  I          t      I                                                                SAfe4co4ecoovoes'lll.locA'5e II Vvff. fffeff5. l4fvoe voooN 528 F                                                                                                    IIIOIAIAICICloA
Assuming that the vessel is 100%stress free at the stress relief temperature of 1150'F, the original cooling to 528'F induced tensile residual stresses in the cladding thus contributing to crack tip stress intensity factors.This uniform cooling was modeled in a separate analysis to determine the level of initial residual stress.The difference in thermal expansion behavior also results in discontinuous WC 27 axial and hoop stresses across the material interface.
        $ 00-                                                                    ~ -- - ..300. F/hr--
Since the fracture mechanics evaluation involves fitting the stresses with a cubic polynomial, this discontinuous behavior impacts the quality of the polynomial fits.Therefore, as described in Section 5.0, the fracture mechanics model was configured to minimize the sensitivity of the analysis to the effects of stress field discontinuities at the interface.
prAIR 400                                                                  .I.
Figure 4-2 shows the axial and hoop residual stresses that exist due to uniform cooling from a stress free condition at 1150'F to 528'F.This residual stress was not included in the st:ss distribution plots for the various Level C and Level D transients that follow.This approach was adopted as part of the approach to more accurately handle the discontinuous stress field.The final stress distributions do include the differential expansion coefficient effects due to cooling from 528'F during the transient.
                                                                    + IAfll
The method for including the residual stress load in the fracture mechanics analysis is described in Section 5.0.The WELP3 stress output for each analysis was scanned for the time of the most severe stresses induced by the combined transient thermal and pressure loading.Since crack depths of no larger than one inch are of interest[ASME92], the time at which the stresses would be most severe for a one inch deep crack was identified.
                                                  +  IAf4 I                  I IAfll                                              I I
This was done without actually calculating stress intensity factors for each transient stress distribution and was possible only because the stresses over the inner inch of the wall tended to peak at about the same point in time.Figures 4-3 through 4-10 contain plots of the transient temperatures and stresses.The times of the most damaging stresses for crack depths of about an inch are plotted with a solid line.Temperatures and stresses at other times are plotted using broken lines.It can be seen from these plots that for deeper cracks, the critical time would tend to be later in the transient.
28t oF
For very shallow cracks, slightly larger stress intensity factors may occur at earlier times than for the identified times.Table 4-1 summarizes the results of the WELD3 analyses.4.3, Limiting Transients The hoop and axial stress behaviors are very similar and tend to experience their peak values at about the same time.The magnitudes of the hoop stresses tend to be larger than the axial stresses.Without inputting these stresses into a fracture mechanics analysis it is not possible to determine which stress component is limiting.As discussed further in Section 5.0, the axially oriented flaw (hoop stress loading)is the limiting case.Of the two Level C cases considered; the"NMP-1 Design Basis 250'F/7.5 min.Blowdown" resulted in the larger stresses.Of the three Level D cases, the"Steam Line Break" resulted in the largest stresses.As shown in Figures 4-3 through 4-5, the time dependence of the heat transfer coefficient plays an important role in defining the limiting Level D transient.
@35 psig 200 Reference 2        In'a'll cases, level is at TAF prior to complete depressurization.
In particular, although the Steam Line Break is not the most rapid depressurization transient, it is limiting since the heat transfer is more efficient over the first 300 seconds of the event.
Downcomer Level is assumed to follow core level. Therefore, 100-                        .assurpe.saturated steam. conditions. in,cfowncomqr.during,...
rc 28 Table 4-1 Summ of Peak Claddin and Peak Base Metal Stresses at the Indicated Times stress units are ksi Case residual C1 D1 D2 D3 Critical Time NA 9.15 min 6.65 min 240 sec 500 sec 320 sec~Hoo 20.6 60.6 42.6 78.4 47.7 65.5 Clad Axial 20.0 50.2 34.8 65.9 39.5 54.6~Hoo-0.7 40.5 29.6 52.3 31.7 43.9 Base Axial-1.3 29.8 21.5 39.4 23.2 32.7 C1: NMP-1 Design Basis 250'F/7.5 min, Blowdown C2: NMP-2 Design Basis Thermal Transient Blowdown D1: Steam line Break D2: Recirculation Line Break NMP-2 D3: Recirculation Line Break NMP-1 DBA ec  
depressurization until TAF is recover by ECCS. Then assume free convection to subcooled ECCS.
'9 123 4 5 6 7 8 9 13141516171819202122 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Figure 4-1 One Dimensional Finite Element Mesh for NMP-1 Pressure Vessel Analysis er 22 20 H C20.6 ksi)A (20.0 ksi)30 18 16 14 A: Axi al Stress H: Hoop Stress 12 (o 8 0 2 3 5 6.Distance fr om inner sur face (in)Figure 4-2 Residual Stress at 528'F Due to Cladding Differential Expansion  
0           100        200        300      400      $ 00      600        700    800      900          1,000        1,100 Time (Seconds)
                              ~DBA +40%                  DBA      I Ft 2 +.$ Ft 2 Hj.l Fl 2 +.0$            Ft 2 Figure 3-5 Level D Recirculation Line Break Spectrum Pressure Profile
 
Jf 4
 
26 Finite Element Analysis The candidate transients listed in Tables 3-7 and 3-8 were analyzed using the finite element method to determine the most severe Level C and Level D loadings. The WELD3 finite element code package IWELD3] was used to perform the calculations.
4.1     Model Description The WELD3 model assumes axisymmetric behavior. A single column of elements was used, thus making the solution essentially one dimensional (i.e., temperatures and stresses only depend on the radial position within the vessel wall). The finite element grid is shown in Figure 4-1. Elements 1 and 2 represent the cladding. The cladding inner surface radius is 106.344 inches, the base metaVclad interface is at 106.5 inches, and the vessel outer radius is 113.781 inches. The axial dimension of the model is 0.15 inches.
For thermal modeling, the outer vessel surface was treated as perfectly insulated. The inner surface has a prescribed heat transfer coefficient and fluid temperature (both functions of time). All heat flow is radial. Temperature dependent properties were used in the thermal analysis.
The mechanical model is constrained to'ave a uniform axial strain so that plane sections remain plane. The average axial stress and the internal pressure are input to the model based on the pressure transient input.       Thermal transients are input via element temperatures. Temperature dependent properties are also used for the stress calculations.
The WELD3 calculations assumed linear elastic behavior for both the cladding and base metal so as to be consistent with the use of the small scale yielding assumption (linear elastic fracture mechanics with plastic zone corrections) in the subsequent fracture mechanics analyses.
4.2     Finite Element Analysis Results Two Level C cases and three Level D cases were analyzed. The transient thermal and pressure boundary conditions are described in Tables 3-7 and 3-8. Although the pressure and thermal loadings could be analyzed separately due to the use of linear elasticity, it was judged more expedient to combine the loadings.
The cladding has a different coefficient of thermal expansion than the base metal. This impacted the analysis in several ways.. First, there willbe some residual stress even when the vessel is at a uniform temperature. Assuming that the vessel is 100% stress free at the stress relief temperature of 1150'F, the original cooling to 528'F induced tensile residual stresses in the cladding thus contributing to crack tip stress intensity factors.
This uniform cooling was modeled in a separate analysis to determine the level of initial residual stress. The difference in thermal expansion behavior also results in discontinuous
 
WC 27 axial and hoop stresses across the material interface. Since the fracture mechanics evaluation involves fitting the stresses with a cubic polynomial, this discontinuous behavior impacts the quality of the polynomial fits. Therefore, as described in Section 5.0, the fracture mechanics model was configured to minimize the sensitivity of the analysis to the effects of stress field discontinuities at the interface.
Figure 4-2 shows the axial and hoop residual stresses that exist due to uniform cooling from a stress free condition at 1150'F to 528'F. This residual stress was not included in the st:ss distribution plots for the various Level C and Level D transients that follow.
This approach was adopted as part of the approach to more accurately handle the discontinuous stress field. The final stress distributions do include the differential expansion coefficient effects due to cooling from 528'F during the transient. The method for including the residual stress load in the fracture mechanics analysis is described in Section 5.0.
The WELP3 stress output for each analysis was scanned for the time of the most severe stresses induced by the combined transient thermal and pressure loading. Since crack depths of no larger than one inch are of interest [ASME92], the time at which the stresses would be most severe for a one inch deep crack was identified. This was done without actually calculating stress intensity factors for each transient stress distribution and was possible only because the stresses over the inner inch of the wall tended to peak at about the same point in time. Figures 4-3 through 4-10 contain plots of the transient temperatures and stresses. The times of the most damaging stresses for crack depths of about an inch are plotted with a solid line. Temperatures and stresses at other times are plotted using broken lines. It can be seen from these plots that for deeper cracks, the critical time would tend to be later in the transient. For very shallow cracks, slightly larger stress intensity factors may occur at earlier times than for the identified times.
Table 4-1 summarizes the results of the WELD3 analyses.
4.3, Limiting Transients The hoop and axial stress behaviors are very similar and tend to experience their peak values at about the same time. The magnitudes of the hoop stresses tend to be larger than the axial stresses. Without inputting these stresses into a fracture mechanics analysis it is not possible to determine which stress component is limiting. As discussed further in Section 5.0, the axially oriented flaw (hoop stress loading) is the limiting case.
Of the two Level C         cases   considered; the "NMP-1 Design Basis 250'F/7.5 min.
Blowdown" resulted in the larger stresses. Of the three Level D cases, the "Steam Line Break" resulted in the largest stresses. As shown in Figures 4-3 through 4-5, the time dependence of the heat transfer coefficient plays an important role in defining the limiting Level D transient. In particular, although the Steam Line Break is not the most rapid depressurization transient, it is limiting since the heat transfer is more efficient over the first 300 seconds of the event.
 
rc 28 Table 4-1 Summ     of Peak Claddin and Peak Base Metal Stresses at the Indicated Times stress units are ksi Critical              Clad                      Base Case         Time        ~Hoo          Axial          ~Hoo      Axial residual        NA         20.6          20.0          -0.7      -1.3 C1          9.15 min       60.6          50.2          40.5      29.8 6.65 min      42.6         34.8          29.6      21.5 D1          240 sec        78.4          65.9           52.3      39.4 D2          500 sec        47.7         39.5           31.7     23.2 D3          320 sec        65.5          54.6          43.9      32.7 C1: NMP-1 Design Basis 250'F/7.5 min, Blowdown C2: NMP-2 Design Basis Thermal Transient Blowdown D1: Steam line Break D2: Recirculation Line Break NMP-2 D3: Recirculation Line Break NMP-1 DBA
 
ec
                                                                                                  '9 123 4 5 6 7 8 9 13141516171819202122 23 24 25 26 27 28   29 30 31 32   33   34   35 36 37 38 Figure 4-1 One Dimensional Finite Element Mesh for NMP-1 Pressure Vessel Analysis
 
er 30 22 H C20. 6 ksi) 20 A (20. 0   ksi) 18 16         A:   Axi al Stress 14 H:   Hoop   Stress 12 (o
8 0
2         3                     5           6.
Distance fr om inner sur face (in)
Figure 4-2 Residual Stress at 528'F Due to Cladding Differential Expansion


31 6DD 1$t 1.65 min.2$t=3.3 min.9$t=6.65 min.500 400 I-300 r//4//c'//g6/J'1$t=2min.2$t~4min.3$t=6min.4$t=7.5 min.5$t=9.15 min.6$t 14.1 min.500 8 I 400 0 I 8 o E I-300 t~15 min.6$t 20 min.2<(/3 r/~s (y 6 e 7H r~r~8 4$t=10 min./5$7$t~20.7 min.'\S$t=25 min.t=98.8 min.20D 0 l 2 3 4 5 6 7 8 Distance from inner surface (in)Level CI 250 F/7.5-min.'lowdown 200 0 l 2 3 4 5 6 7 8 Distance from inner surface (in)Level C: NMP-2 Blowdown Figure 4-3 Pressure Vessel Thermal Gradients for Level C Transients pc
31 6DD                                                                                                       1$ t   1. 65 min.
'2 600 500 400 300 3s t 18D sec.7s t SDD sec.1(/2/'//y6t'1s t 6D sec.I/yw 2s t 120 sec./II I//I Iy 4s t 240 sec.I I/I Ss t 30D sec./I/r/6s t 400 sec.540 520 , 500 480 460 440 420 a 400 380 360 340 320 6s t 20D sec.II34/g//S/////I///7Y/I I//~8 I I/~g~I//y 1s t~1Ssec.I I/2s t~20 sec.I/3s t 40 sec.I/I 4s t 60 sec./Ss t 1DD sec.//7s t 30D sec.I 8s t SDD sec./gs t 700 sec.200 0 l 2 3 4 5 6 7 8 Distance from inner sur face (in)Level Ds Steam Line Br eok 300 0 l 2 3 4 5 6 7 8 Distance from inner surfoca (in)Level Ds Recirculation Line Br eok Figure 4-4 Pressure Vessel Thermal Gradients for Level D Transients c
2$ t = 3.3 min.
600 33 500~.400 0 L a E 300 3c t BD sec.4c t 140 sec.G: t 320 sec.Bs t 5GD sec.gs t GBD sec.1~~r r/r 5//1s t 15 sec.//r'/.2 t 30 sec./////I///i (/p///7s t 440 sec.200 0 l 2 3 4 5 6 7 8 Distance from inner sUrface (in)Level Ds Recirculation Line Br eak NHP-l DBA Figure 4-5 Pressure Vessel Thermal Gradients for Level D Transients  
9$ t = 6. 65 min.
500                         r                                             500          2<
              /                                                                   (    /     3      r 8
                                                                                      /         ~s
            / 4/                                                         I        (          y 6e 400
            /
              /       c'               1$ t = 2min.                   0 I
8 o
400 r7H 2$ t ~4min.                     E
          /
min.'\
I-                g6                          t =6min.                    I                            8
        /    J' 3$
                                                                                    ~r  ~                      t = 10 min.
4$ t = 7.5 min.                                                   4$
300 5$ t = 9. 15 min.
300  /                        5$ t ~ 15 min.
6$ t   14.1 min.                                                 6$ t   20 min.
7$ t ~ 20. 7                                                         t = 25 min.
S$  t = 98. 8 min.
20D                                                                       200 0       l     2   3     4   5     6     7     8                       0       l   2     3     4   5     6     7   8 Distance from inner surface (in)                                           Distance from inner surface (in)
Level   CI  250 F /  7.5-min.'lowdown                                            Level C:  NMP-2 Blowdown Figure 4-3 Pressure Vessel Thermal Gradients for Level C Transients


34 70 60 50 4p g 30 o 20 a lp 0 0 D-10-20 L+2: 3r t 4: t 5: t 6r t 7: t 0 2 min.4 min.6 min.7.5 min.9.15 min.14.1 min.ZO.7 min.2 3 60 50 40 ro 3p 20 10 0-10 0: t-0 1r t 2 min.2: t~4min.3r t~6min.4r t 7.5 min.5r t~9.15 min.6: t 14.1 mfn.7r't 20.7 mfn.0 1--~2 3-30 0 1 2 3 4 5 6-7 8 Distance from inner sur face (in)Lovel C: 250 F/7.5 min.Blowdown 2D 0 1 2 3 4 5 6 7 8 Distance fr om inner surface (in)Level C: 250 F/?.5 min.Blowdown Figure 4-6 Axial and Circumferential Stress Distributions for Level C 250'F/7.5 Min.Blowdown
pc
                                                                                                                        '2 600                                                                    540 520 II34/S g
                                                                    , 500            //
                                                                                /////
500
        /
1(
2/'
480 460 I///
                                                                              //I
                                                                              /II I
                                                                                          / ~7Y
                                                                                          ~
8 g~
      /      / y6t'          1s  t   6D sec.                          440      I / /            y      1s t ~1Ssec.
I /        yw t                                           I I /                    2s t ~ 20 sec.
400
                  /          2s      120 sec.                         420 I I/ /
II I/  /
3s  t  18D sec.                   a    400    I 3s 4s t
t 40 sec.
60 sec.
I Iy                      t I I/
4s      240 sec.                         380            /                Ss t    1DD sec.
300
      /I/ I                  Ss  t   30D sec.                         360          /                  6s t   20D sec.
r/                        t                                               /                    7s t   30D sec.
6s      400 sec.
340    I                        8s t   SDD sec.
7s  t   SDD sec.
320
                                                                            /                          gs t   700 sec.
200                                                                    300 0     l    2   3   4    5    6    7    8                        0       l    2     3     4 5   6     7     8 Distance from inner sur face (in)                                     Distance from inner surfoca (in)
Level Ds Steam Line Br eok                                        Level Ds Recirculation Line Br eok Figure 4-4 Pressure Vessel Thermal Gradients for Level D Transients


" 35 40 30 Ds t 0 t 1.65 min.2s t=3.3 min.3s t 6.65 min.4s t=1D min.5s t-" 15 min.6s t~2D min.40 30 Ds t-0 1s t I.65 min.2s t~9.9 min.9s t=6.65 min.4s t=10 min.5s t=15 min.20 vl 10 0 0 7s t 8s=25 min." 98.8 min.20 10 6s t=20 min.7s t~25 min.8s t=98.8 min.-10 3 0 20 0 1 2 3 4 5 6 7 8 Distance from inner svr face (in)Level Cs NMP-2 Blowdown 10 0 1 2 3 4 5 6 7 8 Distance from inner svr face (in)Level Cs NMP-2 Blowdown Figure 4-7 Axial and Circumferential Stress Distributions for Level C NMP-2 Blowdown
c 33 600 1~    ~
r r r 500
              /
                  / 5/                        t
~.
                /
                  /    r'/    .
1s 2    t 15 sec.
30 sec.
0 L
400
            //                          3c    t  BD  sec.
a
          // /                          4c    t  140 sec.
I/ //i E
                /p 300
(
            /                          G:    t  320 sec.
          //                            7s    t  440 sec.
Bs    t  5GD  sec.
gs    t  GBD  sec.
200 0        l    2    3      4    5      6    7      8 Distance from inner sUrface (in)
Level    Ds   Recirculation Line    Br  eak NHP-l    DBA Figure 4-5 Pressure Vessel Thermal Gradients      for Level D Transients
 
34 70 0
60 0:  t-0 2 min.                                                                t 60                                                                                            1r      2 min.
2:    4 min.                                      50 3r t  6 min.                                                            2:  t ~4min.
50 4: t  7.5 min.
40                    3r  t ~6min.
5: t   9. 15 min.
4p 6r t   14.1 min.
4r  t   7. 5 min.
7: t   ZO. 7 min.                             ro 3p                    5r  t ~ 9. 15 min.
g  30 6:  t    14.1 mfn.
o  20                                                                      20                    7r 't   20. 7 mfn.
a 0
0 lp L+                                                            10 0
D                                                                                                                      1 2
  -10                                              3 0
                                                                                                                        ~ 2 3
                                                                          -10
  -20
  -30                                                                      2D 0    1    2    3      4    5    6    - 7    8                        0    1      2    3      4    5      6  7      8 Distance from inner sur face (in)                                      Distance fr om inner surface (in)
Lovel C:  250 F  / 7.5 min. Blowdown                                    Level  C:  250 F  /  ?.5 min. Blowdown Figure 4-6 Axial and Circumferential Stress Distributions for Level C 250'F/7.5 Min. Blowdown
 
                                                                                                                    "
35 Ds  t    0                                        40 Ds t-0 t    1. 65 min.
1s t     I. 65 min.
40 2s  t  = 3.3 min.
2s t ~ 9.9 min.
3s  t    6. 65 min.
30                  9s t = 6. 65 min.
4s t = 1D min.
4s t  = 10 min.
30                5s t -" 15 min.
5s  t = 15 min.
6s t  ~ 2D min.
6s  t  = 20 min.
20 7s t = 25 min.                                   20 7s t   ~ 25 min.
8s   "  98. 8 min.
t   = 98. 8 min.
8s vl  10 10 0
0 0
  -10                                         3 20                                                                    10 0 1    2    3      4      5    6  7      8                        0   1     2     3     4     5     6 7   8 Distance from inner svr face (in)                                       Distance from inner svr face (in)
Level  Cs  NMP-2 Blowdown                                              Level Cs   NMP-2 Blowdown Figure 4-7 Axial and Circumferential Stress Distributions for Level C NMP-2 Blowdown
 
BD                                                                  70 OL  t    D                                                            D:  t=O 70                  1s  t  = 60 sec.
60 1~  t    60 sec.
60 2:  t  = 1ZD sec.                                                    2~    t  120 sec.
3:  t    1BO sec.                            50                    9:  t    1BO sec.
50                  4:  t    240 sec.                                                    4s  t    240 sec.
40                  5:  t  = 3DO  sec.                            40                    5s  t  3DD  sec.
6:  t    400 sec.                                                    6:  t    400 sec.
e    30 e  30 7:  t-  500 sec.                                                    7s  t  500 sec.
20                                                                  20 o
ao  10 x    10 2
  -10                                        3
  -20 w- -5                              -10 30                                                                  20 0 1     2   3     4     5     6   7    8                        0    1    2    3      4    5    6  7 8 Distance from .inner surface (in)                                      Distance from inner surface (in)
Level D: Steam    Line Break                                          Level D: Steam    Line Break Figure 4-8 Axial and Circumferential Stress Distributions for Level D Steam Line Break


BD 70 60 50 40 e 30 20 ao 10 OL t D 1s t=60 sec.2: t=1ZD sec.3: t 1BO sec.4: t 240 sec.5: t=3DO sec.6: t 400 sec.7: t-500 sec.70 60 50 40 e 30 20 o x 10 D: t=O 1~t 60 sec.2~t 120 sec.9: t 1BO sec.4s t 240 sec.5s t 3DD sec.6: t 400 sec.7s t 500 sec.-10-20 2 3 w----5-10 30 0 1 2 3 4 5 6 7 8 Distance from.inner surface (in)Level D: Steam Line Break 20 0 1 2 3 4 5 6 7 8 Distance from inner surface (in)Level D: Steam Line Break Figure 4-8 Axial and Circumferential Stress Distributions for Level D Steam Line Break
/>>
/>>
70 60 50 40 30 u)20 10 Qo t aD i: t i5 sec.2: t ZD sec.9: t 4D sec.4s t 6D sec.5: t-i00 sec.6s t 200 sec.7s t~300 sec.B: t 5DO sec.gs t 700 sec.70 60 50 40 e 30 20 0 x 10 i l 0: t-0 is t i5 sec.2: t 2D sec.9: t 40 sec.60 sec.5: t i00 sec.6: t 2DO sec.7: t=900 sec.B: t 5DO sec.gc t 700 sec.-10 5--6 7-10-20 0 1 2 3 4 5 6 7 8 Distonca from inner surface (in)Level D: Recirculation Line Breah 20 0 1 2 3 4 5 6 7 8 Distance from inner surface (in)Level D~Recirculation Line Break Figure 4-9 Axial and Circumferential Stress Distributions for Level D Recirculation Line Break for NMP-2  
70                         Qo t aD                                   70                              0: t-0 i: t i5 sec.                                                               is t    i5 sec.
60                          2: t   ZD sec.                           60 i                        2: t    2D sec.
9: t   4D sec.                               l                          9: t    40 sec.
50                                                                    50 4s t   6D sec.                                                                   60 sec.
5: t - i00 sec.                                                           5: t    i00 sec.
40                                                                    40 6s t   200 sec.                                                           6: t    2DO sec.
30 7s t ~ 300 sec.
e  30 7:  t = 900 sec.
B: t   5DO sec.                                                           B: t    5DO sec.
u)  20                          gs t   700 sec.                           20                             gc t    700 sec.
0 10                                                                x   10 5
  -10                                      6                          -10 7
  -20                                                                    20 0    1    2    3    4    5    6      7    8                      0       1    2    3    4    5    6      7 8 Distonca from inner surface (in)                                          Distance from inner surface (in)
Level D:   Recirculation Line Breah                                        Level D~  Recirculation Line Break Figure 4-9 Axial and Circumferential Stress Distributions for Level D Recirculation Line Break for NMP-2
 
                                                                                                                          "
38 70                          Os  t    0                                  60                          Os t     0 ls  t    15 sec.                                                        1: t    15 sec.
60                          Zs  t   30 sec.                                                       2: t     90 sec.
9s  t ~ 80  sec.                                                       9: t     80 sec.
50 4s  t    140 sec.
40 4: t    140 sec.
40 200 sec.                                                       Ss t     200 sec.
Gs        320 sec.                       w                              6: t     920 sec.
30 30                          7:       440 sec.                                                      7s t     440 sec.
8: t    560 sec>>                      8 8                              8s t     560 sec.
20                          9s    -  680 sec.                           20                          9: t     680 sec.
U) o  10 0                                                                          10 0
0 9
4  .                                                                  9
  -10                                               5                                                                     4
  -20                                ~=z.          6
: e. a
                                                                          -10 5
6z
                                                                                                                    <<=7. 8, 9 30                                                                      20 0     1     2   3     4     5       6     7     8                     0     1     2   3   4   5       6     7   8 Distance from inner surface (in)                                         Distance from inner surfoce (in)
Level Dc  Recirculotion Line Break      NHP-1 DBA                      Level D~   Recirculation Line Br eak NHP-1 DBh Figure 4-10 Axial and Circumferential Stress Distributions for Level D Recirculation Line Break for NMP-1 DBA
 
gC 39
            ~        ~
5.0
~    Elastic-Plastic Fracture Mechanics Assessment The limiting Level C and D transient loads were applied to a fracture mechanics model of the NMP-1 pressure vessel in accordance with the guidance provided in References [ASME92] and
[WGFE92]. The USE' (3.0) code package [USE93] was used to perform the calculations. A copy of the draft Appendix X [ASME92] is provided in Appendix A and the ASME Working Group on Flaw Evaluation draft stress intensity calculation procedure [WGFE92] is given in Appendix B.
5.1      Model Description 5.1.1    Vessel Geometry The A302B material model used in the analysis was described in Section 2.0. In addition to the material model, USE' (3.0) requires the following parameters:
Vessel Wall Thickness                                  7.281 in. (UFSAR Table V-1)
Vessel Inner Radius                                    106.344 in. (UFSAR Table V-1)
Vessel Clad Thickness                                0.15625 in.
Crack Depth/Length Ratio                                0.166667 5.12      Applied Loads The results of the finite element calculations to determine the limiting Level C and D transients and loadings are described in Section 4.0. As a result of these calculations, the limiting Level C transient is the "NMP-1 Design Basis 250'F/7.5 min. Blowdown", and the limiting Level D transient is the "Steam Line Break".
The limiting stress distribution was determined by examining the radial stress profiles at various times in the transient. As mentioned in Section 4.0, using stress distribution data at a time when the stresses are most severe for a one-inch crack may be slightly non-conservative when shorter cracks are considered. This small non-conservatism was ciicumvented by using an upper bound envelope of the actual stress distributions.
The limiting stress distributions were fit to a cubic polynomial using the guidance given in [WGFE92]. In order to provide good fits to the data, the base metal stresses were extrapolated to the ID surface.          The remaining discontinuous component of the clad stresses are treated using a line load formulation as described in Section 5.1.4. The equivalent clad line loads are given in Table 5-1.
The pressure acting along the crack surface was conservatively included in the clad line load. The fit to the base metal stress distribution is shown in Figures 5-1
 
gC
'1
 
40 through 5-4. Table 5-2 summarizes the stress distribution coefficients for use in the Appendix X analysis. The R-squared value for all of the fits is very close to unity which indicates accurate representation of the data.
5.19    Limits for Small Scale Yielding Analysis As stated in Reference [ASME92], when the conditions fall in the category of elastic fracture mechanics with small-scale yielding, the J-integral may be calculated using crack-tip stress intensity formulae with plastic-zone correction.
In order to estimate the limits of validity of the small-scale yielding assumption, an axially cracked cylindrical vessel with a radius to thickness ratio of 10, a wall thickness t=10 inand a crack depth to thickness ratio a/t&.25, was loaded by internal pressure and the resulting stress intensities were calculated, The effective crack depths were calculated using:
where, a e =:a P  + 1 6m
(
K aya
                                                )
2 a, = effective crack 'size (in.)
a = physical crack depth (in.)
K = linear elastic stress intensity (ksi4in) a~ = yield stress (ksi) .
Two Ramberg-Osgood stress-strain models were analyzed: one with n=8.4 and alpha=2,6; the second with ri=5.3 and alpha=7.2. The higher n-value case is more representative of the NMP-1 plates.          The elastic calculations approximated pressure stresses by a linear distribution that matched the exact thick walled cylinder solution at the inner and outer surfaces. The plastic solution was
'calculated using the exact internal pressure induced stresses.
The results are summarized in Figure 5-5. The difference in solutions for small loads is due to the use of different elastic solution F factors in the two models.
Based on this analysis, it is concluded that the small-scale yielding formulation is valid for stress intensity levels up to 100 ksi4in (J-335 in-lbfin ) for an axial crack in a cylinder with an aspect ratio of 10. Since the calculated stress intensities for NMP-1 are well below 100 ksi4in., the small scale yielding analysis is appropriate for the NMP-1 vessel analysis.
5.1.4    Fracture Mechanics Model The Reference PVGFE92] method for calculating stress intensities for surface flaws was used. A copy of the procedure proposed by the ASME Working Group on Flaw Evaluation is given in Appendix B. The procedure requires accurately fitting the stress distribution using the following polynomial fit:
 
>r 41 a = A, + A,X'+ APE +                                                          (5-1)
A,X'here, A, = regression constants X = distance through the wall The postulated flaw is a semi-elliptical surface crack with a surface length which is six times the depth. The stress intensity for the continuous component of the stresses was calculated from the following expression:
Kz            = [A G          + A~G~a + A~G~a + A3G3a']  ~ira7g      (5-2) where, a  = crack depth A, = coefficients from Eq. 3-1 which represent the stress
(
distribution over the crack (0( X a)
G, = influence coefficients as a function of flaw aspect ratio and crack penetration (Appendix B)
Q = flaw shape parameter Q=    1 + 4.593 (a/1)'        qy 1  = flaw surface length q= plastic    zone correction factor q= 0.212 (A Ja,)',
        = material yield stress Since the slope of the stress distribution at the clad-base metal interface changes abruptly, the base metal stress distribution was extrapolated to the ID surface to provide an accurate flit over the postulated flaw depths. The Reference [TA73]
linear elastic formulation was used to calculate the discontinuous component of the stress fields contribution to the crack tip stress intensity using:
 
/p 42 K  res~              2P P
                          ~ma
            '
where,
                      ~ 52 (1-c/a)      4 35-5. 28c/a
                                            ~
(1-a/b)                (1-a/b) 3 0 3 (c/a) i.s +
~
  +(  1 '
(1- (c/a)  ')"        0.83-1.76c/a) (1-(1-c/a) a/b)
P = equivalent line load a =  flaw depth b = wall thickness c = load application position as measured from the ID surface Equation 5-3 provides conservative estimates of the discontinuous stress component contribution of the total stress intensity since the formulation is for an infinite crack length, Since Eq, (3-3) is a linear elastic equation, the small scale yielding correction was applied:
where, a = physical crack depth a, = effective crack depth In order to simplify the computer algorithm and to ensure conservative results, the small scale yielding correction was applied to both the cladding and base metal stress intensity factors. This approach yields very conservative results since the flaw shape parameter in equation 5-2 includes a plastic zone correction factor.
The total stress intensity factor was obtained by superposition:
KcoHTLNPN/s + KDLscoNTLNUoUs Z              Z
 
rc 43 In accordance with Reference [ASME92], a spectrum of initial flaws, up to 1/10 of the base metal wall thickness, were assumed. The smallest flaw assumed was 0.05 in., and the postulated flaws were increased in size by increments of 0.05 in.,
up to a maximum flaw depth of 0.75 in.
5.2      Calculations for A302B Material Model The pointwise input model was used for the A302B material model calculations. Using this model, the J-R curve is assumed flat after the initial 0.1 in. of crack extension. The G-8-1 plate was analyzed using the A302B material. model since it is the limiting plate from a ductile fracture perspective (Reference [MA93]).
5.2.1    Level C Loading The results of the calculations for the Level C loading have shown that the limiting flaw orientation is the axial flaw. For initial base metal flaw depths of up to 1/10 of the vessel wall thickness, the ASME Appendix X criteria are satisfied at USE levels as low as 10 ft-lbs. In all cases, the largest applied-J values for the flaw growth of 0.1 in. criterion are obtained at the deepest initial postulated flaw depth. The results for the Level C analysis are summarized in Table 5-3 for the axial flaw.
5.22    Level D Loading Analysis The results of the calculations for the Level D loading also show that the limiting flaw orientation is the axial flaw. For initial base metal flaw depths of up to 1/10 of the vessel wall thickness, the ASME Appendix X criteria are satisfied at USE
      'levels as low as 20 ft-lbs. The results for the Level D analysis are summarized in Table 5-4 for the axial flaw.
5.2.3    Tensile Instability Analysis Based on the analysis performed, the deepest flaw during the most severe Level C or D transient is less than 1.2 inches. Conservatively assuming the flaw extends completely around the circumference, and using the finite element stress profiles, the remaining ligament will experience stresses well below the yield strength and is therefore safe in terms of tensile instability.
 
Table 5-1 NMP-1 Clad Stresses Extrapolated      Clad Stress Minus                      Clad            Crack      Clad Surface          Extrapolated              Residual      Total          Surface    Equivalent Case      Stress            Surface                  Stress        Stress          Pressure  Line Stress (ksi)            Stress (ksi)              (ksi)        (ksi)          (ksi)      (kp/in)
Hoop-Level C          45.207              16.557              20.6        37.157            1.05        6.856 Axial-Level C          35.264              16.790              20.0        36.790            1.05        6.798 Hoop-Level D          58.690              19.886              20.6        40.486            1.05        7.376 Axial-Level D          45.476              21.377              20.0        41.377            1.05        7.515 Table 5-2 Base Metal Stress Distribution Coefficients Ao                        A,                                                A, Level C-- Hoop                45.165                    -22.335                    2.571                  0.228 Level C - Axial              35.294                    -25.420                    9.941                -2.183 Level D - Hoop                58.791                    -33.934                    7.967                -1.052 Level D - Axial              45.651                    -33.636                    12.136                -2.263
 
pC r"c C
 
                                                                                                      'able 5-3 Orientation'5 Comparison of Applied Loads with ASME Criteria for Level C Loading Conditions and an Axial Flaw ha&.l Criterion                      Flaw Stabili  Criterion USE        Applied J            Material J            Applied      Material          Criteria Level      ~in-1b                ~in-1b ini                T              T            Satisfied in'83 10                                      199                            2.6            yes 20                ,183                  230              <0.5          3.7            yes 30                183                  261              <0.5          7.3            yes 40                183                292              <0.5          13.2            yes 50                183                  323              <0.5        18.3            yes 60                183                353                                            yes, J, cJ<<
70                183                384                                            yes, J, <J<<
80                183                438                                            yes, J  <Jic 90                183                517                                            yes, J, <J,c 100                183                                                                yes, J, <J,c
'esults shown are for the most limiting initial flaw over the spectrum of flaws analyzed
 
USE Level 10
                            ~AIied T Jape JMAx Material T 5-4 Comparison of Applied Loads with ASME Criteria for Level D Loading Conditions and an Axial Flaw Orientation Flaw Stabilit Criterion Satisfied no Criteria
                                                                                              '6'able 20                      <0.8                  11.0              yes 30                      <0.8                  18.3              yes 40                                                                yes, J,~<Junc 50                                                                yes, J~<Jic 60                                                                yes'app~rc 70                                                                yes'app~tc 80                                                                yes, Jo~<Jrc 90                                                                yes J    <Jrc 100                                                                yes, J, <Jrc
'esults  shown are for the most limiting initial flaw over the spectrum of flaws  analyzed.
 
,
  ~


" 38 70 60 50 40 30 20 o 10 0 0 0-10-20 30 Os t 0 ls t 15 sec.Zs t 9s t 30 sec.~80 sec.4s t Gs 7: 8: t 9s 140 200 320 440 560-680 sec.sec.sec.sec.sec>>sec.9 4.-5 6~=z.e.a 0 1 2 3 4 5 6 7 8 60 40 w 30 8 8 20 U)10-10 20 Os t 0 1: t 15 sec.2: t 90 sec.9: t 80 sec.4: t 140 sec.Ss t 200 sec.6: t 920 sec.7s t 440 sec.8s t 560 sec.9: t 680 sec.9 4 5 6z<<=7.8, 9 0 1 2 3 4 5 6 7 8 Distance from inner surface (in)Level Dc Recirculotion Line Break NHP-1 DBA Distance from inner surfoce (in)Level D~Recirculation Line Br eak NHP-1 DBh Figure 4-10 Axial and Circumferential Stress Distributions for Level D Recirculation Line Break for NMP-1 DBA gC 39~~~5.0 Elastic-Plastic Fracture Mechanics Assessment The limiting Level C and D transient loads were applied to a fracture mechanics model of the NMP-1 pressure vessel in accordance with the guidance provided in References
47 HOOP STRESS DISTRIBUTION FOR LEVEL C TRANSIENT 100 80 co    60 CO U)
[ASME92]and[WGFE92].The USE&#x17d;(3.0)code package[USE93]was used to perform the calculations.
LU 40 CO 20 0.0         0.6           1.0         1.5       2.0 CRACK LENGTH        (In.)
A copy of the draft Appendix X[ASME92]is provided in Appendix A and the ASME Working Group on Flaw Evaluation draft stress intensity calculation procedure[WGFE92]is given in Appendix B.5.1 Model Description 5.1.1 Vessel Geometry The A302B material model used in the analysis was described in Section 2.0.In addition to the material model, USE&#x17d;(3.0)requires the following parameters:
Figure 5-1 Peak Circumferential Base Metal Stress Distribution for NMP-1 Design Basis 250'F/7.5 Min. Blowdown Transient
Vessel Wall Thickness Vessel Inner Radius Vessel Clad Thickness Crack Depth/Length Ratio 5.12 Applied Loads 7.281 in.(UFSAR Table V-1)106.344 in.(UFSAR Table V-1)0.15625 in.0.166667 The results of the finite element calculations to determine the limiting Level C and D transients and loadings are described in Section 4.0.As a result of these calculations, the limiting Level C transient is the"NMP-1 Design Basis 250'F/7.5 min.Blowdown", and the limiting Level D transient is the"Steam Line Break".The limiting stress distribution was determined by examining the radial stress profiles at various times in the transient.
As mentioned in Section 4.0, using stress distribution data at a time when the stresses are most severe for a one-inch crack may be slightly non-conservative when shorter cracks are considered.
This small non-conservatism was ciicumvented by using an upper bound envelope of the actual stress distributions.
The limiting stress distributions were fit to a cubic polynomial using the guidance given in[WGFE92].In order to provide good fits to the data, the base metal stresses were extrapolated to the ID surface.The remaining discontinuous component of the clad stresses are treated using a line load formulation as described in Section 5.1.4.The equivalent clad line loads are given in Table 5-1.The pressure acting along the crack surface was conservatively included in the clad line load.The fit to the base metal stress distribution is shown in Figures 5-1 gC'1 40 through 5-4.Table 5-2 summarizes the stress distribution coefficients for use in the Appendix X analysis.The R-squared value for all of the fits is very close to unity which indicates accurate representation of the data.5.19 Limits for Small Scale Yielding Analysis a=:a+-(-)1 K 2 e P 6m aya where, a,=effective crack'size (in.)a=physical crack depth (in.)K=linear elastic stress intensity (ksi4in)a~=yield stress (ksi).As stated in Reference[ASME92], when the conditions fall in the category of elastic fracture mechanics with small-scale yielding, the J-integral may be calculated using crack-tip stress intensity formulae with plastic-zone correction.
In order to estimate the limits of validity of the small-scale yielding assumption, an axially cracked cylindrical vessel with a radius to thickness ratio of 10, a wall thickness t=10 inand a crack depth to thickness ratio a/t&.25, was loaded by internal pressure and the resulting stress intensities were calculated, The effective crack depths were calculated using: Two Ramberg-Osgood stress-strain models were analyzed: one with n=8.4 and alpha=2,6; the second with ri=5.3 and alpha=7.2.
The higher n-value case is more representative of the NMP-1 plates.The elastic calculations approximated pressure stresses by a linear distribution that matched the exact thick walled cylinder solution at the inner and outer surfaces.The plastic solution was'calculated using the exact internal pressure induced stresses.The results are summarized in Figure 5-5.The difference in solutions for small loads is due to the use of different elastic solution F factors in the two models.Based on this analysis, it is concluded that the small-scale yielding formulation is valid for stress intensity levels up to 100 ksi4in (J-335 in-lbfin)for an axial crack in a cylinder with an aspect ratio of 10.Since the calculated stress intensities for NMP-1 are well below 100 ksi4in., the small scale yielding analysis is appropriate for the NMP-1 vessel analysis.5.1.4 Fracture Mechanics Model The Reference PVGFE92]method for calculating stress intensities for surface flaws was used.A copy of the procedure proposed by the ASME Working Group on Flaw Evaluation is given in Appendix B.The procedure requires accurately fitting the stress distribution using the following polynomial fit:
>r 41 a=A,+A,X'+APE+A,X'here, (5-1)A,=regression constants X=distance through the wall The postulated flaw is a semi-elliptical surface crack with a surface length which is six times the depth.The stress intensity for the continuous component of the stresses was calculated from the following expression:
Kz=[A G+A~G~a+A~G~a+A3G3a']~ira7g (5-2)where, a=crack depth A,=coefficients from Eq.3-1 which represent the stress distribution over the crack (0(X (a)G,=influence coefficients as a function of flaw aspect ratio and crack penetration (Appendix B)Q=flaw shape parameter Q=1+4.593 (a/1)'qy 1=flaw surface length q=plastic zone correction factor q=0.212 (A Ja,)',=material yield stress Since the slope of the stress distribution at the clad-base metal interface changes abruptly, the base metal stress distribution was extrapolated to the ID surface to provide an accurate flit over the postulated flaw depths.The Reference[TA73]linear elastic formulation was used to calculate the discontinuous component of the stress fields contribution to the crack tip stress intensity using:
/p 42 K res~2P P~ma where,'~52 (1-c/a)4~35-5.28c/a (1-a/b)(1-a/b)1 3 0 3 (c/a)i.s~+('+0.83-1.76c/a)
(1-(1-c/a) a/b)(1-(c/a)')" P=equivalent line load a=flaw depth b=wall thickness c=load application position as measured from the ID surface Equation 5-3 provides conservative estimates of the discontinuous stress component contribution of the total stress intensity since the formulation is for an infinite crack length, Since Eq, (3-3)is a linear elastic equation, the small scale yielding correction was applied: where, a=physical crack depth a,=effective crack depth In order to simplify the computer algorithm and to ensure conservative results, the small scale yielding correction was applied to both the cladding and base metal stress intensity factors.This approach yields very conservative results since the flaw shape parameter in equation 5-2 includes a plastic zone correction factor.The total stress intensity factor was obtained by superposition:
KcoHTLNPN/s
+KDLscoNTLNUoUs Z Z rc 43 In accordance with Reference[ASME92], a spectrum of initial flaws, up to 1/10 of the base metal wall thickness, were assumed.The smallest flaw assumed was 0.05 in., and the postulated flaws were increased in size by increments of 0.05 in., up to a maximum flaw depth of 0.75 in.5.2 Calculations for A302B Material Model The pointwise input model was used for the A302B material model calculations.
Using this model, the J-R curve is assumed flat after the initial 0.1 in.of crack extension.
The G-8-1 plate was analyzed using the A302B material.model since it is the limiting plate from a ductile fracture perspective (Reference
[MA93]).5.2.1 Level C Loading The results of the calculations for the Level C loading have shown that the limiting flaw orientation is the axial flaw.For initial base metal flaw depths of up to 1/10 of the vessel wall thickness, the ASME Appendix X criteria are satisfied at USE levels as low as 10 ft-lbs.In all cases, the largest applied-J values for the flaw growth of 0.1 in.criterion are obtained at the deepest initial postulated flaw depth.The results for the Level C analysis are summarized in Table 5-3 for the axial flaw.5.22 Level D Loading Analysis The results of the calculations for the Level D loading also show that the limiting flaw orientation is the axial flaw.For initial base metal flaw depths of up to 1/10 of the vessel wall thickness, the ASME Appendix X criteria are satisfied at USE'levels as low as 20 ft-lbs.The results for the Level D analysis are summarized in Table 5-4 for the axial flaw.5.2.3 Tensile Instability Analysis Based on the analysis performed, the deepest flaw during the most severe Level C or D transient is less than 1.2 inches.Conservatively assuming the flaw extends completely around the circumference, and using the finite element stress profiles, the remaining ligament will experience stresses well below the yield strength and is therefore safe in terms of tensile instability.


Table 5-1 NMP-1 Clad Stresses Case Hoop-Level C Axial-Level C Hoop-Level D Axial-Level D Extrapolated Surface Stress (ksi)45.207 35.264 58.690 45.476 Clad Stress Minus Extrapolated Surface Stress (ksi)16.557 16.790 19.886 21.377 Residual Stress (ksi)20.6 20.0 20.6 20.0 Clad Total Stress (ksi)37.157 36.790 40.486 41.377 Crack Surface Pressure (ksi)1.05 1.05 1.05 1.05 Clad Equivalent Line Stress (kp/in)6.856 6.798 7.376 7.515 Table 5-2 Base Metal Stress Distribution Coefficients Level C--Hoop Level C-Axial Level D-Hoop Level D-Axial Ao 45.165 35.294 58.791 45.651 A,-22.335-25.420-33.934-33.636 2.571 9.941 7.967 12.136 A, 0.228-2.183-1.052-2.263 pC r"c C
48 AXIAL STRESS DISTRIBUTION FOR LEVEL C TRANSIENT 100 80 60
'able 5-3 Comparison of Applied Loads with ASME Criteria for Level C Loading Conditions and an Axial Flaw Orientation'5 ha&.l Criterion Flaw Stabili Criterion USE Level 10 20 30 40 50 60 70 80 90 100 Applied J~in-1b in'83 ,183 183 183 183 183 183 183 183 183 Material J~in-1b ini 199 230 261 292 323 353 384 438 517 Applied T<0.5<0.5<0.5<0.5 Material T 2.6 3.7 7.3 13.2 18.3 Criteria Satisfied yes yes yes yes yes yes, J, cJ<<yes, J,<J<<yes, J<Jic yes, J,<J,c yes, J,<J,c'esults shown are for the most limiting initial flaw over the spectrum of flaws analyzed
      'CO CO UJ 40 CO 20 0
0.0         0.5                                2.0 CRACK LENGTH        (In.)
Figure 5-2 Peak Axial Base Metal Stress Distribution for NMP-1 Design Basis 250'F/7.5 Min. Blowdown Transient


'able 5-4 Comparison of Applied Loads with ASME Criteria for Level D Loading Conditions and an Axial Flaw Orientation
49 HOOP STRESS DISTRIBUTION FOR LEVEL D TRANSIENT 100 80 60 40 20 0
'6 USE Level 10~AIied T Jape JMAx Material T Flaw Stabilit Criterion Criteria Satisfied no 20<0.8 11.0 yes 30<0.8 18.3 yes 40 50 60 70 80 90 100 yes, J,~<Junc yes, J~<Jic yes'app~rc yes'app~tc yes, Jo~<Jrc yes J<Jrc yes, J,<Jrc'esults shown are for the most limiting initial flaw over the spectrum of flaws analyzed.
0.0         0.5                                  2.0
,~
                            <3RACK LENGTH (In.)
47 HOOP STRESS DISTRIBUTION FOR LEVEL C TRANSIENT 100 80 co 60 CO U)LU 40 CO 20 0.0 0.6 1.0 1.5 CRACK LENGTH (In.)2.0 Figure 5-1 Peak Circumferential Base Metal Stress Distribution for NMP-1 Design Basis 250'F/7.5 Min.Blowdown Transient  
Figure 5-3 Peak Circumferential Base Metal Stress Distribution for Steam Line Break Transient


48 AXIAL STRESS DISTRIBUTION FOR LEVEL C TRANSIENT 100 80 60'CO CO UJ 40 CO 20 0 0.0 0.5 CRACK LENGTH (In.)2.0 Figure 5-2 Peak Axial Base Metal Stress Distribution for NMP-1 Design Basis 250'F/7.5 Min.Blowdown Transient
gC 50 O'XIAL STRESS DIST RI BUT ION FOR LEVEL D TRAN IENT 100 80 60 CO 03 LLI 40 K
20 0
0.0         0.5           1.0          1.5 2.0 CRACK LEN9TH (ln.)
Figure 5-4 Peak Axial Base Metal Stress Distribution for Steam Line Break Transient
 
In Small Scale Yield Limits Study Axially Cracked Cylinder {R/t = 10) 4.5 3.5 3
.~ 2.5 2
0.5 0
0    0.5                  1.6      -
2        2.5                    3.5 Pressure (ksi)
            ~      J(BSY/ae)      ~    Jep(n=5.3)      ~    Jep(n=8.4)
Figure 5-5 Comparison Between Small Scale Yielding Solution (J(SSY/ae)) and the Elastic-Plastic Solutions with Hardening Exponents of 5.3 (Jep(n=5.3)) and 8.4 (Jep(n=8.4))


49 HOOP STRESS DISTRIBUTION FOR LEVEL D TRANSIENT 100 80 60 40 20 0 0.0 0.5<3RACK LENGTH (In.)2.0 Figure 5-3Peak Circumferential Base Metal Stress Distribution for Steam Line Break Transient gC 50 O'XIAL STRESS DIST RI BUT ION FOR LEVEL D TRAN IENT 100 80 60 CO 03 LLI 40 K 20 0 0.0 0.5 1.0 1.5 2.0 CRACK LEN9TH (ln.)Figure 5-4 Peak Axial Base Metal Stress Distribution for Steam Line Break Transient In Small Scale Yield Limits Study Axially Cracked Cylinder{R/t=10)4.5 3.5 3.~2.5 2 0.5 0 0 0.5 1.6-2 2.5 Pressure (ksi)3.5~J(BSY/ae)~Jep(n=5.3)
~Jep(n=8.4)
Figure 5-5 Comparison Between Small Scale Yielding Solution (J(SSY/ae))
and the Elastic-Plastic Solutions with Hardening Exponents of 5.3 (Jep(n=5.3))
and 8.4 (Jep(n=8.4))
/'
/'
6.0 Summary and Conclusions 52 The results of the elastic-plastic fracture mechanics assessment are shown in Table 6-1.As discussed in Reference tMA93], the A302B material model best represents the NMP-1 beltline plates.The A302B material model, applied to the case of an axial flaw orientation, yields the most conservative results.Based on the calculations reported in Reference PvIA93]and herein, it has been concluded that the NMP-1 plate G-8-1 is limiting from a ductile fracture perspective, and the USE must be maintained above 23 ft-lbs.Based on the data reported in Reference[MA93], none of the NMP-1 beltline plates are expected to fall below the 23 ft-lb level.Although the Appendix X criteria are satisfied at or above the 23 ft-lb level, it is not clear that the plant should be operated at this ductility level.It is anticipated that future federally funded research and subsequent regulations will address this issue.
52 6.0     Summary and Conclusions The results of the elastic-plastic fracture mechanics assessment are shown in Table 6-1. As discussed in Reference tMA93], the A302B material model best represents the NMP-1 beltline plates. The A302B material model, applied to the case of an axial flaw orientation, yields the most conservative results. Based on the calculations reported in Reference PvIA93] and herein, it has been concluded that the NMP-1 plate G-8-1 is limiting from a ductile fracture perspective, and the USE must be maintained above 23 ft-lbs. Based on the data reported in Reference
fi~
[MA93], none of the NMP-1 beltline plates are expected to fall below the 23 ft-lb level.
53 Table 6-1 Minimum Upper Shelf Energy Level for NMP-1 Plates Based on the ASME Draft Appendix X Evaluation Criteria for Service Levels A, B, C and D Minimum USE (Ft-Lbs)Plate ASME Service Level A&B Material Model Flaw Growth of 0.1 in.Criterion Ji (Jo.i Flaw Stability Criterion G-8-1 A&B A302B 13 23 G-307-4 A&B A302B 13 23 G-8-1 G-8-1 D A302B A302B 10 10 20
Although the Appendix X criteria are satisfied at or above the 23 ft-lb level, it is not clear that the plant should be operated at this ductility level. It is anticipated that future federally funded research and subsequent regulations will address this issue.
 
fi
~
 
53 Table 6-1 Minimum Upper Shelf Energy Level for NMP-1 Plates Based on the ASME Draft Appendix X Evaluation Criteria for Service Levels A, B, C and D Minimum USE (Ft-Lbs)
ASME Service   Material Plate  Level     Model         Flaw Growth of 0.1       Flaw Stability A&B                    in. Criterion               Criterion
(
Ji Jo.i G-8-1   A&B       A302B                 13                   23 G-307-4 A&B       A302B                 13                   23 G-8-1             A302B                  10                  10 G-8-1     D       A302B                                       20
 
54 7.0  References
[ASME92]    ASME Draft Code Case N-XXX, "Assessment of Reactor Vessels with Low Upper Shelf Charpy Energy Levels", Revision 11; May 27, 1992.
[CENC]      Unit 1 Analytical Report for Niagara Mohawk Reactor Vessel, Report No. CENC 1142, ACC No. 002301187, Appendix B Thermal Analysis.
[FSAR]      Updated FSAR Volume IV, Section I, Page I-11.
[HI89], 'iser,      A.L., Terrell, J.B., "Size Effects on J-R Curves for A302B Plate",
NUREG/CR-5265, January, 1989.
[MA92]        Manahan, M.P., Soong, Y., "Response to NRC General Letter 92-01 for Nine Mile Point Unit 1", NMPC Project 03-9425, June 12, 1992.
[MA93]        Manahan, M.P., Final Report to NRC, "Elastic-Plastic Fracture Mechanics Assessment of Nine Mile Point Unit 1 Beltline Plates for Service Level A and B Loadings", February 19, 1993.
[NEDC]        NEDC-31446P, NMP-1 SAFER/CORECOOL/GESTR-LOCA Loss of Coolant Accident Analysis.
[NMP1DP]      NMP-1 Drywell Pressure Calculation, SO-TORUS-M009, GENE-770-91-34.
[NMP2TC]      NMP-2, 762E673, Reactor Vessel Thermal Cycles.
[STRS]        Section E9, Emergency'& Faulted Analysis of Recirculation Outlet Nozzle 251" BWR Vessel. STRS 16.010-5039A, page E11, 12. Unit 2 Stress Analysis.
[TA73]        Tada, H., Paris, P.C., Irwin, G.R., "The Stress Analysis of Cracks Handbook", Del Research Corp., 1973.
[TCD]        Unit 2 Reactor Vessel Thermal Cycles Diagram 762E673.
[TRUMP)      Manahan, M.P., 'TRUMP/MPM: Thermal Transient Heat Transfer Analysis Code, Version 1.0, September, 1989.
[USE93]      USE' (3.0)Code Package for Elastic-Plastic Fracture Mechanics Assessment of Nuclear Reactor Pressure Vessels, MPM Research & Consulting, 1993.
[WELD3]      "WELD3 Computer Code Verification", MPM Research & Consulting, Calculation No. MPM-NMPC-99205, Rev. 0, January 21, 1993.-


7.0 References 54[ASME92]ASME Draft Code Case N-XXX,"Assessment of Reactor Vessels with Low Upper Shelf Charpy Energy Levels", Revision 11;May 27, 1992.[CENC][FSAR]Unit 1 Analytical Report for Niagara Mohawk Reactor Vessel, Report No.CENC 1142, ACC No.002301187, Appendix B Thermal Analysis.Updated FSAR Volume IV, Section I, Page I-11.[HI89],'iser, A.L., Terrell, J.B.,"Size Effects on J-R Curves for A302B Plate", NUREG/CR-5265, January, 1989.[MA 92][MA 93][NEDC]Manahan, M.P., Soong, Y.,"Response to NRC General Letter 92-01 for Nine Mile Point Unit 1", NMPC Project 03-9425, June 12, 1992.Manahan, M.P., Final Report to NRC,"Elastic-Plastic Fracture Mechanics Assessment of Nine Mile Point Unit 1 Beltline Plates for Service Level A and B Loadings", February 19, 1993.NEDC-31446P, NMP-1 SAFER/CORECOOL/GESTR-LOCA Loss of Coolant Accident Analysis.[NMP1DP]NMP-1 Drywell Pressure Calculation, SO-TORUS-M009, GENE-770-91-34.
[NMP2TC]NMP-2, 762E673, Reactor Vessel Thermal Cycles.[STRS]Section E9, Emergency'&
Faulted Analysis of Recirculation Outlet Nozzle 251" BWR Vessel.STRS 16.010-5039A, page E11, 12.Unit 2 Stress Analysis.[TA73]Tada, H., Paris, P.C., Irwin, G.R.,"The Stress Analysis of Cracks Handbook", Del Research Corp., 1973.[TCD]Unit 2 Reactor Vessel Thermal Cycles Diagram 762E673.[TRUMP)Manahan, M.P.,'TRUMP/MPM:
Thermal Transient Heat Transfer Analysis Code, Version 1.0, September, 1989.[USE93][WELD3]USE&#x17d;(3.0)Code Package for Elastic-Plastic Fracture Mechanics Assessment of Nuclear Reactor Pressure Vessels, MPM Research&Consulting, 1993."WELD3 Computer Code Verification", MPM Research&Consulting, Calculation No.MPM-NMPC-99205, Rev.0, January 21, 1993.-
~<
~<
55[WGFE92]ASME Working Group on Flaw Evaluation, Proposed Changes to Article A-3000 entitled,"Method for K, Determination", August, 1992.  
55
[WGFE92] ASME Working Group on Flaw Evaluation, Proposed Changes to Article A-3000 entitled, "Method for K, Determination", August, 1992.
 
56 Acknowledgement Dr. Randall B. Stonesifer of Computational Mechanics, Inc. performed all of the finite element analyses and provided many valuable suggestions related- to the fracture mechanics model.
 
57 Appendices
 
58 Appendix A
                            'SME Draft Appendix X "Assessment of Reactor Vessels with Low Upper Shelf Charpy Energy Levels"
 
(i DRAFT CODE CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS May 27, 1992 REVISZON 11 DRAFT HISTORY REVISION 0                          AUGUST 25 g 1 987 REVISION 1                          JANUARY 19, 1988
) REVISION 2                          APRIL 19, 1988 REVISION 3                          AUGUST 30, 1988 REVISION 4                          NOVEMBER 30, 1988 REVISION 5                          FEBRUARY 27, 1989 REVISION 6                          JANUARY 5i 1990 REVISION .7                        APRIL 12, 1990 REVISION 8                          JANUARY 10, 1991 REVISION 8  MARKED COPY            APRIL 15, 1991 REVISION 9                          JANUARY 17, 1992 REVISION 10                        APRIL 17'' 1992 REVISION  ll                        CURRENT
 
gC
(-
 
ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS TABLE OF CONTENTS CASE N-XXX  ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS APPENDIX A  ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGYLEVELS A-1000      INTRODUCTION A-1100        Scope A-1200        Procedure Overview A-1300        General Nomenclature A-2000      ACCEPTANCE CRITERIA A-3000      ANALYSIS A-3100        Scope A-3200        Applied J-Integral A-3300        Selection of the J-Integral Resistance Curve A-3400        Flaw  Stability A-3500        Evaluation Approach for Level  A and B  Service Loadings r
A-4000      EVALUATION PROCEDURES    FOR LEVEL A AND B SERVICE LOADINGS A-4100        Scope A-4200        Evaluation Procedure for the Applied J-Integral A-4210        Calculation of the Applied J-Integral A-4220        Evaluation Using Criterion for Flaw Growth of 0.1 in.
A-4300        Evaluation Procedures for Flaw Stability A-4310        J-R Curve  Crack Driving Force Diagram Procedure


56 Acknowledgement Dr.Randall B.Stonesifer of Computational Mechanics, Inc.performed all of the finite element analyses and provided many valuable suggestions related-to the fracture mechanics model.
r l


57 Appendices
A-4320        Failure Assessment Diagram Procedure A-4321        Failure Assessment 'Diagram Curve A-4322        Failure Assessment, Point Coordinates A-4322.1      Axial Flaws A-4322.2      Circumf erential Flaws A-4323        Evaluation Using Criterion for Flaw Stability A-4330        J-Integral/Tearing Modulus Procedure A-4331        J-Integral at Flaw Instability A-4332        Internal Pressure at Flaw Instability A-4333        Evaluation Using Criterion for Flaw Stability A-5000        LEVEL C AND  D SERVICE LOADINGS


58 Appendix A'SME Draft Appendix X"Assessment of Reactor Vessels with Low Upper Shelf Charpy Energy Levels" (i
/i Case N-XXX Assessment   of Reactor Vessels Nith Low Upper Shelf Charpy Energy Levels Section XI, Division 1 Inquiry: Section XI, Division 1, XWB-3730, requires that during reactor operation, load and temperature conditions shall be maintained to 'provide protection against failure due to the presence of postulated flaws in the ferritic portions of the reactor coolant pressure boundary. Under Section XI, Division 1, what procedure may be used to evaluate a reactor vessel with a low upper, shelf Charpy.impact energy level as defined in ASTM E 185-82 to .demonstrate integrity for continued service at upper shelf conditions?
DRAFT CODE CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS May 27, 1992 REVISZON 11 REVISION REVISION)REVISION REVISION REVISION REVISION REVISION REVISION REVISION REVISION REVISION REVISION REVISION DRAFT HISTORY 0 1 2 3 4 5 6.7 8 8-MARKED COPY 9 10 ll AUGUST 25 g 1 987 JANUARY 19, 1988 APRIL 19, 1988 AUGUST 30, 1988 NOVEMBER 30, 1988 FEBRUARY 27, 1989 JANUARY 5i 1990 APRIL 12, 1990 JANUARY 10, 1991 APRIL 15, 1991 JANUARY 17, 1992 APRIL 17''1992 CURRENT gC (-
Rep2y:   It is the opinion.'f the Committee that a reactor vessel with a low upper shelf Charpy impact energy level may be evaluated to demonstrate integrity for continued service for upper
ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS TABLE OF CONTENTS CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS APPENDIX A ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGYLEVELS A-1000 INTRODUCTION A-1100 A-1200 A-1300 Scope Procedure Overview General Nomenclature A-2000 ACCEPTANCE CRITERIA A-3000 ANALYSIS A-3100 A-3200 A-3300 A-3400 A-3500 Scope Applied J-Integral Selection of the J-Integral Resistance Curve Flaw Stability Evaluation Approach for Level A and B Service Loadings A-4000 r EVALUATION PROCEDURES FOR LEVEL A AND B SERVICE LOADINGSA-4100 A-4200 A-4210 A-4220 A-4300 A-4310 Scope Evaluation Procedure for the Applied J-Integral Calculation of the Applied J-Integral Evaluation Using Criterion for Flaw Growth of 0.1 in.Evaluation Procedures for Flaw Stability J-R Curve-Crack Driving Force Diagram Procedure r l A-4320 A-4321 A-4322 A-4322.1 A-4322.2 A-4323 A-4330 A-4331 A-4332 A-4333 Failure Assessment Diagram Procedure Failure Assessment
.shelf conditions in accordance with the following.
'Diagram Curve Failure Assessment, Point Coordinates Axial Flaws Circumf erential Flaws Evaluation Using Criterion for Flaw Stability J-Integral/Tearing Modulus Procedure J-Integral at Flaw Instability Internal Pressure at Flaw Instability Evaluation Using Criterion for Flaw Stability A-5000 LEVEL C AND D SERVICE LOADINGS
1.0   EVALUAT1ON PROCEDURES AND ACCEPTANCE CRITERIA Section XI, Division 1, Appendix G, "Fracture Toughness Criteria for Protection Against Failure", provides analytical procedures based on the principles of linear-elastic fracture mechanics that may be used to define load and temperature conditions to provide protection against nonductile failure due to the presence of postulated flaws in the ferritic portions of the reactor coolant pressure boundary. To prevent ductile failure of a reactor vessel with a low upper shelf Charpy impact energy level the vessel shall be evaluated using the principles 'of elastic-plastic fracture mechanics. Flaws shall be postulated in the reactor vessel at, locations of predicted low upper shelf Charpy impa'ct energy and the applied Z-integral for these flaws shall be calculated and compared with'he     J-integral fracture resistance of the material to determine acceptability. Factors of safety on applied load for limited ductile flaw growth, and on flaw stability due to ductile tearing, shall be satisfied. All specified design'transients for the reactor vessel shall be considered. Evaluation procedures and acceptance criteria based on the principles .of elastic-plastic fracture mechanics are given in Appendix A of this Code Case.
/i Case N-XXX Assessment of Reactor Vessels Nith Low Upper Shelf Charpy Energy Levels Section XI, Division 1 Inquiry: Section XI, Division 1, XWB-3730, requires that during reactor operation, load and temperature conditions shall be maintained to'provide protection against failure due to the presence of postulated flaws in the ferritic portions of the reactor coolant pressure boundary.Under Section XI, Division 1, what procedure may be used to evaluate a reactor vessel with a low upper, shelf Charpy.impact energy level as defined in ASTM E 185-82 to.demonstrate integrity for continued service at upper shelf conditions?
The evaluation shall be the responsibility of the Owner and shall be subject to review by the regulatory and enforcement authorities -having jurisdiction at the plant site.
Rep2y: It is the opinion.'f the Committee that a reactor vessel with a low upper shelf Charpy impact energy level may be evaluated to demonstrate integrity for continued service for upper.shelf conditions in accordance with the following.
1.0 EVALUAT1ON PROCEDURES AND ACCEPTANCE CRITERIA Section XI, Division 1, Appendix G,"Fracture Toughness Criteria for Protection Against Failure", provides analytical procedures based on the principles of linear-elastic fracture mechanics that may be used to define load and temperature conditions to provide protection against nonductile failure due to the presence of postulated flaws in the ferritic portions of the reactor coolant pressure boundary.To prevent ductile failure of a reactor vessel with a low upper shelf Charpy impact energy level the vessel shall be evaluated using the principles
'of elastic-plastic fracture mechanics.
Flaws shall be postulated in the reactor vessel at, locations of predicted low upper shelf Charpy impa'ct energy and the applied Z-integral for these flaws shall be calculated and compared with'he J-integral fracture resistance of the material to determine acceptability.
Factors of safety on applied load for limited ductile flaw growth, and on flaw stability due to ductile tearing, shall be satisfied.
All specified design'transients for the reactor vessel shall be considered.
Evaluation procedures and acceptance criteria based on the principles.of elastic-plastic fracture mechanics are given in Appendix A of this Code Case.The evaluation shall be the responsibility of the Owner and shall be subject to review by the regulatory and enforcement authorities-having jurisdiction at the plant site.
I APPENDIX A TO CODE CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS ARTICLE A-1000 INTRODUCTION A-1100 SCOPE This Appendix provides acceptance criteria and evaluation procedures for determining the acceptability for operation of a reactor vessel when the vessel metal temperature is in the upper shelf range.The methodology is based on the principles of elastic-plastic fracture mechanics.
Flaws are postulated in the reactor vessel at locations of predicted low upper shelf Charpy impact energy and the applied J-integral for these flaws is calculated and compared with th'e J-integral fracture resistance of the material to determine acceptability.
All specified design transients for the reactor vessel shall be considered.
A-1200 PROCEDURE OVERVIEW The following is a summary of the analytical procedure which may be used.(a)Postulate flaws in the reactor vessel according to the criteria in A-2000.(b)Determine the loading conditions at the location of the postulated flaws for Level A, B, C and D Service loadings.(c)Obtain the material properties, including Z, a~, and the J-integral resistance curve (J-R curve), at the locations of the postulated flaws.Requirements for determining the J-R curve are given in A-3300'd)Evaluate the postulated flaws according to the acceptance criteria in'A-2000.Requirements for evaluating the applied J-integral are given in A-3200, and for determining flaw stability in A-3400'hree permissible evaluation approaches are described in~~A-3500.Detailed calculation procedures for Level A and B Service loadings are given in A-4000.A-1


A-1300 GENERAL NOMENCLATURE flaw depth which includes ductile flaw growth effective flaw depth which includes ductile flaw growth and a plastic-zone correction (in.)(in.)Be Bo effective flaw depth at flaw instability, which includes ductile flaw growth and a-plastic-zone
I APPENDIX A TO CODE CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS ARTICLE A-1000 INTRODUCTION A-1100    SCOPE This Appendix provides acceptance criteria and evaluation procedures for determining the acceptability for operation of a reactor vessel when the vessel metal temperature is in the upper shelf range.          The methodology is based on the principles of elastic-plastic fracture mechanics. Flaws are postulated in the reactor vessel at locations of predicted low upper shelf Charpy impact energy and the applied J-integral for these flaws is calculated and compared with th'e J-integral fracture resistance of the material to determine acceptability.            All specified design transients for the reactor vessel shall be considered.
.correction postulated initial flaw depth amount of ductile flaw growth (in.)(in.)(in.)dB'mount of ductile flaw growth , at flaw instability (in.)E'oung's modulus E/(2-VR)CCR=material constants used to describe the power-law fit to the J-integral resistance curve for the material,.
A-1200    PROCEDURE OVERVIEW The following      is a summary  of the analytical procedure which may be used.
ZR=C,(dB)'CR)=cooldown rate (F/hour)(ksi)(ksi)Fzr F~r F~geometry factors used to calculate the stress intensity factor (dimensionless)
(a)    Postulate      flaws in the reactor vessel    according to the criteria in     A-2000.
Far Fur Fg geometry factors used to calculate the stress intensity factor at flaw instability I J-integral'ue to the applied loads (dirtensionless
(b)     Determine the loading conditions at the location of the postulated flaws for Level A, B, C and D Service loadings.
)(in.-lb/in.')
(c)   Obtain the material properties, including Z, a~, and the J-integral resistance curve (J-R curve), at the locations of the postulated flaws. Requirements for determining the J-R curve are given in A-3300 Evaluate the postulated flaws according to the acceptance
+R J-integral fracture resistance for the material (in.-,1b/in.~)A-2
                  'd) criteria in 'A-2000. Requirements for evaluating the applied J-integral are given in A-3200, and for determining flaw stability in A-3400  'hree    permissible evaluation approaches are described in A-3500. Detailed calculation procedures for Level A and B Service loadings are given in A-4000.
      ~
A-1


J-integral f racture resistance f or the material at a ductile flaw growth of 0.10 in.(in.-lb/in.~)
A-1300  GENERAL NOMENCLATURE flaw depth which includes ductile flaw growth                               (in.)
Jz Kz applied J-integral at a flaw depth of a,+0.10 in.J-integral at flaw instability mode I stress intensity factor C (in.-lb/in.')(in.-lb/in.~)(ksi v'in.)Kzp mode I'stress intensity factor due to internal pressure, calculated with no plastic-zone correction (ksi v'in.)Kzp Kzp ca 1 cu 1 ated with a p 1 astic-zone correction (ksi V'in.)Kzp Kzp at f law-instability, calculated with a plastic-zone correcti'on (ksi V'in.)Kze Kz mode I stress intensity factor due to a radial thermal gradient through the vessel wall, calculated with no plastic-zone correction Kcalculated with a plastic-zone correction (ksi V'in.)'I (ksi Min.)Kze Kat flaw instability, calculated with a plastic-zone correction ordinate of the failure assessment diagram curve (ksi Min.)(dizransionless) ratio of the stress intensity factor to the fracture toughness for the material internal pressure (dixransionless)(ksi)accumulation pressure as defined in the plant-specific Overpressure Protection Report, but not exceeding l.l times the design pressure (ksi)A-3
effective flaw depth which includes ductile flaw growth and a plastic-zone correction                  (in.)
Be            effective flaw depth at flaw instability, which includes ductile flaw growth      and a -plastic-zone
                . correction                                (in.)
Bo            postulated  initial flaw depth            (in.)
amount  of ductile flaw growth            (in.)
dB'mount              of ductile flaw growth at flaw instability
              ,                                             (in.)
C      =    material constants used to describe CR the power-law      fit  to the J-integral resistance curve for the material,.
ZR = C,(dB)
            =    cooldown  rate
                              'CR)
( F/hour)
E'oung's              modulus                          (ksi)
E/(2-VR)                                  (ksi)
Fzr F~r      geometry factors used      to calculate F~            the stress intensity factor              (dimensionless)
Far Fur      geometry factors used      to calculate Fg            the stress intensity factor at flaw instability                        I (dirtensionless )
J-integral'ue to       the applied loads                                    (in.-lb/in.')
    +R            J-integral fracture resistance for the material                             (in. ,1b/in.~)
A-2


Ps P Po Rq pressure used to calculate the applied J-integral/tearing modulus line internal pressure at'law instability reference limit-load internal pressure inner radius of the vessel'bscissa of the failure assessment diagram curve (ksi)(ksi)(ksi)(in.)(LQmnsionless
J-integral fracture resistance for the material at a ductile flaw growth of 0.10 in.                      (in.-lb/in.~)
)ratio of internal pressure to reference limit-.load internal pressure (SF)=saf ety f actor vessel wall thickness (dhransionless)(dhransionless
Jz  applied J-integral at     a  flaw depth of a, + 0.10 in.                  (in.-lb/in.')
)(in.)tearing modulus due to the applied loads tearing modulus resistance for the material (diz~nsionless)(dUransionless) parameter used to relate the applied J-integral to the applied tearing modulus (dimensionless)
J-integral at flaw instability          (in.-lb/in.~)
Poisson's ratio reference flow stress, specified as 85 ksi (dirmnsionless)(ksi)yield strength for the material (ksi)  
Kz  mode I stress intensity factor          (ksi v'in.)
C Kzp mode I'stress intensity factor due to internal pressure, calculated with no plastic-zone correction          (ksi v'in.)
Kzp Kzp ca 1 cu 1 ated with a p 1 astic-zone correction                              (ksi V'in. )
Kzp Kzp  at flaw- instability, calculated with a plastic-zone correcti'on          (ksi V'in.)
Kze mode  I  stress intensity factor due to a radial thermal gradient through the vessel wall, calculated with no plastic-zone correction          (ksi V'in.)
Kz  K calculated with a plastic-zone            'I correction                              (ksi Min.)
Kze K at flaw instability, calculated with a plastic-zone correction          (ksi Min.)
ordinate of the failure assessment diagram curve                            (dizransionless) ratio of the stress intensity factor to the fracture toughness for the material                        (dixransionless) internal pressure                        (ksi) accumulation pressure as defined in the plant-specific Overpressure Protection Report, but not exceeding l.l  times the design pressure          (ksi)
A-3


ARTICLE A-2000 ACCEPTANCE CRITERIA The adequacy of the upper shelf toughness of the reactor vessel shall be determined by analysis.The reactor vessel is.acceptable for continued service when the criteria of Paragraphs (a), (b), and (c)are satisfied.(a)Level A and B Service Loadings When evaluating the adequacy of the upper shelf toughness for the weld material for Level A and B Service loadings, postulate an.interior semi-elliptical surface flaw with a depth one-quarter of the wall thickness and a length six times the depth, with the flaw'.s major axis oriented along the weld of concern and the flaw plane oriented in the radial direction.
Ps      pressure used to calculate the applied J-integral/tearing modulus line                                (ksi)
When evaluating.
P      internal pressure at'law instability                          (ksi)
the adequacy of the upper shelf toughness for the base material, postulate both interior axial and circumferential flaws with depths one-quarter of the wall thickness and lengths six times the depth and use the toughness properties for the corresponding orientation.
Po      reference limit-load internal pressure                            (ksi)
Smaller flaw sizes may be used on-an individual case basis when justified.
Rq      inner radius of the                 (in.)
Two criteria shall be satisfied:
vessel'bscissa of the failure assessment diagram curve                        (LQmnsionless  )
(i)The applied J-integral evaluated at a pressure which is 1.15 times the accumulation pressure as defined in the plant-specific Overpressure Protection Report, with a factor of safety of 1.0 on thermal loading for the plant specified heatup and cooldown conditions, shall be shown to be less than the J-integral characteristic of the material resistance to ductile tearing at a flaw growth of 0.10 in.(2)The flaw shall be shown to be stable, with the possibility of ductile flaw growth, at a pressure which is 1.25 times the accumulation pres'sure defined in Subparagraph (1), with a factor of safety of 1.0 on thermal loading for the plant specified heatup and cooldown conditions.
ratio of internal pressure to reference limit-. load internal pressure                            (dhransionless)
The J-integral resistance versus crack growth curve shall be a conservative representation for the vessel material under evaluation.
(SF) = saf ety factor                       (dhransionless  )
A-5
vessel wall thickness               (in.)
~/(
tearing modulus  due to the applied loads                        (diz~nsionless) tearing modulus resistance for the material                             (dUransionless) parameter used to relate the applied J-integral to the applied tearing modulus                              (dimensionless)
(b)Level C Service Loadings When e: aluatin the ade g quacy of the upper shelf toughness for the weld material for Level C Service loadings, postulate interior semi-elliptical surface flaws with depths up to 1/10 of the base metal wall thickness, plus the cladding thickness, with total depths not to exceed 1.0 in., and a surface length six times the depth, with the flaw's major axis oriented along the weld of concern and the flaw plane oriented in the radial direction.
Poisson's  ratio                    (dirmnsionless) reference flow stress, specified as 85  ksi                          (ksi) yield strength for the material     (ksi)
When evaluating the adequacy of the upper shelf toughness for the base material, postulate both interior axial and circumferential flaws, and use the toughness properties for the corresponding orientation.
Flaws of various depths, ranging up to the maximum postulated depth, shall be analyzed to determine the most limiting flaw depth.Smaller maximum flaw sizes may be used on an individual case basis when justified.
Two criteria shall be satisfied:
(1)The applied J-integral shall be shown to be less than the J-integral characteristic of the material resistance to ductile tearing at a flaw growth of 0.10 in., using a factor of safety of 1.0 on loading., (2)The flaws shall be shown to be stable, with the possibility of ductile flaw growth, using a factor of safety of 1.0 on loading.The J-integral'esistance versus crack growth curve shall be a conservative representation for the vessel material under evaluation.(c)Level D Service Loadings When evaluating the adequacy of the u'pper shelf toughness for Level D Service loadings, post'ulate flaws as specified for Level C Service loadings'in Paragiaph b), and use the toughness properties for the corresponding orientation.
Flaws of various depths, ranging up to the maximum postulated depth, shall be analyzed to determine the most limiting flaw depth.Smaller maximum flaw sizes may be used on an individual case basis when justified.
The flaws shall be shown to be stable, with the possibility of ductile flaw"'rowth, using a factor of safety of 1.0 on loading.The J-integral resistance versus crack growth curve shall be a best estimate representation for the vessel material under evaluation.
The stable flaw depth.shall not exceed 75%of the vessel wall~~~~~~~~thickness, and the remaining ligament shall be safe from tensile instability.
A-6


ARTICLE A-3000\ANALYSIS A-3100 SCOPE This Article contains a general description of procedures which shall be used to evaluate the applied fracture mechanics parameters, as well as requirements for selecting the J-R curve for the material.References are made to acceptable approaches to apply the criteria.A-3200 APPLIED J-INTEGRAL The calculation of the J-integral due to the applied loads.shall account for the full elastic.-plastic behavior of the stress-strain curve for the material.When the conditions fall into the category of elastic fracture mechanics with small-scale yielding, the J-integral may alternately be calculated.by using crack-tip stress intensity factor formulae with a plastic-zone correction.
ARTICLE A-2000 ACCEPTANCE CRITERIA The adequacy of the upper shelf toughness of the reactor vessel shall be determined by analysis.      The reactor vessel is.
acceptable for continued service when the criteria of Paragraphs (a), (b), and (c) are satisfied.
(a)  Level  A and B Service Loadings When evaluating the adequacy of the upper shelf toughness for the weld material for Level A and B Service loadings, postulate an
.interior semi-elliptical surface flaw with a depth one-quarter of the wall thickness and a length six times the depth, with the flaw'.s major axis oriented along the weld of concern and the flaw plane oriented in the radial direction.        When evaluating. the adequacy of the upper shelf toughness for the base material, postulate both interior axial and circumferential flaws with depths one-quarter of the wall thickness and lengths six times the depth and use the toughness properties for the corresponding orientation.
Smaller flaw sizes may be used on-an individual case basis when justified. Two criteria shall be satisfied:
(i) The applied J-integral evaluated at a pressure    which  is 1.15 times the accumulation pressure      as defined in the plant-specific Overpressure Protection Report, with a factor of safety of 1.0 on thermal loading for the plant specified heatup and cooldown conditions, shall be shown to be less than the J-integral characteristic of the material resistance to ductile tearing at a flaw growth of 0.10 in.
(2)  The  flaw shall be shown to be stable, with the possibility of ductile flaw growth, at a pressure which is 1.25 times the accumulation pres'sure defined in Subparagraph (1), with a factor of safety of 1.0 on thermal loading for the plant specified heatup and cooldown conditions.
The J-integral resistance versus crack growth curve shall be a conservative representation      for the vessel material under evaluation.
A-5
 
  ~ /
(
 
(b)  Level    C  Service Loadings When e: aluatin g the ade quacy of the upper shelf toughness for the weld material for Level C Service loadings, postulate interior semi-elliptical surface flaws with depths up to 1/10 of the base metal wall thickness, plus the cladding thickness, with total depths not to exceed 1.0 in., and a surface length six times the depth, with the flaw's major axis oriented along the weld of concern and the flaw plane oriented in the radial direction. When evaluating the adequacy of the upper shelf toughness for the base material, postulate both interior axial and circumferential flaws, and use the toughness properties for the corresponding orientation.
Flaws of various depths, ranging up to the maximum postulated depth, shall be analyzed to determine the most limiting flaw depth.
Smaller maximum flaw sizes may be used on an individual case basis when  justified.      Two criteria shall  be satisfied:
(1) The applied J-integral shall be shown to be less than the J-integral characteristic of the material resistance to ductile tearing at a flaw growth of 0.10 in., using a factor of safety of 1.0    on  loading.,
(2)  The  flaws shall be shown to be stable, with the possibility of ductile flaw growth, using a factor of safety of 1.0 on loading.
The  J-integral'esistance          versus crack growth curve shall be a conservative        representation    for the vessel material under evaluation.
(c)  Level    D  Service Loadings When evaluating the adequacy of the u'pper shelf toughness for Level D Service loadings, post'ulate flaws as specified for Level C Service loadings 'in Paragiaph b), and use the toughness properties for the corresponding orientation.              Flaws of various depths, ranging up to the maximum postulated depth, shall be analyzed to determine the most limiting flaw depth. Smaller maximum flaw sizes may be used on an individual case basis when justified. The flaws shall be shown to be stable, with the possibility of ductile flaw using a factor of safety of 1.0 on loading. The J-integral    "'rowth, resistance versus crack growth curve shall be a best estimate representation for the vessel material under evaluation.
The  stable flaw depth .shall not exceed 75% of the vessel wall thickness, and the remaining ligament shall be safe from tensile
    ~                          ~ ~    ~
instability.
~      ~  ~
                ~
A-6
 
ARTICLE A-3000
                                      \
ANALYSIS A-3100   SCOPE This   Article contains   a general description of procedures which shall be used to evaluate the applied fracture mechanics parameters, as well as requirements for selecting the J-R curve for the material.     References are made to acceptable approaches to apply the criteria.
A-3200     APPLIED J-INTEGRAL The calculation of the J-integral due to the applied loads.
shall account for the full elastic.-plastic behavior of the stress-strain curve for the material. When the conditions fall into the category of elastic fracture mechanics with small-scale yielding, the J-integral may alternately be calculated .by using crack-tip stress intensity factor formulae with a plastic-zone correction.
The method of calculation shall be validated and documented.
The method of calculation shall be validated and documented.
A-3300 SELECTION OF THE J-INTEGRAL RESISTANCE CURVE When evaluating the vessel for Level A, B and C Service loadings, the J-integral
A-3300     SELECTION OF THE J-INTEGRAL RESISTANCE CURVE When evaluating the vessel for Level A, B and C Service loadings, the J-integral 'resistance versus crack growth curve (J-R curve) shall be a conservative representation of the toughness of the controlling beltline material at upper shelf temperatures in the operating range.       When evaluating the vessel for Level D Service loadings, the J-R curve shall be a best estimate
'resistance versus crack growth curve (J-R curve)shall be a conservative representation of the toughness of the controlling beltline material at upper shelf temperatures in the operating range.When evaluating the vessel for Level D Service loadings, the J-R curve shall be a best estimate.representation of the toughness of the controlling beltline material at upper shelf temperatures in the operating range.One of the following optioris: shall be used to determine the J-R curve.(a)A J-R curve generated for the actual material under consideration by following accepted test procedures may be used.The J-R curve shall be based on the'roper combination of crack orientation, temperature and fluence level.'he crack growth shall include ductile tearing with no occurrence of cleavage.A-7 S'
.representation of the toughness of the controlling beltline material at upper shelf temperatures in the operating range. One of the following optioris: shall be used to determine the J-R curve.
A J-R curve generated from a J-integral database obtained from the same class.of material under consideration with the same orientation using appropriate correlations for the effects of temperature, chemical composition and fluence level may he used.The crack growth shall include ductile tearing with no occurrence of cleavage.(c)When the approaches of (a)or (b)are not possible, indirect methods of estimating the J-R curve may be used provided these methods are justified for the material under consideration.
(a)   A   J-R   curve generated   for the actual material under consideration by following accepted test procedures may be used. The J-R curve shall be based on the'roper combination of crack orientation, temperature and fluence level.'he crack growth shall include ductile tearing with no occurrence of cleavage.
A-3400 FLAW STABILITY The equilibrium equation for stable flaw growth is J=Jwhere J is the J-integral due to-the applied loads for the postulated flaw in the'vessel, and Jis the J-integral resistance to ductile tearing for the material.The inequality for flaw stability due to ductile tearing is Q J dLTg aa da where BJ/Ba is the partial derivative of the applied J-integral with respect to the flaw depth a with load held constant, and d J/da is the slope o f the J-R curve.'nder a condition o f increasing load, stable flaw growth will continue as long as BJ/Ba remains less than dJ/da.A-3500 EVALUATION APPROACH FOR LEVEL A AND B SERVICE LOADINGS The procedure given in A-4200 shall be used to evaluate the applied J-integral-for a specified amount of ductile flaw growth.There are three approaches that are equally acceptable for applying the flaw stability acceptance criteria according to the governing flaw stability rules in A-3400.The first is a J-R curve crack driving force diagram approach.In this approach flaw stability is evaluated by a direct application of the flaw stability rules given in A-3400.Guidelines for using this~~~approach are given in A-4310.The second is a failure assessment diagram approach.A procedure based on this approach for the A-8 t I~
A-7
postulated initial one-quarter wall thickness flaw is given in A-4320.The third is a J-integral/tearing modulus approach.A procedure based on this approach for the postulated initial one-quarter wall thickness flaw is given in A-4330.ARTICLE A-4000 EVALUATION PROCEDURES FOR LEVEL A AND B SERVICE LOADINGS A-4100 SCOPE This Article contains calculation procedures to be used to.satisfy the acceptance criteria in A-2000 for Level A and B Service loadings.A procedure to be used to satisfy the J-integral criterion for a specified amount of flaw growth of 0.10 in.is given in A-4200.Procedures to satisfy-the flaw stability criterion are given in A-4300.These procedures include the ax'ial and circumferential flaw orientations.
 
A-4200 EVALUATION PROCEDURE FOR THE APPLIED J-INTEGRAL A-4210 CALCULATION OF THE APPLIED J-INTEGRAL The calculation of.the"applied J-integral consists of two steps: Step 1 is to calculate the effective flaw depth which includes a plastic-zone correction; and-Step 2 is to calculate the J-integral for small-scale yielding based on this effective flaw depth.~Ste 1 For.an axial flaw with a depth a, calculate the stress intensity factor due to internal pressure with a safety factor (SF)on pressure by using R>>=(SF)p (I+(R,/t)J (na)', F~=0.982+1.006(a/t)~
S' A J-R curve generated from a     J-integral database obtained from the   same class. of material under consideration with the same orientation using appropriate correlations for the effects of temperature, chemical composition and fluence level may he used. The crack growth shall include ductile tearing with no occurrence of cleavage.
This equation the effect of for R>>is valid for 0.20 s a/t s 0'0, and includes pressure acting on the flaw faces.A-9
(c)   When the approaches of (a) or (b) are not possible, indirect methods of estimating the J-R curve may be used provided these methods are justified for the material under consideration.
A-3400       FLAW STABILITY The   equilibrium equation for stable flaw growth is J= J where      J is the J-integral due to- the applied loads for the postulated flaw in the'vessel, and J is the J-integral resistance to ductile tearing for the material.
The inequality for flaw stability due to ductile tearing is QJ    dLTg aa     da where BJ/Ba       is the partial derivative of the applied J-integral with respect to the flaw depth a with load held constant, and d J/da is the slope o f the J-R curve. 'nder a condition o f increasing load, stable flaw growth will continue as long as BJ/Ba remains less than dJ/da.
A-3500       EVALUATION APPROACH FOR LEVEL A AND B SERVICE LOADINGS The procedure     given in A-4200 shall be used to evaluate the applied J-integral       -for a specified amount of ductile flaw growth.
There are three approaches that are equally acceptable for applying the flaw stability acceptance criteria according to the governing flaw stability rules in A-3400. The first is a J-R curve crack driving force diagram approach.           In this approach flaw stability is evaluated by a direct application of the flaw stability rules given in A-3400. Guidelines for using this
      ~   ~
approach are given in A-4310. The second is a failure assessment diagram approach.         A procedure based on this approach for the
  ~
A-8
 
t I~


~~~For a circumferential flaw with a depth a, calculate the stress intensity factor due to internal pressure with a safety factor (SF)on pressure by'using Kzp=(SF)p (1+(RE/(2t))J (za).Fz F,=0.885+0.233(a/t)
postulated    initial one-quarter    wall thickness flaw is given in A-4320. The  third is  a  J-integral/tearing modulus approach.      A procedure based on this approach for the postulated initial one-quarter wall thickness flaw is given in A-4330.
+0.345(a/t)3 (2)This equation for K>>is valid for 0.20 s a/t s 0.50, and includes the effect of pressure acting on the flaw faces.For an axial or circumferential flaw with a depth a, calculate the stress intensity factor due to radial thermal gradients by using KE0=((CR)/I 000)t F3 F,=.0.584+2;647(a/t)
ARTICLE A-4000 EVALUATION PROCEDURES FOR LEVEL A AND B SERVICE LOADINGS A-4100    SCOPE This Article contains calculation procedures to be used to          .
-6.294(a/t)'
satisfy the acceptance criteria in A-2000 for Level A and B Service loadings.        A procedure to be used to satisfy the J-integral criterion for a specified amount of flaw growth of 0.10 in. is given in A-4200.          Procedures to satisfy- the flaw stability criterion are given in A-4300. These procedures include the ax'ial and  circumferential flaw orientations.
2.990(a/t)3 (3)This equation for Kz, is valid for 0.20 c a/t~0.50, and 0 c (CR)~100 F/hour.Calculate the effective flaw depth for small-scale yielding, aby using a,=a+(I/(6'))((Kzp
A-4200    EVALUATION PROCEDURE FOR THE APPLIED J-INTEGRAL A-4210      CALCULATION OF THE APPLIED J-INTEGRAL The calculation of. the "applied J-integral consists of two steps: Step 1 is to calculate the effective flaw depth which includes a plastic-zone correction; and-Step 2 is to calculate the J-integral for small-scale yielding based on this effective flaw depth.
+KE0)/<y J~Ste 2 For an axial flaw, calculate-the stress intensity factor due to internal pressure for small-scale yielding, Kzp, by substituting a, in place of a in equation (1), including the equation for F,.For a circumferential flaw, calculate Kz py substituting a, in place of a in equation (2), including the equation for F,.For an axial or circumferential.
~Ste    1 For. an axial flaw with a depth a, calculate the stress intensity factor due to internal pressure with a safety factor (SF) on pressure      by using R>>  =  (SF) p  (I  + (R,/t) J (na)',
flaw, calculate the stress intensity factor due to ra'dial thermal gradients for small-scale yielding, Kzby substituting a in place of a in equation (3), including the equation for F3.Equations (1), (2)and (3)are valid for 0.20 c a,/t c 0.50.The J-integral due to the applied loads for small-scale yielding is given by Z=1000(Kzp+K'/E'  
F~ =  0.982 +  1.006(a/t)~
This equation for R>> is valid for 0.20 s a/t s 0 the effect of pressure acting on the flaw faces.
                                                        '0,  and includes A-9
 
For a circumferential flaw with a depth a, calculate the
                ~
stress intensity factor due to internal pressure with a safety
        ~        ~
factor (SF) on pressure by 'using Kzp       =   (SF) p (1 + (RE/(2t) ) J (za)   .
Fz           (2)
F,       =   0.885 + 0.233(a/t) + 0.345(a/t)3 This equation       for     K>>   is valid for     0.20 s a/t s 0.50, and includes the effect of pressure acting               on the flaw faces.
For an axial or circumferential flaw with a depth a, calculate the stress   intensity factor due to radial thermal gradients by using KE0   =     ( (CR) /I000) t       F3                                   (3)
F,   = .0.584 +           2;647(a/t) - 6.294(a/t)'       2.990(a/t)3 This equation for           Kz, is valid for     0.20 c a/t ~ 0.50, and   0 c (CR)
~ 100 F/hour.
Calculate the effective flaw depth for small-scale yielding, aby using a,   =   a + (I/(6'))((Kzp + KE0)/<yJ
~Ste 2 For an axial flaw, calculate- the stress intensity factor due to internal pressure for small-scale yielding, Kzp, by substituting a, in place of a in equation (1), including the equation for F,.
For a circumferential flaw, calculate Kz py substituting a, in place of a in equation (2), including the equation for F,. For an axial or circumferential. flaw, calculate the stress intensity factor due to ra'dial thermal gradients for small-scale yielding, Kz by substituting a in place of a in equation (3), including the equation for F3. Equations (1), (2) and (3) are valid for 0.20 c a,/t c 0.50.
The J-integral             due   to the applied loads for small-scale yielding is given by Z =     1000(Kzp +   K' /E'
 
A-4220  EVALUATIONgUSING CRITERION FOR FLAN GRONTH OF    0.1 ZN Calculate the J-integral due to the apple.ed loads, J by following A-4210. Use a flaw depth a equal to 0.25t + 0.10 in.; a pressure p equal to the accumulation pressure for Level A and B Service loadings,' and a safety factor (SF) on pressure equal to 1;Z5. The acceptance. criterion for Level A and B Service loadings based on a ductile flaw growth of'.10 in. in A-2000(a)(1') is satisfied when the following inequality is satisfied.
Js ~ Jo.i where      J, = the    applied J-integral for a safety factor on
                                                  =
pressure of 1.15, and a safety factor of 1.0 on thermal loading, J,,  =  the J-integral resistance at a ductile flaw growth of 0.10 in.
A-4300  EVALUATION PROCEDURES FOR FLAN STABILITY A-4310  J-R  CURVE  CRACK DRIVING FORCE DIAGRAM PROCEDURE Zn thxs procedure flaw stabzlzty xs evaluated by a direct
                                      ~  ~
application of the flaw stability rules given in A-3400. The applied J-integral is calculated for a series of flaw depths corresponding to increasing amounts of ductile flaw growth. The applied J-integral for Level A and B Service loadings shall be calculated by using the procedures given in A-4210. The appliep pressure p is set equal to the accumulation pressure for Level A and B Service loadings, p; and the safety factor (SF) on pressure is equal to 1.25. The applied J-integral is .plotted against crack depth on the crack driving force diagram to produce the applied J-integral curve, as illustrated in Figure A-4310-1. The J-R curve is also plotted on the crack driving force diagram, and intersects the horizontal axis at the initial flaw depth, a,. Flaw stability at a given applied load is demonstrated when the slope of the applied J-integral curve is less than the slope of the J-R curve at the point on the J-R curve where the two curves intersect.
 
Jr Material JR
                                      'pplied J Evaluation Point ap FIGURE A-4310-1 COMPARISON OF THE SLOPES OF THE APPLIED J-INTEGRAL CURVE AND THE J-R CURVE ~


A-4220 EVALUATIONgUSING CRITERION FOR FLAN GRONTH OF 0.1 ZN Calculate the J-integral due to the apple.ed loads, Jby following A-4210.Use a flaw depth a equal to 0.25t+0.10 in.;a pressure p equal to the accumulation pressure for Level A and B Service loadings,'
and a safety factor (SF)on pressure equal to 1;Z5.The acceptance.
criterion for Level A and B Service loadings based on a ductile flaw growth of'.10 in.in A-2000(a)(1')
is satisfied when the following inequality is satisfied.
Js~Jo.i where J,=the applied J-integral for a=safety factor on pressure of 1.15, and a safety factor of 1.0 on thermal loading, J,,=the J-integral resistance at a ductile flaw growth of 0.10 in.A-4300 EVALUATION PROCEDURES FOR FLAN STABILITY A-4310 J-R CURVE-CRACK DRIVING FORCE DIAGRAM PROCEDURE~~Zn thxs procedure flaw stabzlzty xs evaluated by a direct application of the flaw stability rules given in A-3400.The applied J-integral is calculated for a series of flaw depths corresponding to increasing amounts of ductile flaw growth.The applied J-integral for Level A and B Service loadings shall be calculated by using the procedures given in A-4210.The appliep pressure p is set equal to the accumulation pressure for Level A and B Service loadings, p;and the safety factor (SF)on pressure is equal to 1.25.The applied J-integral is.plotted against crack depth on the crack driving force diagram to produce the applied J-integral curve, as illustrated in Figure A-4310-1.The J-R curve is also plotted on the crack driving force diagram, and intersects the horizontal axis at the initial flaw depth, a,.Flaw stability at a given applied load is demonstrated when the slope of the applied J-integral curve is less than the slope of the J-R curve at the point on the J-R curve where the two curves intersect.
Jr Material JR Evaluation Point'pplied J ap FIGURE A-4310-1 COMPARISON OF THE SLOPES OF THE APPLIED J-INTEGRAL CURVE AND THE J-R CURVE~
I~
I~
A-4320 FAILURE ASSESSMENT DIAGRAM PROCEDURE This procedure is restricted to a postulated initial flaw depth equal to one-quarter of the wall thickness.
A-4320     FAILURE ASSESSMENT DIAGRAM PROCEDURE This procedure is restricted to a postulated depth equal to one-quarter of the wall thickness.
A-4321 FAZLURE ASSESSMENT DIAGRAM CURVE The same failure assessment diagram curve shall be used for axial and circumferential flaws, and is given in.Figure A-4320-1.The coordinates (SR,)of the failure assessment diagram curve are given in Table A-4320-1.This curve is based on material properties which are characteristic of reactor pressure vessel steels.A-4322 FAILURE ASSESSMENT POINT COORDINATES The flaw depth a for,a ductile flaw growth of h,a is given by a-=0250+ha~~The failure assessment point coordinates (S', K')for a ductile flaw growth of ha shall be calculated by using the following expressions:
initial  flaw A-4321     FAZLURE ASSESSMENT DIAGRAM CURVE The same failure assessment diagram curve shall be used for axial   and circumferential flaws, and is given in. Figure A-4320-1.
Kz R~(I 000/(E J))V where the stress intensity factor shall be calculated using the flaw.depth a without the plastic-zone correction, and is given by K~=Kzp+R~, and s:=(sz)p/p.where (SZ)is the required safety factor on pressure.The procedure for calculating Kz~Kz and p, for axial flaws is given in A-4322.1, and for.circumferential flaws in A-4322.2.A-13  
The coordinates (SR,) of the failure assessment diagram curve are given in Table A-4320-1.               This curve is based on material properties which are characteristic of reactor pressure vessel steels.
-0 A-4322.1 Axial Flaws The stress intensity factor due to internal pressure for axial flaws with a safety factor (SZ)on pressure is given by equation (1').The stress intensity factor due,to radial thermal gradients is given by equation (3)~The reference limit-load pressure is given by H (2/~3}o[Q.905-Q.379 (h,a/t)I[0.379+(R~/t)+0.379 (ha/t}1 For materials with a yield strength ogreater than 85 ksi, set aequal to 85 ksi in this equation.This equation for p, is valid for 0 s za/t s 0.10.A-4322.2 Circumferential Flaws ()thermal gradients is>given by equation (3).The reference limit-load pressure is given by C The stress intensity factor due to internal pressure for circumferential flaws with a safety factor (SF)on pressure is given by equation 2.The stress intensit factor due to radial p o[1-0.91 (0.25+(Aa/t})~(t!R~)l[1+(R/(2t}})For materials with a yield strength oz greater than 85 ksi, set oy equal to 85 ksi in this equation.This equation for p is valid for 0 s za/'t s 0.25.A-4323 EVALUATION USING CRITERION FOR FLAN'TABILITY Assessment points shall be calculated for each loading condition according to A-4322, and plotted on Figure A-4320-1 as follows.Plot a series of assessment points for various amounts of ductile flaw growth ba up to the validity limit of the J-R curve.Use a pressure p equal to the accumulation pressure for Level.A and B Service loadings, pand a safety factor (SF)on pressure equal to 1.25.When one or more assessment points lie inside the failure assessment curve, the acceptance criterion based on flaw stability.
A-4322     FAILURE ASSESSMENT POINT COORDINATES The   flaw depth   a for,a ductile flaw growth of       h,a is given by a- =     0250   + ha The failure     assessment point coordinates (S', K') for a ductile
in A-2000(a)(2) is satisfied.  
                                ~
/r TABLE A-4320-1 COORDINATES OF THE FAILURE ASSESSMENT DIAGRAM CURVE OP FIGURE A-4320-1 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.650 0.700 0.750 0.800 0.850 0.900 0.950 1.000 1.050 1.100 1.150'.K 1.000 1 F 000 0.999 0.998'.996 0.993 0.990 0.987 0.981 0.973 0.960 0.939 0.908 0.864 0.807 0.737 0.660 0.581 0.505 0'35 0.374 0.321 0.276 0.238 A-15 Js 1.2 1.0, 0.8 0.6 K, 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 S, 1.4 FIGURE A-4320-1 FAILURE ASSESSMENT DIAGRAM FOR THE ONE-QUARTER MALL THICKNESS FLAN A-16 J
flaw   growth of ha shall be calculated by using the following expressions:
A-4330 J-ZNTEGRAL/TEARZNG MODULUS PROCEDURE This procedure is restricted to a postulated initial flaw depth equal to one-quarter of the wall.thickness.
          ~
A-4331 J-ZNTEGRAL AT FLAN ZNSTABZLZTY 1 Referring to Figure A-4330-1, the onset of.flaw instability is the point of intersection of the applied and material curves plotted on a graph of the J-integral versus tearing modulus (J versus T).The expression for the applied J/T curve is given by J=(1000 V t Oi/Z)T (4)(5)where oi is a reference flow stress which is set to 85 ksi in equation (4).For axial flaws p=0.235(l+(0.083 x 10')(CR)t'/((SF)p,)J where p, is the pressure under evaluation.
Kz       R~ (I 000/(E J ) )
Equation (5)is valid for 6 s t s 12 in., 2.25 s ((SF)p,)s 5.00 ksi, and 0 s (CR)100 F/hour.For circumferential flaws~~~~~V=0.21(1+(0.257 x 10)(CR)t/((SF)p,)J (6)Equation (6)is valid for 6 s t s 12 in., 2.25 s ((SF)p,)s 9.00 ksi, and 0 s (CR)s 100 F/hour.Equations (4), (5)and (6)are based on material properties which are characteristic of reactor pressure vessel steels.The tearing modulus for the material is determined by differentiation of the J-R curve with respect to flaw depth a.(Z/(1000 Qi))dJ/da (7)The-same values for Z and oi shall be used in equations (4)and (7).The J-integral versus tearing modulus J~/T~curve for the material is given by plotting Jagainst T~for a series of increments in ductile flaw growth.Each coordinate for JR is evaluated at the same amount of ductile flaw growth as the coordinate for T~.  
V where the stress       intensity factor shall       be calculated using the flaw. depth a without the plastic-zone correction, and             is given by K~ =     Kzp + R~,
/  
and s:   =     (sz) p/p.
~~~~~~~~The'value of the J-integral at the onset of flaw instability, J', corresponds to the intersection of the applied J/T curve given: by equation (4)with the material J~/T~curve, as illustrated in Figure A-4330-1.h The J-integral at the onset of flaw instability may be determined analytically when a power-law curve fit to the J-R curve of the form J-Ci(ha)+is available.
where   (SZ) is the required safety factor on pressure.                     The procedure for calculating Kz~ Kz and p, for axial flaws is given in A-4322.1, and for. circumferential flaws in A-4322.2.
The J-integral at the onset of flaw instability, J, in this case is given by A-4332 ZNTERNAL PRESSURE AT FLAN ZNSTABZLZTY
A-13
~~~~~~~~~~~The calculation of the internal pressure at the onset of flaw instability is based on the value of the J-integral at.the onset of flaw instability, J.The ductile flaw growth at the onset.of flaw instability, ha, is taken from the J-R curve.The effective flaw depth at the onset of flaw instability includes the ductile flaw growth b.a', and is given by a=0.25t+ha+(1/(6n))fZ'8'/(1000 o~'))The stress intensity factor due to radial thermal gradients at the onset of flaw instability, Zifor axial:or circumferential flaws is given by.." Zzi=((CR)/1000) t~'~Z'~=0.584+2.647(a,'/t)
 
-6.294(a,'/t)~
-0 A-4322.1     Axial Flaws The stress intensity factor due to internal pressure for axial flaws with a safety factor (SZ) on pressure is given by equation (1'). The stress intensity factor due,to radial thermal gradients is given   by equation (3)   ~
+2.990(a,'/t)~
The reference limit-load pressure is given by             H (2/~3 } o [ Q . 905 Q . 379 (h,a/ t) I
This equation for'Ri, is valid for 0.20~a,/t~0.50,'nd 0 s (CR)s 100'F/hour.
[0.379 + (R~/t) + 0.379 (ha/t}         1 For materials with a yield strength o greater than 85 ksi, set a equal to 85 ksi in this equation. This equation for p, is valid for 0 s za/t s 0.10.
The stress intensity factor for small-scale yielding due to internal pressure at the onset of flaw instability, Eppes is given by  
A-4322.2     Circumferential Flaws C
,0 For a given value of K,'~, the internal pressure at the onset of flaw instability for axial flaws is given by p=Ksp/((1+(R,/t))(za)o.s F,']F~.=0.982+,, 2.006(a,/t)~
The  stress  intensity factor       due to internal pressure for circumferential flaws with       a safety factor (SF) on pressure is given by equation ( 2 ) . The stress intensit factor due to radial thermal gradients is> given by equation (3).
and for circumferential flaws by p=Ki/((1+(Ri/(2t)))(za,)'~J F'0.885+0.233(a,/t)
The  reference limit-load pressure is given by o  [1  0.91 (0.25   + (Aa/t} ) ~ ( t!R~) l p                [1+ (R/(2t} })
+0.345(a,/t)
For materials with a yield strength oz greater than 85 ksi, set oy equal to 85 ksi in this equation. This equation for p is valid for 0 s za/'t s 0.25.
These equations for p are valid for 0.20 s a,/t s 0.50, and include the effect of pressure acting on the flaw faces.A-4333 EVALUATION USING CRITERION FOR FLAN STABILITY Calculate the value of the J-integral at the onset of flaw instability, J', by following A-4331 using a pressure p, in equations (5)and (6)equal to the accumulation pressure for Level A and B Service loadings, pand a safety factor (SF)on pressure equal to 1.25.Calculate the internal pressure at the onset of flaw instability, p, by following A-4332.The acceptance criterion based on flaw stability in A-2000(a)(2) is satisfied when the following inequality is satisfied.
A-4323     EVALUATION USING CRITERION FOR       FLAN'TABILITY Assessment points shall be calculated for each loading condition according to A-4322, and plotted on Figure A-4320-1 as follows. Plot a series of assessment points for various amounts of ductile flaw growth ba up to the validity limit of the J-R curve.
p>I 25p, ARTICLE A-5000 LEVEL C AND D SERVICE LOADINGS The possible combinations of loadings and material properties which may be encountered during Level C and D Service loadings are too diverse to allow the application of pre-specified procedures and it is recommended that each situation be evaluated on an individual case basis.A-19 0
Use a pressure p equal to the accumulation pressure for Level. A and B Service loadings, p and a safety factor (SF) on pressure equal to 1.25. When one or more assessment points lie inside the failure assessment curve, the acceptance criterion based on flaw stability.
Instability.Material JR vs TR Jtc Applied J vs T FIGURE A-4330-1 ILLUSTRATION OP THE J-INTEGRAL/TEARING MODULUS PROCEDURE A-20 A
in A-2000(a)(2) is satisfied.
83 Appendix B ASME Working Group on Flaw Evaluation Draft Modification to Article A-3000  
 
/r TABLE A-4320-1 COORDINATES OF THE FAILURE ASSESSMENT DIAGRAM CURVE OP FIGURE A-4320-1 K
0.000          1.000 0.050           1  F 000 0.100           0.999 0.150          0.998'.996 0.200 0.250           0.993 0.300           0.990 0.350           0.987 0.400           0.981 0.450           0.973 0.500          0.960 0.550          0.939 0.600          0.908 0.650          0.864 0.700          0.807 0.750          0.737 0.800          0.660 0.850          0.581 0.900          0.505 0.950          0 '35 1.000          0.374 1.050          0.321 1.100          0.276
: 1. 150'.       0.238 A-15
 
Js 1.2 1.0, 0.8 0.6 K,
0.4 0.2 0.0 0.0 0.2   0.4   0.6     0.8 1.0   1.2   1.4 S,
FIGURE A-4320-1     FAILURE ASSESSMENT DIAGRAM FOR THE ONE-QUARTER MALL THICKNESS FLAN A-16
 
J A-4330     J-ZNTEGRAL/TEARZNG MODULUS PROCEDURE This procedure is restricted to a postulated depth equal to one-quarter of the wall. thickness.
initial  flaw A-4331     J-ZNTEGRAL AT FLAN ZNSTABZLZTY 1
Referring to Figure A-4330-1, the onset of. flaw instability is the point of intersection of the applied and material curves plotted on a graph of the J-integral versus tearing modulus (J versus T). The expression for the applied J/T curve is given by J = (1000 V t Oi/Z) T                           (4) where oi     is a   reference     flow stress which is set to     85 ksi in equation (4).       For axial flaws p =     0.235(l   +   (0.083 x 10 ')(CR)t'/((SF)p,)J         (5) where p,   is the pressure under evaluation.           Equation (5) is valid for 6 s     t s 12 in.,~  2.25 s ((SF)p,) s 5.00
                                ~                          ksi, and 0 s (CR) 100 ~ F/hour.
For circumferential flaws
        ~             ~
V   =   0.21(1 + (0.257 x 10 ) (CR)t /((SF)p,)     J         (6)
Equation (6)
: ksi, t
is valid for 6 s s 12 in., 2.25 s ((SF)p,) s 9.00 and   0 s (CR) s 100 F/hour. Equations (4), (5) and (6) are based on     material properties which are characteristic of reactor pressure vessel steels.
The   tearing     modulus for the material           is determined by differentiation of the           J-R curve with respect     to flaw depth a.
(Z/(1000 Qi )) dJ/da                   (7)
The- same values for Z and oi shall be used in equations (4) and (7). The J-integral versus tearing modulus J~/T~ curve for the material is given by plotting J against T~ for a series of increments in ductile flaw growth.                 Each coordinate for JR is evaluated at the same amount of ductile flaw growth as the coordinate for       T~.
 
/
The'value of the J-integral at the onset of flaw instability,
            ~
J', corresponds to the intersection of the applied J/T curve given
                                    ~                ~              ~
by equation (4) with the material J~/T~ curve, as illustrated in
                                ~                  ~                    ~
:
Figure A-4330-1.         ~
h The     J-integral at the onset of flaw instability may be determined analytically when a power-law curve fit to the J-R curve of the form J-     Ci(ha) +
is available. The J-integral at the                     onset of flaw instability, J, in this case is given by A-4332     ZNTERNAL PRESSURE AT FLAN ZNSTABZLZTY The   calculation of the internal pressure at the onset of flaw
                              ~            ~
instability is based on the value of the J-integral at. the onset of
                    ~
flaw instability, J . The ductile flaw growth at the onset. of flaw
        ~              ~                          ~
instability, ha, is taken from the J-R curve. The effective flaw depth at the onset of flaw instability includes the ductile flaw growth b.a', and           is given   by a       =     0.25t   + ha   +     (1/(6n)) fZ'8'/(1000 o~'))
The stress intensity factor due to radial thermal gradients at the onset of flaw instability, Zi for axial:or circumferential flaws is given     by .."
Zzi   =     ((CR)/1000) t~'~     Z'~
                =     0.584 + 2. 647(a,'/t) 6.294(a,'/t)~ + 2.990(a,'/t)~
This equation for'Ri, is valid for 0.20 ~ a,/t ~ 0.50,'nd 0 s (CR) s 100'F/hour. The stress intensity factor for small-scale yielding due to internal pressure at the onset of flaw instability, Eppes is given by
 
,0 For a given value of       K,'~, the internal pressure at the onset of flaw instability   for axial flaws is given by p     =   Ksp / ((1   + (R,/t)) (za )o.s F,']
F~ . =   0.982   +,, 2. 006(a,/t)~
and for circumferential flaws             by
                                /
p = Ki ((1 + (Ri/(2t))) (za,)                 '~   J F'         0.885 + 0.233(a,/t) + 0.345(a,/t)
These equations     for p are valid for 0.20 s a,/t s 0.50, and include the effect of pressure acting on the flaw faces.
A-4333   EVALUATION USING CRITERION FOR FLAN STABILITY Calculate the value of the J-integral at the onset of flaw instability, J',       by following A-4331 using a pressure p, in equations (5) and (6) equal to the accumulation pressure for Level A and B Service loadings, p and a safety factor (SF) on pressure equal to 1.25. Calculate the internal pressure at the onset of flaw instability, p, by following A-4332.                             The acceptance criterion based on flaw stability in A-2000(a)(2) is satisfied when the following inequality is satisfied.
p     >   I 25p, ARTICLE A-5000 LEVEL C AND D SERVICE LOADINGS The possible combinations of loadings and material properties which may be encountered during Level C and D Service loadings are too diverse to allow the application of pre-specified procedures and   it   is recommended that each situation be evaluated on an individual case basis.
A-19
 
0 Instability
                          .Material JR vs TR Jtc Applied J vs T FIGURE A-4330-1 ILLUSTRATION OP THE J-INTEGRAL/TEARING MODULUS PROCEDURE A-20
 
A 83 Appendix B ASME Working Group on Flaw Evaluation Draft Modification to Article A-3000
 
ART<.CI,E A.-3OoO NETHOD FOR Es DETERMINATION pg~W                CV r    iH      ABC&
A-3100      SCOPE A-3100        SCOPE Thia Aructe provider a method for calculating atrcaa intcnrity This Atticle provides a method for calculating stress  factor K< from the reprerenrartve arreraer at the flaw location intensity factor Kr from the membrane and bending          determined from arrear analysis. More aophirticatcd techniques may be stresses determined from stress analysis.                  used ln determining I4 pmvldcd the methods aed aeatyaea are documented.
f A-3MO                                                    h-3200        STQBSES STRE55ES The stresses at the flaw location should be resolved            (a) For the caro of a subsurface fiaw, th atromca at the flaw into membrane and bending stresses with respect to the    location shall be resolved into membrane and bending atrcrrca with respect to the wall thlcknecr. Rertduat strcasca and applied arrccaca wall thickness. Residual stresses and applied stresses    from all fonna of loadmg, including pressure arreaaee and chddag.
from all forms of loading. including pressure stresses,    induced atrearor, abaQ be oonrutcred. For nonlinear strcaa varianres thermal stresses. discontinuity stresses. and cladding    through the wall, the actual arreaa distributio can be conaervanvely induced stresses. should be considered. ln the case of    approximated      by the linearization techruque illuarrared in Fig. h-3200-1(b). The bncariaed atrea'e dtrrributton ahoutd rbcn be a nonlinear stress distribution through the wall, the ac- characterised by the membrane atrcaa e'nd the beudurg arreea g aa tual stress distribution should be conservatively ap-    rhown in Fig. A-3200.1(b).
proximated using the linearigation technique illustrated in Fig. A-3200-1. The linearized stress distribution                (b) For the care of a surface flaw, rhe arrerrca at the flaw location shall be reprerrntrd by a polynornlat fit given by the foUowiag should then be charicterized by the membrane stress      relationship:
cr and thc bending stress era, as shown in Fig.
A-3200-1  ~
o  - A, ~ A,x        ~  A,xa    -A,x' where x is the dirrauce through tho wall and AA,. Aand A, are constants. The derermiua6on of codflcteors Ao through          +  rhall provide a conservative reprrccntation of atrear over rhe crack one 0 c x 4 a for au vat~ of crack dcptha covered by the analysis.
Stresrea from aourcea iMocr&d ln A-3200(a) ahall be coasidcrcd. ln the case whra a nonlinear arrcaa dlarrlbutiou la dlfflcuttto fit be Eq. 1, thc actual dlrrribunon can be coeacrvarlvely appro6rnared by 0>>
hncarizatlon rcchntquo Ulurrrared tn Figure A-3200 t(a) fottowteg the diacuaaion given tn h-3200(a) for aubcuzface flawa.
 
A-3300        STRESS INTENSITY EQUATION                                    h-3300        SIILESS INTENSITY FACTOR EQUATIONS (a) Stress intensity factors for the Aaw model should be calculated from the membrane and bending stresses                                  The flaw shall be tepteseated by an elGpse that cbcumacdbaa at the flaw location using the following equation:                          the detected flaw as  iilutttated in Fig. A 3300 1. The stress iattosity iactots for the flaw model shall bo detencined ftom the stresses and K/~e NYrr~alQ+ tr>M>Va'Valg                                  (I)    flaw geometry as desctibed ia h-3310 for subsurface flaws aad ln h-3320 for sutfaco flaws.
where cr, tre~ membrane    and bending stresses. psi. in ac-                h-3310        Subsuttace Flaw Equations cordance 'with A-3200 a minor haifdiamcter, in., of embedded                                    (a) Stress attensity factors for subsurface flaw shall be calculated from tho as:mbrane and beading suesses at the fLaw location flaw: flaw depth for surface flaw by the following cquatioa:
Qmflaw shape parameter as determined fmm Fig. A-3300-l using (tr+ rr,)/a, and the Raw geometry                                                                      a    toMm + ob        Mbj f~ 0/0            (2)
M =correction factor for membrane stress (sce Fig. A-3300-2 for subsurface flaws; Fig. A-3300-3 for surface flaws)          ~
where, factor for bending stress (see
                                                  'emcorrcction Fig. A-3300-4 for subsurface laws: Fig. A-            ~              0>>  IJg    Membrane and beading stresses ia accordance with 3300-5 for surface flaws)                                    A-3200(a)
      %here variations in K/ amund thc periphery of
                  ~  ~                                                            a                Minor halMmnetes M                Conection factor for membrane sttess glvcat in occur. thc maximum value is to be used.
D                                                  ~
Fig. A 3200-2
                            ~
(c) The use of Eq. (1) is only a tecomn>>ndation for
                        ~
M,                Conection factor for beading stress givtst in determination of A'/. More sophisticated techniques may
                                                  ~
Pig. h-3200.3 bc used, provided the methods and analyses are doc-                                Q                Flaw sbapo pataateter as given by Eq. 3 urnented. In many cases involving complex geometries                    The flaw shape panttnctct Q is calculated firom the following equatioa:
and sttess distributions, the methods outlined above may be inadequate.
Q        1  -  4.598 (a/>)' - q whete a/r is the flaw aspect ratio 0 s a/r    s'8, aad q, is the ptastic soue cottectioa factor equal to 0.212 I (o      + eJ / o)'.
(b) Whete variatioas ia K, around the pcriphetv of tbe flavv occur. the maximum value is to be used ia the delcnniaatioa of tbe ctiticat flaw luuamctcra a, and +.
(c) The uso of Eq.2 is only a tecomaamdatioa foe detenainatioa of Kv Ia some cases iavolviag comptca geometries and sttess distribution. the method outlined above may aot be adequate.
 
I A.3320        Sur&ce Flaw Equations (a) Stress intensity factors for strrfsce flaws should be calculated from the cubic polyaoaual stress relation by the followieg equstl orv (4)
K      QOo'A t3tarAtotat AsOsaj~x Crack depth A, AAs, A,          ~ Coefficieats from Eq.      1 that ~utsrtsrts the stress distribution over the crack (0 s.x5a)
Oor  Oo Gte Or          Free surface correction factors for tbe given stress variation provided ia Tables A-3320 1 and A.3320.2 as a function ot flaw aspeN ratio a/f, crack eaetration s/t, aad crack tip positiott (PTL aad F72)
Q                        Flaw shape psrstaetcr ss given by Eg. 3 with q, defiaed  as 0.212  [A,/trP (b) ~      the Line Iraaen method ls used to convert tho actual stress fieM into tr aad tr, stresses as illustrated ia Hg. A-3200-1(a),
then Eq. 2 shall be Used to calculate )(t with tho followingequations for M, Msrd Q:
M Mi        Go  2 (a/t) Gr Q    ~    Sq.3whereq,isdefinedas0.212((re+
                                                                    ~/o'e)
              %hue variation ia Kr sra the peripher of the fLaw occur, the trLaxitaum value is to be used ia the detertainatlon of a, aad tt (d) The uso of the above methods Is only a recotrutMadatlcsr for determination of Q. ln some cases iavolviag comply geotnesries and stress    duuribunons. the methods outlined above may nce be adequate.
 
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lr 3la  '.j o62 os o bP(    p($ 2/    44 7    0(783    '0 o 7r"b  ohio    . ob7(          7/7
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G FUNCTION RESULTS FOR  A/L=O.1 CfKK TlP  PT1 a  Shiratori, o  Raju-Newman
        +  Extropofated Point 1.4 G2 .
G3 0.4 Q.Q O.Q S.1    0.>    0~  0.4  u n        0,7  OZ QS  u)
Crack Oepth a/t
 
~e J


ART<.CI,E A.-3OoO NETHOD FOR Es DETERMINATION pg~W CV r iH ABC&A-3100 SCOPE This Atticle provides a method for calculating stress intensity factor Kr from the membrane and bending stresses determined from stress analysis.A-3100 SCOPE Thia Aructe provider a method for calculating atrcaa intcnrity factor K<from the reprerenrartve arreraer at the flaw location determined from arrear analysis.More aophirticatcd techniques may be used ln determining I4 pmvldcd the methods aed aeatyaea are documented.
                  . G FUNCTION RESULTS FOR    A/L=0.1 2.0 CRACK TlP PT2 0  Shiratori o  Raju-Neo<man
f A-3MO STRE55ES The stresses at the flaw location should be resolved into membrane and bending stresses with respect to the wall thickness.
          +  Extrapolated Point g  U
Residual stresses and applied stresses from all forms of loading.including pressure stresses, thermal stresses.discontinuity stresses.and cladding induced stresses.should be considered.
)'
ln the case of a nonlinear stress distribution through the wall, the ac-tual stress distribution should be conservatively ap-proximated using the linearigation technique illustrated in Fig.A-3200-1.The linearized stress distribution should then be charicterized by the membrane stress cr and thc bending stress era, as shown in Fig.A-3200-1~h-3200 STQBSES (a)For the caro of a subsurface fiaw, th atromca at the flaw location shall be resolved into membrane and bending atrcrrca with respect to the wall thlcknecr.
0.6 0.4 G2 0.0 0.1   0.2    03    OA  0.5  0.6    0.7  03 09 IQ Crack Depth  a/t
Rertduat strcasca and applied arrccaca from all fonna of loadmg, including pressure arreaaee and chddag.induced atrearor, abaQ be oonrutcred.
For nonlinear strcaa varianres through the wall, the actual arreaa distributio can be conaervanvely approximated by the linearization techruque illuarrared in Fig.h-3200-1(b).
The bncariaed atrea'e dtrrributton ahoutd rbcn be characterised by the membrane atrcaa e'nd the beudurg arreea g aa rhown in Fig.A-3200.1(b).(b)For the care of a surface flaw, rhe arrerrca at the flaw location shall be reprerrntrd by a polynornlat fit given by the foUowiag relationship:
o-A,~A,x~A,xa-A,x'where x is the dirrauce through tho wall and AA,.Aand A, are constants.
The derermiua6on of codflcteors Ao through+rhall provide a conservative reprrccntation of atrear over rhe crack one 0 c x 4 a for au vat~of crack dcptha covered by the analysis.Stresrea from aourcea iMocr&d ln A-3200(a)ahall be coasidcrcd.
ln the case whra a nonlinear arrcaa dlarrlbutiou la dlfflcutt to fit be Eq.1, thc actual dlrrribunon can be coeacrvarlvely appro6rnared by 0>>hncarizatlon rcchntquo Ulurrrared tn Figure A-3200 t(a)fottowteg the diacuaaion given tn h-3200(a)for aubcuzface flawa.


A-3300 STRESS INTENSITY EQUATION (a)Stress intensity factors for the Aaw model should be calculated from the membrane and bending stresses at the flaw location using the following equation: K/~e NYrr~alQ+
0 G FUNCTiON RESULTS FOR    A/L=D.2 CRACK-TlP PT3 Shiratori 0  Raju-Newman' Extrapolated Point Q
tr>M>Va'Valg (I)where cr, tre~membrane and bending stresses.psi.in ac-cordance'with A-3200 a minor haifdiamcter, in., of embedded flaw: flaw depth for surface flaw Qmflaw shape parameter as determined fmm Fig.A-3300-l using (tr+rr,)/a, and the Raw geometry M=correction factor for membrane stress (sce Fig.A-3300-2 for subsurface flaws;Fig.A-3300-3 for surface flaws)~'emcorrcction factor for bending stress (see Fig.A-3300-4 for subsurface laws: Fig.A-D~~~~~~~3300-5 for surface flaws)%here variations in K/amund thc periphery of occur.thc maximum value is to be used.(c)The use of Eq.(1)is only a tecomn>>ndation for determination of A'/.More sophisticated techniques may bc used, provided the methods and analyses are doc-urnented.In many cases involving complex geometries and sttess distributions, the methods outlined above may be inadequate.
Hl CD Og 0.4 0.2
h-3300 SIILESS INTENSITY FACTOR EQUATIONS The flaw shall be tepteseated by an elGpse that cbcumacdbaa the detected flaw as iilutttated in Fig.A 3300 1.The stress iattosity iactots for the flaw model shall bo detencined ftom the stresses and flaw geometry as desctibed ia h-3310 for subsurface flaws aad ln h-3320 for sutfaco flaws.h-3310 Subsuttace Flaw Equations a toMm+ob Mbj f~0/0 (2)where, 0>>IJg A-3200(a)a M Fig.A 3200-2 M, Pig.h-3200.3 Q Membrane and beading stresses ia accordance with Minor halMmnetes Conection factor for membrane sttess glvcat in Conection factor for beading stress givtst in Flaw sbapo pataateter as given by Eq.3 The flaw shape panttnctct Q is calculated firom the following equatioa: Q 1-4.598 (a/>)&#x17d;-q(a)Stress attensity factors for subsurface flaw shall be calculated from tho as:mbrane and beading suesses at the fLaw location by the following cquatioa: whete a/r is the flaw aspect ratio 0 s a/r s'8, aad q, is the ptastic soue cottectioa factor equal to 0.212 I (o+eJ/o)'.(b)Whete variatioas ia K, around the pcriphetv of tbe flavv occur.the maximum value is to be used ia the delcnniaatioa of tbe ctiticat flaw luuamctcra a, and+.(c)The uso of Eq.2 is only a tecomaamdatioa foe detenainatioa of Kv Ia some cases iavolviag comptca geometries and sttess distribution.
    .0 Oo O.~   0.2     0,3   04  Oa  0.S    07  Oa 09 ]a Crack Depth  a/t
the method outlined above may aot be adequate.
I A.3320 Sur&ce Flaw Equations (a)Stress intensity factors for strrfsce flaws should be calculated from the cubic polyaoaual stress relation by the followieg equstl orv (4)K QOo'A t3tarAtotat AsOsaj~x Crack depth A, AAs, A,~Coefficieats from Eq.1 that~utsrtsrts the stress distribution over the crack (0 s.x5a)Oor Oo Gte Or Q with q, defiaed as Free surface correction factors for tbe given stress variation provided ia Tables A-3320 1 and A.3320.2 as a function ot flaw aspeN ratio a/f, crack eaetration s/t, aad crack tip positiott (PTL aad F72)Flaw shape psrstaetcr ss given by Eg.3 0.212[A,/trP (b)~the Line Iraaen method ls used to convert tho actual stress fieM into tr aad tr, stresses as illustrated ia Hg.A-3200-1(a), then Eq.2 shall be Used to calculate)(t with tho following equations for M, Msrd Q: M Mi Go 2 (a/t)Gr Q~Sq.3whereq,isdefinedas0.212((re+
~/o'e)%hue variation ia Kr sra the peripher of the fLaw occur, the trLaxitaum value is to be used ia the detertainatlon of a, aad tt(d)The uso of the above methods Is only a recotrutMadatlcsr for determination of Q.ln some cases iavolviag comply geotnesries and stress duuribunons.
the methods outlined above may nce be adequate.


O(O P 2 0 5/oui/Ao/D<gd/io2//M8'.j o62 lr 3la'.os o bP(o 7r"b/ail p($2/44 7 ohio.ob7(0 i/07 O(7Sk o&#xc3;8 d/Co 0(783'0 7/7 47~733 d.7&8 Oi$28 o st o 81K o,pe o.g/I d,see o sory b WS 0(~6 d 6&2 d,bob o ssP o(A%7 o.br'WZ o 07b o.b(7 O.358 o gs/oi470 0 (52.2 OA02 o 082 o,<bO b 988 o 5z7 d.SQ o scan y(S30
0 FUNCTII3N RfSULTS FOR  A/L=02 2.0 CRACK TlP PT2 0 Shiratori o Roju-Newman e  Extrapolated Point 0.4 G4
  . 0,0 0.1  02      03    0.4  0.5  0.6  07  B 09 5 Crack Oapth a/t


7H/3t 5 p-33g0-2.OiO o./'ig dE gni arm d 0 oi 2 d 5 o,8 c-&7 e 7g o sII o 784 o 8'Ib uf&S I, 2hZ,/i&9/./~V/150 l zw7 g.Qd0 , l/f)81 V oi0 0.0'/3 o.o&o./gE d 27'./zs o./27 o/85 0>75 a./7g g, 200 o.zzf o 2&8 walrus.P c 6~d jg gi Q yc5 o8 8.0/$'i 023 d, 055 o//3'.d38 o, ov4 ,QiO'U oiI/2.O,o&2 Oi d7$ch odg o./04 y0 ot2 dc+o, 8'.oo&o.o/0 geg29 d,ae0 O.O/g o 022 dcO38 y, oS'P o.os4 Oi 0+Oc 0~d cOS"j
f G FUNCTION RESULTS FOR    A/L=0.3
  '2.0 CRACK TIP PT1 o Shirotori o Raju-Newman 1,6      +  Extrapotated Point 1.4 00 1+2 1.0
-  0.8 0,6 0.2
                                    .
0.0 0.1    02    03    0.4  0.5 0.6  0,7  03 0.9 1.0 Crack Depth a/t


G FUNCTION RESULTS FOR A/L=O.1 1.4 CfKK TlP PT1 a Shiratori, o Raju-Newman
G FUNCTION RESULTS FOR     A/L=D3 2,0 CRACK TIP PT2 c3 Shiratori 0  Raju-Newman
+Extropofated Point G2.0.4 G3 Q.Q O.Q S.1 0.>0~0.4 u n 0,7 OZ QS u)Crack Oepth a/t
        +   Extrapofated Point G]
~e J
0.2 0.0 0,0 0.1   02      03   04  0.5 0.6   07  0,8 09 $ 0 Crack Depth a/t
.G FUNCTION RESULTS FOR A/L=0.1 2.0 CRACK TlP PT2 0 Shiratori o Raju-Neo<man
+Extrapolated Point g U)&#x17d;0.6 0.4 G2 0.0 0.1 0.2 03 OA 0.5 0.6 0.7 03 09 IQ Crack Depth a/t 0
G FUNCTiON RESULTS FOR A/L=D.2 CRACK-TlP PT3 Shiratori 0 Raju-Newman' Extrapolated Point Q Hl CD Og 0.4 0.2.0 Oo O.~0.2 0,3 04 Oa 0.S 07 Oa 09]a Crack Depth a/t  


0 FUNCTII3N RfSULTS FOR A/L=02 2.0 CRACK TlP PT2 0 Shiratori o Roju-Newman e Extrapolated Point 0.4 G4.0,0 0.1 02 03 0.4 0.5 0.6 07 B 09 5 Crack Oapth a/t f
0 G FUNCTIQN RESULTS FQR    A/L=D.5 2.0 I            I CRACK TIP PT5 1,8      0 Shiratori o Roju-Newman
G FUNCTION RESULTS FOR A/L=0.3'2.0 1,6 1.4 1+2 1.0-0.8 CRACK TIP PT1 o Shirotori o Raju-Newman
        +  Extrapoloted Point U
+Extrapotated Point 00 0,6 0.20.0 0.1 02 03 0.4.0.5 0.6 0,7 03 0.9 1.0 Crack Depth a/t  
1.0 0,4 0,2 0,0 oa O.~  Oa      O,Z  a.4 O,S  0.6  0.7 03 09 I Crack Depth a/t


G FUNCTION RESULTS FOR A/L=D3 2,0 CRACK TIP PT2 c3 Shiratori 0 Raju-Newman
G FUNCTION RESULTS FOR   A/L=O.5 2.0 CfIACK Te Pt2 1.8      0 Shirotori 0 Raju-Headman
+Extrapofated Point 0.2 G]0.0 0,0 0.1 02 03 04 0.5 0.6 07 0,8 09$0 Crack Depth a/t 0
            +   Extrapolated Point GO
G FUNCTIQN RESULTS FQR A/L=D.5 2.0 1,8 I I CRACK TIP PT5 0 Shiratori o Roju-Newman
.=  1ll 0.6 02
+Extrapoloted Point U 1.0 0,4 0,2 0,0 oa O.~Oa O,Z a.4 O,S 0.6 0.7 03 09 I Crack Depth a/t  
    .0 0.0 0.1   02     03   0.4  0.5 (M    0.7   (M 09 5 Crack Depth a/t


2.0 1.8 G FUNCTION RESULTS FOR A/L=O.5 CfIACK Te Pt2 0 Shirotori 0 Raju-Headman
G FUNCTION RESULTS FOR AjL=D.D 4.0 CRACK TlP PT1 x  Tgdg 3.9 1.0 0.0 00 0.$  02   03   0.4   0.5 0.6  07  08 09 Ul Crxk  Depth a/t
+Extrapolated Point GO.=1ll 0.6 02.0 0.0 0.1 02 03 0.4 0.5 (M 0.7 (M 09 5 Crack Depth a/t  


G FUNCTION RESULTS FOR A jL=D.D 4.0 CRACK TlP PT1 x Tgdg 3.9 1.0 0.0 00 0.$02 03 0.4 0.5 0.6 07 08 09 Ul Crxk Depth a/t 8%0}}
8%
0}}

Revision as of 22:34, 21 October 2019

Final Rept, Elastic-Plastic Fracture Mechanics Assessment of Nine Mile Point Unit 1 Beltline Plates for Service Level C & D Loadings.
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NMPC Project 03-9425 MPM-USE-293216 FINAL REPORT entitled ELASTIC-PLASTIC FRACTURE MECHANICS ASSESSMENT OF NINE MILE POINT UNIT 1 BELTLINE PLATES FOR SERVICE LEVEL C AND D LOADINGS MPM Research dr ConsuIting wi<~~~'//j~j~~Zp/>>

February 22, 1993 PDR P 'DR 9303040ih7 '730226

.ADQCK.05000220

3 Table of Contents 1.0 Introduction ~ \ ~ ~ ~ ~ ~ ~

2.0 Material Model .

3.0 Transient Selection 7 3.1 Level C Transient Selection .... 7 3.2 Level D Transient Selection .... 7 3.3 Screening Analysis 8 3.3.1 Model Description.......... 8 3.3.2 Level C Transient Analysis 9 3.3.3 Level D Transient Analysis 9 3.3.4 Summary of Candidate Transients 10 4.0 Finite Element Analysis ..........,....... 26 4.1 Model Description .. 26 4.2 Finite Element Analysis Results 26 4.3 Limiting Transients ............ 27

'lastic-Plastic Fracture Mechanics Assessment ..... 39 5.1 Model Description.... 39 5.1.1 Vessel Geometry............ 39 5.1.2 Applied Loads 39 5.1.3 Limits for Small Scale Yielding Analysis 40 5.1.4 Fracture Mechanics Model........ 40 5.2 Calculations for A302B Material Model...... 43 5.2.1 Level C Loading...... 43 5.2.2 Level D Loading Analysis,......... 43 5,2.3 Tensile Instability Analysis 43 6.0 Summary and Conclusions t

................... 52

'.0 References ................... 54 Acknowledgement ......... 56 Appendtces ...................

+0 57 Appendix A 58 Appendix B ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 83

1.0 Introduction Nuclear reactor pressure vessel materials must be tested and evaluated to ensure that they are safe in terms of both brittle and ductile fracture under normal operation and during design basis transients. With regard to ductile fracture protection, Appendix G to 10 CFR 50 prescribes a screening criterion of 50 ft-lbs. If any beltline materials are expected to exhibit Charpy Upper Shelf Energy (USE) (T-L orientation) lev'els below 50 ft-lbs, then additional analyses must be performed to ensure continued safe operation. The Draft ASME Appendix X [ASME92] was developed to assist licensees in performing elastic-plastic fracture mechanics evaluations for beltline materials with low upper shelf energies. This report documents application of the draft Appendix X calculative procedures and criteria to two Nine Mile Point Unit 1 (NMP-1) beltline plates for Service Level C and D loadings.

The NMP-1 beltline materials were evaluated to determine whether any materials would exceed the 50 ft-lb screening criterion. The results of these evaluations are summarized in Reference

[MA93] and were presented in the response to NRC Generic Letter 92-01 [MA92]. As a result of these evaluations, NMPC concluded that an Appendix X analysis must be performed for beltline plates G-8-1 and 6-307-4. The results of the Appendix X analysis for Service Level A and B loadings were reported in Reference [MA93]. This report presents the results of the Service Level C and D loading analysis.

/

2.0 Material Model The NMP-1 beltline plates were fabricated using A302B modified (A302M) steel. At present, sufficient J-R data are not available to construct an A302M model. As discussed in Reference

[MA93], the NMP-1 plates are best modelled using an A302B J-R material model. The A302B material model is fully described in Reference [MA93]. For Service Level C loadings, the J-R curve inputs are two sigma lower bound curves which are the same as for Service Levels A and B. However, for Service Level D analysis, Reference [ASME92] allows the use of J-R curves which are a best estimate representation for the vessel material being analyzed. Therefore, the best estimate, or mean, J-R curves, as a function of USE level, were determined. The J,c versus USE model reported in Reference [MA93] was used to calculate the mean J,c data given in Table 2-1. The 6T JD-ha data reported in Reference [HI89] were used to determine the J-R curves at the USE levels shown in Table 2-1. The 6T JD-ha data were reduced or increased by the difference between the 6T test J<<value (525 in-lb/in') and the J,c data listed in Table 2-1. The yield stress, modulus, and Poisson ratio used in the analysis are identical to the Reference

[MA93] data.

Table 2-1 Mean J,c Data as a Function of USE Level USE -LBS ~J -LB 10 79.2 20 158.3 30 237.5 40 316.6 50 395.8 60 474.9

'0 554.1 80 633.2 90 712.4 100 791.5

>p 3.0 Transient Selection The ASME draft Appendix X does not specify procedures for calculating Level C and D service loadings since the combinations of loadings and material properties encountered in practice are too diverse. Therefore, the most limiting transients for Levels C and D, from a ductile fracture perspective, were identified as follows:

The NMP-1 and NMP-2 plant documentation was carefully examined to identify potential limiting transients.

A screening calculation was then performed to reduce the spectrum of transients to a few most likely candidates.

Finite element calculations were performed on the reduced set of transients to determine the most limiting Level C transient and the most limiting Level D transient and the resultant loading.

3.1 . Level C Transient Selection The NMP-1 and NMP-2 updated FSARs and thermal cycle diagrams were reviewed to determine a spectrum of candidate Level C transients for further analysis. Prior to performing the screening calculations, it was not clear whether the rapid pressure loss transients or the slow depressurization transients would provide the largest combined pressure and,thermal gradient loads. Therefore, the transients shown in Figure 3-1 were chosen for analysis since they bound all Level C transients in terms of cooldown rate.

Table 3-1 lists the temperature/pressure variation at various times during the transient.

The classification of the automatic blowdown transient and emergency cooldown transient as Level'C events is consistent with the definition of the emergency condition transients.

, Figure 3-1 includes two events described in the Unit 1 updated FSAR (References

[FSAR] and [CENC]) and the Unit 2 (References [STRS] and [TCD]) emergency condition automatic blowdown.

3.2 Level D Transient Selection As with the Level C transient selection, the Level D transients were selected after careful examination of the NMP-1 and NMP-2 plant documentation. A set of transients were chosen which bound all Level D events in terms of cooldown rate. Plots of the selected transients are shown in Figures 3-2 through 3-5 (pressure/temperature profile data are also given in Tables 3-2 and 3-3.) The NMP-2 faulted condition events are specified based on the Reference [NEDC] analysis. The events included for consideration include the break spectrum for the recirculation line breaks, the steam line break, core spray line break, and the feedwater line break.

tp 3.3 Screening Analysis 3.3.1 Model Description The transients described earlier were analyzed using a simple linear elastic fracture mechanics model to determine those transients which require a detailed finite element analysis to determine the limiting loads. The temperature difference across the vessel wall for the Level C transients was calculated using the TRUMP/MPM code [TRUMP]. The NMP-1 vessel was modelled using cylindrical coordinates, The vessel is 7.281 in. thick with an inner radius of 106.5 inches. The 0.1563 in. stainless steel liner was modelled as having the physical properties of 316 SS, and the rest of the vessel thickness was modelled as A302B ferritic steel. A total of 17 radial nodes, each of approximately OA4 in. thickness, were used to discretize the vessel thickness. A nodel temperature boundary condition was applied at the ID surface of the vessel. The surface node was modelled as being in thermal equilibrium with the downcomer fluid temperature.

This assumption leads to conservative through wall gradient estimates, particularly for the Level D transients during which phase change occurs. Therefore, the initial temperature of all vessel nodes were set to 500'F.

Once the temperature difference across the wall was calculated, the relative contribution of the pressure loading and the thermal loading was approximated using the linear elastic fracture mechanics model given in Appendix G to the ASME code. It should be emphasized that these equations are based on linear elastic fracture mechanics principles and are strictly applicable for thermal ramps of up to 100'F/hr. Nevertheless, for screening purposes, these equations are adequate for assessing the relative contributions of the pressure and thermal loads to the total crack tip stress intensity for the various Level C and D events.

Appendix G uses the following equations to calculate the stress intensities:

I K = K~ + K~

where, K~ = Ma = membrane stress intensity factor (ksi V in)

K~ = MT bT = stress intensity factor due to thermal gradient (ksi 0 in)

M= ASME membrane factor (0 in)

MT = ASME thermal factor (ksi 0 in/'F)

lpe

!

bT = temperature difference across vessel wall ('F) o= stress (ksi)

(A~ + B~)

(3-2)

(B~ A2)

A = vessel inner radius (in.)

B = vessel outer radius (in.)

P = internal pressure (psig)

Since the Appendix X flaw growth criterion is more severe at deep crack depths under Level C and D event loads, the screening calculations were performed assuming a one-quarter thickness flaw. This flaw exceeds the deepest postulated flaw analyzed under the Level C and D analysis.

3.3.2 Level C Transient Analysis The blowdown transients are terminated when the pressure reaches 35 psig to account for the containment pressure level at that time in the transient. In the TRUMP/MPM calculations, these transients were extended to longer times, conservatively assuming a 300'F/hr cooldown to a 212'F vessel ID temperature.

The thermal gradient and pressure data for the Level C transients are summarized in Table 3-4. Based on the data in Table 3-4, the 250'F/7.5 min. Blowdown and the Thermal Transient Blowdown are limiting in terms of ductile fracture.

Therefore, detailed finite element calculations were performed for both of these transients to determine the most limiting vessel wall stress distribution.

3.39 Level D Transient Analysis Since the Level D transient depressurization occurs over a relatively short time period, and it has been assumed that the downcomer fluid temperature equals the wall surface temperature for the purpose of performing a screening analysis, it was not necessary to perform a thermal transient heat transfer analysis for the Level D transients. Based on the Level C analysis results, the vessel wall bT is approximately equal to 528'F minus the current downcomer fluid temperature for the initial five minutes of the transient. Therefore, the crack tip stress intensities can be calculated directly. It should be recognized that these assumptions are increasingly over-conservative after the initial five minutes of the transient.

The results of the stress intensity factor calculations for the Service Level D

10 transients are shown in Tables 3-5 and 3-6. Based on these calculations, the Steam Line Break Transient, NMP-2 Recirculation Line Break Transient, and the NMP-1 Recirculation Line Break Transient were analyzed in further detail using the finite element method. The other transients yield lower peak stress intensities.

In addition, the stress intensity factor estimates for the other transients are very conservative since a significant portion of the transient is spent in a steam forced convection and/or subcooled free convection heat transfer regime.

3.3.4 Summary of Candidate Transients A simplified model was developed to determine the limiting Service Level C and D transients. Perfect heat transfer between the downcomer fluid and the vessel wall surface was assumed to provide conservative estimates of the through wall thermal gradient. A quarter thickness flaw was assumed and the ASME Appendix G linear elastic model was used to estimate the crack tip stress intensities. Based on the simplified model for screening calculations, the most limiting transients, from a ductile fracture perspective, are summarized in Tables 3-7 and 3-8.

/

<x

Table 3-1 Level C Transient Temperature/Pressure Variation as a Function of Time Measured From the Initiation of the Event Emergency Condition Level C Transients Unit 1 Design Basis Unit 2 Design Basis Unit 1 Emergency Unit 1 SB-LOCA 250'F/7.5 min Thermal Transient Cooldown ADS Blowdown Blowdown Blowdown 300'F/br

((Ioo SIoooooo ((Ioo SIooooIo (lIII~ SIoo ooI ~ ((Io o SIooooI@

(IOlOoOOI( (SS(SP (IOONOOO( (SS (S( (oIkIIloo( (pS(o) (IIop (SJ (oIooO o I( SoSlA)

JOS5 0 JOSS JJdo JOSS

$ 1$ 3.3 37$ 10 $$ 6 478 730 $ 08 196 zoo g0 121 342 20 344 430 7.7 110 33$

87 JJo g5 87 318 30 191 7.$ 48 pro 20 62 29$ 40 103 330 25 $0 281 $0 $0 281 60 20 228

  • Nominal Subcooling 100% Power Rated Feedwater Temperature

0 12 Table 3-2 Level D Steam Line Break Temperature/Pressure Variation as a Function of Time Measured From the Initiation of the Event Steam Line Break Oyster Creek Analysis Reference (1) Reference (2)

Time Pressure Temp Time Pressure Temp (sec) (PSIA) OF (sec) (PSIA) oF 0 1045 528* 0 1050 552 20 660 497 70 120 350'12 40 310 420 300 0 60 200 381 450 35 281 80 130 347 100 90 320 120 60 .292 140 40 267 160 31 252 180 25 240 300 15 212 Reference 1 - NMP1 SAFER/CORECOOL/GESTR-LOCA Analysis NEDC-31456P, 1987, NMP1, Figure A017 Reference 2 - Oyster Creek Report GENE-523-70-0692 August '92 "Oyster Creek Vessel Fracture Mechanics Analysis" for upper shelf energy requirement. Figure 5-6 Page 5-13

  • Nominal Subcooling 100% Power Rated Feedwater Temperature

+c

~p 0

13 Table 3-3 Level D Recirculation Line Break Spectrum Temperature/Pressure Variation as a Function of Time Measured From Initiation of the Event Recirculation Line Break Spectrum DBA 40% DBA .05 ft ~

Tiae Prrn Trap Tiae Prnr Teap Tlae Prrss Tear Tlae Prrsr leap Ti ae Prrn Teap IINIr Prrrs Teap (eee) PS(A (sh (e eel I'SIA (rh (eeet PS(A (eh (eee) PSIA (eh (eeei PS!A reh (srr) I'SIA 1045 0 104S 0 104$ 0 104$ 0 IO4$ 1045 lo 760 S12 ddo 521 20 920 $3$ 50 $ 39 960 S40 240 S32

'20 417 660 491 $0 doo Sld 100 Sld Ido d60 S21 2do Sld 30 80 312 40 430 452 600 1$ 0 520 411 790 $ 11 130 40 40 261 50 260 404 90 400 Ido 2do 411 300 4do 463 $ 60 419

$0 20 22d 60 150 3$d 100 320 423 200 Sdl 340 440 400 44$

IS 212 70 32d 130 110 300 80 312 411 320 423 90 60 293 1$ 0 120 341 400 40 261 410 220 390 210 3ds 320 IS 212 200 110 300 40 261 80 312 Iodo 40 261

tc 4/

Table 3-4 Stress Intensity Factor Estimates for Service Level C Transients'50'F/7.5 Min. Blowdown Thermal Transient Blowdown Emergency Cooldown 300'F/hr.

Time (Min.) P hT K~ Krr K P hT K~ K P hT K~

1030 57 40 18 58 1030 91 40 29 68 1030 10 40 43 500 101 19 32 51 500 137 19 43 62 1030 15 40 45 500 146 19 46 65 169 155 49 55 1030 20 40 46 181 206 7 65 72 169 162 51 57 1030 30 40 49 33 244 1 77 78 169 167 53 59 1030 39 40 12 52 10 33 245 1 77 78 169 168 53 59 541 48 21 15 36 20 329 81 13 .25 38 30 176 107 7 34 40 40 88 120 3 38 41 50 35 130 1 41 42 60 5 140 0 44 44

'nits- P=psig; AT=max temp diff. ('F); K,=membrane stress intensity (ksi din);

K~thermal stress intensity (ksi din); K=total stress intensity (ksi din)

'eak wall thermal gradient

tC 15 Table 3-5A Stress. Intensity Factor Estimates for Service Level D Transients'lnle Steam Feed water Core Spray Recirc. Line Break Recirc. Line Break Recirc. Line Brcak Line Break Line Break Line Break NMP-2 DBA 4¹ DBA (Sec.) P hT P hT K P P AT K P 6T 10 2$ $ I 615 Sl IO 35 33 33

$5 214 3 QS Sl 10 35

$ 15 74 115 117 135 $ 70 $3 75 10 115 Ill SN 0 71 N 75 45 45 N Ia 715 S3

'nits- P=psig; hT=max temp diff. ('F); KtM=membrane stress intensity (ksi din);

Kn -thermal stress intensity (ksi din); K=total stress intensity (ksi din)

+c

~ f

16 Table 3-5B Stress Intensity Factor Estimates for Service Level D Transients'rme Steam Feedwater Core Spray Recirc. Line Break Recirc. Line Break Recirc. Line Break Line Break Line Break Line Break NMP-2 DBA 40% DBA (Sec.) P dT K P P dT K P P dT 270 715 2l 2l

~I 15 Sr 5 0 27 SIl 0

<<71 205 51 210

<<75 <<75 115 57 247

<<7l 217

<<lt <<tt SIl

<<tt <<tt SI 5

'nits- P=psig; AT=max temp diff. ( F); Km=membrane stress intensity (ksi din);

Kn -thermal stress intensity (ksi din); K=total stress intensity (ksi din)

J

'17

. Table 3-6A Stress Intensity Factor Estimates for Service Level D Recirc. Line Break 1

ft'~ 0.5 ft'ecirc.

Recirc. Line Break Transients'lmc 0.1 Line Break ft'M Recirc. Line Break 0.05 ft sec. K K~ P hT KM 10 15 35 2 37 30 50 785 10 30 3 33 885 11 37 70 585 42 13 36 75 90 385 83 15 26 41 305 105 12 33 45 785 10 30 33 945 12 36 4 120 130 155 160 50 56 140 145 150 105 187 59 63 505 57 19 18 37

'nits- P=psig; AT=max temp diff. ('F); K~=membrane stress intensity (ksi din);

Krr=thermal stress intensity (ksi din); K=total stress intensity (ksi din)

18 Table 3-6B ft'ecirc.

Stress Intensity Factor Estimates for Service Level D Recirc. Line Break 1

Line Break 0.5 ft'~

Recirc. Line Break 0.1 Transients'llllC ft'ecirc. 0.05 Line Break ft'T sec. K~ K P KlM K~ K 160 175 180 265 117 10 37 47 845 33 33 55 225 2 71 73 185 147 46 53 775 30 33 280 785 10 30

. 3 33 261 1 82 83 65 216 3 68 71 465 65 18 38 715 20 28 6 34 320 261 82 83 385 111 15 35 50 440 <316 0 385 83 15 26 41 470 205 138 8 43 51

<316 <99 <99 305 105 12 33 45 195 143 8 45 53 630 95 193 4 61 65 65 <216 3 <68 930 <316 0 1080 25 <216 1 <82 <83 1420 <316 0 <99 <99 mts- =pstg; =max temp 1 .;,=mern rane stress tntenstty st m; K~thermal stress intensity (ksi din); K=total stress intensity (ksi din)

It 0 19 Table 3-7 Level C Transients for Finite Element Analysis 250'F/7.5 Min, Blowdown'MP-2 NMP-1 Design Basis Design Basis Thermal Transient Blowdown~

Heat Transfer Heat Transfer Time Pressure Temp. Coefficient Time Pressure Temp. Coefficient (Min.) (psig) h=BTU/(hr ft'F) (Min.) (psig) P) h=BTU/Ihr fPF) 1030 528 10,000 1030 528 10,000 500 470 10,000 3.3 169 375 10,000 181 380 10,000 10 106 342 10,000 72 318 10,000 15 72 318 10,000 7.5 33 278 10,000 20 47 295 10,000 20.7 212 500 25 35 281 10,000 38.8 212 500

'MP-1 Updated FSAR

~

Reference [STRS]

ec tI

20 Table 3-8 Level D Transients for Finite Element Analysis Steam Line Break

'ecirculation Break' Line NMP-2 Recirculation Line Break' NMP-1 DBA Heat Transfer Heat Transfer Heat Transfer Time pressure Temp Coefficient Time Pressure Temp. Coefficient Time Pressure Temp Coefficient (psig) ('F) h=BTU/(hr (Sec.) (psig) ('F) h=BTU/(hr (Sec.) (psig) ('F) h=BTU/(hr (Sec.)

ft F) ft F) ft F) 1030 528 10,000 , 1030 528 69,188 1030 528 10,000 20 497- 10,000 15 35 281 164 10 512 10,000 40 295 420 10,000 20 23 264 164 15 474 464 164 60 185 381 10,000 60 23 264 164 20 285 417 164 80 115 347 10,000 100 18 256 164 30 312 164 100 75 320 10,000 200 235 164 40 25 267 164 120 45 292 10,000 300 3.5 222 164 50 228 164 140 25 267 10,000 1300 212 500 80 212 500 160 16 252 10,000 180 10 240 10,000 300 212 10,000 380 212 164 400 212 500 Reference [NEDC]

References [NMP2TC], [STRS], and [NMP1DP]

Emergency Condition Level C Transients 600 528'F 500 400 -

300-- ~ ~ 281'F @ 35 slg Data

References:

200

% 300'F/hr Emergency Cooldown Unit 1 FSAR

+ Thermal Unit 2 Design Basis Transient

- Relief valves reset at 50 psia (35 psig),

Blowdown from 762E673 cooldown assumed at 100- ~ '250'F/7.5'min '. 'vent 23 NMP2.Vessel. 300'F/hr to 0 psig- .. " .

Unit 1 FSAR Stress Analysis 'ooldown (Six ERV's open) STRS 16.010-5039A 0-0 5 10 IS 20 25 30 35 40 45 50 55 60 Time (minutes)

Unit 1 Design Basis  % Unit 2 Design Basis A Unit I Emer Cool ~Nom.ADS BD 3 ERVs open Figure 3-1 Level C Transients Analyzed to Determine the Most Limiting Transient for NMP-1

+c t

Steam Break 22 600 TAFU - Uncover 380 sec TAFR - Recover Q 400 sec Oyster Creek GENE-523-70-0692 Steamllne Break profile 500 400 TAFU TAFR I

I I

300 I 281'F+35 psfg 212'F Q 0 psig 200 DATA REFERENCE Assume boiling HTC = Subcooled Boiling HTC thereafter NEOC4N56P, tg87, NMPt (0000 gTUthl.ft).oF from ECCS flow HTC=500 BTR/hr-ft2-'F

.Safei/CoreooofLGESTR-LOCA ....until.TAFR 100 analysis, Figure A-17 0 50 100 150 200 250 300 350 400 450 500 550 600

" Nominal Subcooling 100% power rated feedwater temperature Figure 3-2 Level D Steam Line Break Transient Pressure Profile

ec t

Feedvater Line reak 23 600 528'F 500 400 TAFU - Uncover TAFR - Recover I 145 sec 265 sec

'

TAFU 300' 281'F Q 85 psig TAFR 200 Assume Boiling HTC 10,000 DATA

REFERENCE:

BTU/hr-ft2-'F until TAFR NEDC-31446P 1 987, Subcooled HTC thereafter...

100 'NMP1 Safer/Corecool/ from ECCS flow HTC = 500 GESTR-LOCA. Fig. A-19 - BTU/hr-ft2-'F 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 Time (sec) 10 75 100 200 300 400 500 Pressure (I'SIR) 1,045 960 800 720 400 140 80 50 Saturaled Temp ('F) W 528~ 528" 518 506 444 353 312 281

C

'4 Core Spray Line Break 600 TAFU - Uncover Q 245 sec 528'F i TAFR - Recover 320 sec 500 400 I I I

TAFU TA R 281'F O 35 psig 300 200 -Assume Bolting HTC 10,000- --

DATA

REFERENCE:

BTU/hr-ft2-'F until TAFR NEDC-31446P, 1987, "NMP1 Subcooled HTC thereafter Safer/Corecool/G ESTR-LOCA from ECCS flow HTC = 500 Figure A-16 100 BTU/hr-ft2-'F 0

0 100 200 300 400 500 600 700 800 Time (sec) 145 175 400 500 630 Pressure (I'SIA 1,045 800 730 400 220 130 50

  • Saturated Temp ('F) W 528 ~ 518 507 444 390 347 281

'ominal Subcoollng 100% power rated feedwater temperature Figure 3-4 Level D Core Spray Line Break Pressure Profile

Jc C

Recirculation Line Break Spectrum 25 600- IAfV AKISASIICKS.

I ll AA IIHtOI HHWIV Clltlb4lv IAfV Isa>> 45OCSllif4, I&Sf 'NVAI 4 I t I SAfe4co4ecoovoes'lll.locA'5e II Vvff. fffeff5. l4fvoe voooN 528 F IIIOIAIAICICloA

$ 00- ~ -- - ..300. F/hr--

prAIR 400 .I.

+ IAfll

+ IAf4 I I IAfll I I

28t oF

@35 psig 200 Reference 2 In'a'll cases, level is at TAF prior to complete depressurization.

Downcomer Level is assumed to follow core level. Therefore, 100- .assurpe.saturated steam. conditions. in,cfowncomqr.during,...

depressurization until TAF is recover by ECCS. Then assume free convection to subcooled ECCS.

0 100 200 300 400 $ 00 600 700 800 900 1,000 1,100 Time (Seconds)

~DBA +40% DBA I Ft 2 +.$ Ft 2 Hj.l Fl 2 +.0$ Ft 2 Figure 3-5 Level D Recirculation Line Break Spectrum Pressure Profile

Jf 4

26 Finite Element Analysis The candidate transients listed in Tables 3-7 and 3-8 were analyzed using the finite element method to determine the most severe Level C and Level D loadings. The WELD3 finite element code package IWELD3] was used to perform the calculations.

4.1 Model Description The WELD3 model assumes axisymmetric behavior. A single column of elements was used, thus making the solution essentially one dimensional (i.e., temperatures and stresses only depend on the radial position within the vessel wall). The finite element grid is shown in Figure 4-1. Elements 1 and 2 represent the cladding. The cladding inner surface radius is 106.344 inches, the base metaVclad interface is at 106.5 inches, and the vessel outer radius is 113.781 inches. The axial dimension of the model is 0.15 inches.

For thermal modeling, the outer vessel surface was treated as perfectly insulated. The inner surface has a prescribed heat transfer coefficient and fluid temperature (both functions of time). All heat flow is radial. Temperature dependent properties were used in the thermal analysis.

The mechanical model is constrained to'ave a uniform axial strain so that plane sections remain plane. The average axial stress and the internal pressure are input to the model based on the pressure transient input. Thermal transients are input via element temperatures. Temperature dependent properties are also used for the stress calculations.

The WELD3 calculations assumed linear elastic behavior for both the cladding and base metal so as to be consistent with the use of the small scale yielding assumption (linear elastic fracture mechanics with plastic zone corrections) in the subsequent fracture mechanics analyses.

4.2 Finite Element Analysis Results Two Level C cases and three Level D cases were analyzed. The transient thermal and pressure boundary conditions are described in Tables 3-7 and 3-8. Although the pressure and thermal loadings could be analyzed separately due to the use of linear elasticity, it was judged more expedient to combine the loadings.

The cladding has a different coefficient of thermal expansion than the base metal. This impacted the analysis in several ways.. First, there willbe some residual stress even when the vessel is at a uniform temperature. Assuming that the vessel is 100% stress free at the stress relief temperature of 1150'F, the original cooling to 528'F induced tensile residual stresses in the cladding thus contributing to crack tip stress intensity factors.

This uniform cooling was modeled in a separate analysis to determine the level of initial residual stress. The difference in thermal expansion behavior also results in discontinuous

WC 27 axial and hoop stresses across the material interface. Since the fracture mechanics evaluation involves fitting the stresses with a cubic polynomial, this discontinuous behavior impacts the quality of the polynomial fits. Therefore, as described in Section 5.0, the fracture mechanics model was configured to minimize the sensitivity of the analysis to the effects of stress field discontinuities at the interface.

Figure 4-2 shows the axial and hoop residual stresses that exist due to uniform cooling from a stress free condition at 1150'F to 528'F. This residual stress was not included in the st:ss distribution plots for the various Level C and Level D transients that follow.

This approach was adopted as part of the approach to more accurately handle the discontinuous stress field. The final stress distributions do include the differential expansion coefficient effects due to cooling from 528'F during the transient. The method for including the residual stress load in the fracture mechanics analysis is described in Section 5.0.

The WELP3 stress output for each analysis was scanned for the time of the most severe stresses induced by the combined transient thermal and pressure loading. Since crack depths of no larger than one inch are of interest [ASME92], the time at which the stresses would be most severe for a one inch deep crack was identified. This was done without actually calculating stress intensity factors for each transient stress distribution and was possible only because the stresses over the inner inch of the wall tended to peak at about the same point in time. Figures 4-3 through 4-10 contain plots of the transient temperatures and stresses. The times of the most damaging stresses for crack depths of about an inch are plotted with a solid line. Temperatures and stresses at other times are plotted using broken lines. It can be seen from these plots that for deeper cracks, the critical time would tend to be later in the transient. For very shallow cracks, slightly larger stress intensity factors may occur at earlier times than for the identified times.

Table 4-1 summarizes the results of the WELD3 analyses.

4.3, Limiting Transients The hoop and axial stress behaviors are very similar and tend to experience their peak values at about the same time. The magnitudes of the hoop stresses tend to be larger than the axial stresses. Without inputting these stresses into a fracture mechanics analysis it is not possible to determine which stress component is limiting. As discussed further in Section 5.0, the axially oriented flaw (hoop stress loading) is the limiting case.

Of the two Level C cases considered; the "NMP-1 Design Basis 250'F/7.5 min.

Blowdown" resulted in the larger stresses. Of the three Level D cases, the "Steam Line Break" resulted in the largest stresses. As shown in Figures 4-3 through 4-5, the time dependence of the heat transfer coefficient plays an important role in defining the limiting Level D transient. In particular, although the Steam Line Break is not the most rapid depressurization transient, it is limiting since the heat transfer is more efficient over the first 300 seconds of the event.

rc 28 Table 4-1 Summ of Peak Claddin and Peak Base Metal Stresses at the Indicated Times stress units are ksi Critical Clad Base Case Time ~Hoo Axial ~Hoo Axial residual NA 20.6 20.0 -0.7 -1.3 C1 9.15 min 60.6 50.2 40.5 29.8 6.65 min 42.6 34.8 29.6 21.5 D1 240 sec 78.4 65.9 52.3 39.4 D2 500 sec 47.7 39.5 31.7 23.2 D3 320 sec 65.5 54.6 43.9 32.7 C1: NMP-1 Design Basis 250'F/7.5 min, Blowdown C2: NMP-2 Design Basis Thermal Transient Blowdown D1: Steam line Break D2: Recirculation Line Break NMP-2 D3: Recirculation Line Break NMP-1 DBA

ec

'9 123 4 5 6 7 8 9 13141516171819202122 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 Figure 4-1 One Dimensional Finite Element Mesh for NMP-1 Pressure Vessel Analysis

er 30 22 H C20. 6 ksi) 20 A (20. 0 ksi) 18 16 A: Axi al Stress 14 H: Hoop Stress 12 (o

8 0

2 3 5 6.

Distance fr om inner sur face (in)

Figure 4-2 Residual Stress at 528'F Due to Cladding Differential Expansion

31 6DD 1$ t 1. 65 min.

2$ t = 3.3 min.

9$ t = 6. 65 min.

500 r 500 2<

/ ( / 3 r 8

/ ~s

/ 4/ I ( y 6e 400

/

/ c' 1$ t = 2min. 0 I

8 o

400 r7H 2$ t ~4min. E

/

min.'\

I- g6 t =6min. I 8

/ J' 3$

~r ~ t = 10 min.

4$ t = 7.5 min. 4$

300 5$ t = 9. 15 min.

300 / 5$ t ~ 15 min.

6$ t 14.1 min. 6$ t 20 min.

7$ t ~ 20. 7 t = 25 min.

S$ t = 98. 8 min.

20D 200 0 l 2 3 4 5 6 7 8 0 l 2 3 4 5 6 7 8 Distance from inner surface (in) Distance from inner surface (in)

Level CI 250 F / 7.5-min.'lowdown Level C: NMP-2 Blowdown Figure 4-3 Pressure Vessel Thermal Gradients for Level C Transients

pc

'2 600 540 520 II34/S g

, 500 //

/////

500

/

1(

2/'

480 460 I///

//I

/II I

/ ~7Y

~

8 g~

/ / y6t' 1s t 6D sec. 440 I / / y 1s t ~1Ssec.

I / yw t I I / 2s t ~ 20 sec. 400

/ 2s 120 sec. 420 I I/ /

II I/ /

3s t 18D sec. a 400 I 3s 4s t

t 40 sec.

60 sec.

I Iy t I I/

4s 240 sec. 380 / Ss t 1DD sec. 300

/I/ I Ss t 30D sec. 360 / 6s t 20D sec.

r/ t / 7s t 30D sec.

6s 400 sec. 340 I 8s t SDD sec.

7s t SDD sec. 320

/ gs t 700 sec. 200 300 0 l 2 3 4 5 6 7 8 0 l 2 3 4 5 6 7 8 Distance from inner sur face (in) Distance from inner surfoca (in)

Level Ds Steam Line Br eok Level Ds Recirculation Line Br eok Figure 4-4 Pressure Vessel Thermal Gradients for Level D Transients

c 33 600 1~ ~

r r r 500

/

/ 5/ t

~.

/

/ r'/ .

1s 2 t 15 sec.

30 sec.

0 L

400

// 3c t BD sec.

a

// / 4c t 140 sec.

I/ //i E

/p 300

(

/ G: t 320 sec.

// 7s t 440 sec.

Bs t 5GD sec.

gs t GBD sec. 200 0 l 2 3 4 5 6 7 8 Distance from inner sUrface (in)

Level Ds Recirculation Line Br eak NHP-l DBA Figure 4-5 Pressure Vessel Thermal Gradients for Level D Transients

34 70 0

60 0: t-0 2 min. t 60 1r 2 min.

2: 4 min. 50 3r t 6 min. 2: t ~4min.

50 4: t 7.5 min.

40 3r t ~6min.

5: t 9. 15 min.

4p 6r t 14.1 min.

4r t 7. 5 min.

7: t ZO. 7 min. ro 3p 5r t ~ 9. 15 min.

g 30 6: t 14.1 mfn.

o 20 20 7r 't 20. 7 mfn.

a 0

0 lp L+ 10 0

D 1 2

-10 3 0

~ 2 3

-10

-20

-30 2D 0 1 2 3 4 5 6 - 7 8 0 1 2 3 4 5 6 7 8 Distance from inner sur face (in) Distance fr om inner surface (in)

Lovel C: 250 F / 7.5 min. Blowdown Level C: 250 F /  ?.5 min. Blowdown Figure 4-6 Axial and Circumferential Stress Distributions for Level C 250'F/7.5 Min. Blowdown

"

35 Ds t 0 40 Ds t-0 t 1. 65 min.

1s t I. 65 min.

40 2s t = 3.3 min.

2s t ~ 9.9 min.

3s t 6. 65 min.

30 9s t = 6. 65 min.

4s t = 1D min.

4s t = 10 min.

30 5s t -" 15 min.

5s t = 15 min.

6s t ~ 2D min.

6s t = 20 min.

20 7s t = 25 min. 20 7s t ~ 25 min.

8s " 98. 8 min.

t = 98. 8 min.

8s vl 10 10 0

0 0

-10 3 20 10 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Distance from inner svr face (in) Distance from inner svr face (in)

Level Cs NMP-2 Blowdown Level Cs NMP-2 Blowdown Figure 4-7 Axial and Circumferential Stress Distributions for Level C NMP-2 Blowdown

BD 70 OL t D D: t=O 70 1s t = 60 sec.

60 1~ t 60 sec.

60 2: t = 1ZD sec. 2~ t 120 sec.

3: t 1BO sec. 50 9: t 1BO sec.

50 4: t 240 sec. 4s t 240 sec.

40 5: t = 3DO sec. 40 5s t 3DD sec.

6: t 400 sec. 6: t 400 sec.

e 30 e 30 7: t- 500 sec. 7s t 500 sec.

20 20 o

ao 10 x 10 2

-10 3

-20 w- -5 -10 30 20 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Distance from .inner surface (in) Distance from inner surface (in)

Level D: Steam Line Break Level D: Steam Line Break Figure 4-8 Axial and Circumferential Stress Distributions for Level D Steam Line Break

/>>

70 Qo t aD 70 0: t-0 i: t i5 sec. is t i5 sec.

60 2: t ZD sec. 60 i 2: t 2D sec.

9: t 4D sec. l 9: t 40 sec.

50 50 4s t 6D sec. 60 sec.

5: t - i00 sec. 5: t i00 sec.

40 40 6s t 200 sec. 6: t 2DO sec.

30 7s t ~ 300 sec.

e 30 7: t = 900 sec.

B: t 5DO sec. B: t 5DO sec.

u) 20 gs t 700 sec. 20 gc t 700 sec.

0 10 x 10 5

-10 6 -10 7

-20 20 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Distonca from inner surface (in) Distance from inner surface (in)

Level D: Recirculation Line Breah Level D~ Recirculation Line Break Figure 4-9 Axial and Circumferential Stress Distributions for Level D Recirculation Line Break for NMP-2

"

38 70 Os t 0 60 Os t 0 ls t 15 sec. 1: t 15 sec.

60 Zs t 30 sec. 2: t 90 sec.

9s t ~ 80 sec. 9: t 80 sec.

50 4s t 140 sec.

40 4: t 140 sec.

40 200 sec. Ss t 200 sec.

Gs 320 sec. w 6: t 920 sec.

30 30 7: 440 sec. 7s t 440 sec.

8: t 560 sec>> 8 8 8s t 560 sec.

20 9s - 680 sec. 20 9: t 680 sec.

U) o 10 0 10 0

0 9

4 . 9

-10 5 4

-20 ~=z. 6

e. a

-10 5

6z

<<=7. 8, 9 30 20 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Distance from inner surface (in) Distance from inner surfoce (in)

Level Dc Recirculotion Line Break NHP-1 DBA Level D~ Recirculation Line Br eak NHP-1 DBh Figure 4-10 Axial and Circumferential Stress Distributions for Level D Recirculation Line Break for NMP-1 DBA

gC 39

~ ~

5.0

~ Elastic-Plastic Fracture Mechanics Assessment The limiting Level C and D transient loads were applied to a fracture mechanics model of the NMP-1 pressure vessel in accordance with the guidance provided in References [ASME92] and

[WGFE92]. The USE' (3.0) code package [USE93] was used to perform the calculations. A copy of the draft Appendix X [ASME92] is provided in Appendix A and the ASME Working Group on Flaw Evaluation draft stress intensity calculation procedure [WGFE92] is given in Appendix B.

5.1 Model Description 5.1.1 Vessel Geometry The A302B material model used in the analysis was described in Section 2.0. In addition to the material model, USE' (3.0) requires the following parameters:

Vessel Wall Thickness 7.281 in. (UFSAR Table V-1)

Vessel Inner Radius 106.344 in. (UFSAR Table V-1)

Vessel Clad Thickness 0.15625 in.

Crack Depth/Length Ratio 0.166667 5.12 Applied Loads The results of the finite element calculations to determine the limiting Level C and D transients and loadings are described in Section 4.0. As a result of these calculations, the limiting Level C transient is the "NMP-1 Design Basis 250'F/7.5 min. Blowdown", and the limiting Level D transient is the "Steam Line Break".

The limiting stress distribution was determined by examining the radial stress profiles at various times in the transient. As mentioned in Section 4.0, using stress distribution data at a time when the stresses are most severe for a one-inch crack may be slightly non-conservative when shorter cracks are considered. This small non-conservatism was ciicumvented by using an upper bound envelope of the actual stress distributions.

The limiting stress distributions were fit to a cubic polynomial using the guidance given in [WGFE92]. In order to provide good fits to the data, the base metal stresses were extrapolated to the ID surface. The remaining discontinuous component of the clad stresses are treated using a line load formulation as described in Section 5.1.4. The equivalent clad line loads are given in Table 5-1.

The pressure acting along the crack surface was conservatively included in the clad line load. The fit to the base metal stress distribution is shown in Figures 5-1

gC

'1

40 through 5-4. Table 5-2 summarizes the stress distribution coefficients for use in the Appendix X analysis. The R-squared value for all of the fits is very close to unity which indicates accurate representation of the data.

5.19 Limits for Small Scale Yielding Analysis As stated in Reference [ASME92], when the conditions fall in the category of elastic fracture mechanics with small-scale yielding, the J-integral may be calculated using crack-tip stress intensity formulae with plastic-zone correction.

In order to estimate the limits of validity of the small-scale yielding assumption, an axially cracked cylindrical vessel with a radius to thickness ratio of 10, a wall thickness t=10 inand a crack depth to thickness ratio a/t&.25, was loaded by internal pressure and the resulting stress intensities were calculated, The effective crack depths were calculated using:

where, a e =:a P + 1 6m

(

K aya

)

2 a, = effective crack 'size (in.)

a = physical crack depth (in.)

K = linear elastic stress intensity (ksi4in) a~ = yield stress (ksi) .

Two Ramberg-Osgood stress-strain models were analyzed: one with n=8.4 and alpha=2,6; the second with ri=5.3 and alpha=7.2. The higher n-value case is more representative of the NMP-1 plates. The elastic calculations approximated pressure stresses by a linear distribution that matched the exact thick walled cylinder solution at the inner and outer surfaces. The plastic solution was

'calculated using the exact internal pressure induced stresses.

The results are summarized in Figure 5-5. The difference in solutions for small loads is due to the use of different elastic solution F factors in the two models.

Based on this analysis, it is concluded that the small-scale yielding formulation is valid for stress intensity levels up to 100 ksi4in (J-335 in-lbfin ) for an axial crack in a cylinder with an aspect ratio of 10. Since the calculated stress intensities for NMP-1 are well below 100 ksi4in., the small scale yielding analysis is appropriate for the NMP-1 vessel analysis.

5.1.4 Fracture Mechanics Model The Reference PVGFE92] method for calculating stress intensities for surface flaws was used. A copy of the procedure proposed by the ASME Working Group on Flaw Evaluation is given in Appendix B. The procedure requires accurately fitting the stress distribution using the following polynomial fit:

>r 41 a = A, + A,X'+ APE + (5-1)

A,X'here, A, = regression constants X = distance through the wall The postulated flaw is a semi-elliptical surface crack with a surface length which is six times the depth. The stress intensity for the continuous component of the stresses was calculated from the following expression:

Kz = [A G + A~G~a + A~G~a + A3G3a'] ~ira7g (5-2) where, a = crack depth A, = coefficients from Eq. 3-1 which represent the stress

(

distribution over the crack (0( X a)

G, = influence coefficients as a function of flaw aspect ratio and crack penetration (Appendix B)

Q = flaw shape parameter Q= 1 + 4.593 (a/1)' qy 1 = flaw surface length q= plastic zone correction factor q= 0.212 (A Ja,)',

= material yield stress Since the slope of the stress distribution at the clad-base metal interface changes abruptly, the base metal stress distribution was extrapolated to the ID surface to provide an accurate flit over the postulated flaw depths. The Reference [TA73]

linear elastic formulation was used to calculate the discontinuous component of the stress fields contribution to the crack tip stress intensity using:

/p 42 K res~ 2P P

~ma

'

where,

~ 52 (1-c/a) 4 35-5. 28c/a

~

(1-a/b) (1-a/b) 3 0 3 (c/a) i.s +

~

+( 1 '

(1- (c/a) ')" 0.83-1.76c/a) (1-(1-c/a) a/b)

P = equivalent line load a = flaw depth b = wall thickness c = load application position as measured from the ID surface Equation 5-3 provides conservative estimates of the discontinuous stress component contribution of the total stress intensity since the formulation is for an infinite crack length, Since Eq, (3-3) is a linear elastic equation, the small scale yielding correction was applied:

where, a = physical crack depth a, = effective crack depth In order to simplify the computer algorithm and to ensure conservative results, the small scale yielding correction was applied to both the cladding and base metal stress intensity factors. This approach yields very conservative results since the flaw shape parameter in equation 5-2 includes a plastic zone correction factor.

The total stress intensity factor was obtained by superposition:

KcoHTLNPN/s + KDLscoNTLNUoUs Z Z

rc 43 In accordance with Reference [ASME92], a spectrum of initial flaws, up to 1/10 of the base metal wall thickness, were assumed. The smallest flaw assumed was 0.05 in., and the postulated flaws were increased in size by increments of 0.05 in.,

up to a maximum flaw depth of 0.75 in.

5.2 Calculations for A302B Material Model The pointwise input model was used for the A302B material model calculations. Using this model, the J-R curve is assumed flat after the initial 0.1 in. of crack extension. The G-8-1 plate was analyzed using the A302B material. model since it is the limiting plate from a ductile fracture perspective (Reference [MA93]).

5.2.1 Level C Loading The results of the calculations for the Level C loading have shown that the limiting flaw orientation is the axial flaw. For initial base metal flaw depths of up to 1/10 of the vessel wall thickness, the ASME Appendix X criteria are satisfied at USE levels as low as 10 ft-lbs. In all cases, the largest applied-J values for the flaw growth of 0.1 in. criterion are obtained at the deepest initial postulated flaw depth. The results for the Level C analysis are summarized in Table 5-3 for the axial flaw.

5.22 Level D Loading Analysis The results of the calculations for the Level D loading also show that the limiting flaw orientation is the axial flaw. For initial base metal flaw depths of up to 1/10 of the vessel wall thickness, the ASME Appendix X criteria are satisfied at USE

'levels as low as 20 ft-lbs. The results for the Level D analysis are summarized in Table 5-4 for the axial flaw.

5.2.3 Tensile Instability Analysis Based on the analysis performed, the deepest flaw during the most severe Level C or D transient is less than 1.2 inches. Conservatively assuming the flaw extends completely around the circumference, and using the finite element stress profiles, the remaining ligament will experience stresses well below the yield strength and is therefore safe in terms of tensile instability.

Table 5-1 NMP-1 Clad Stresses Extrapolated Clad Stress Minus Clad Crack Clad Surface Extrapolated Residual Total Surface Equivalent Case Stress Surface Stress Stress Pressure Line Stress (ksi) Stress (ksi) (ksi) (ksi) (ksi) (kp/in)

Hoop-Level C 45.207 16.557 20.6 37.157 1.05 6.856 Axial-Level C 35.264 16.790 20.0 36.790 1.05 6.798 Hoop-Level D 58.690 19.886 20.6 40.486 1.05 7.376 Axial-Level D 45.476 21.377 20.0 41.377 1.05 7.515 Table 5-2 Base Metal Stress Distribution Coefficients Ao A, A, Level C-- Hoop 45.165 -22.335 2.571 0.228 Level C - Axial 35.294 -25.420 9.941 -2.183 Level D - Hoop 58.791 -33.934 7.967 -1.052 Level D - Axial 45.651 -33.636 12.136 -2.263

pC r"c C

'able 5-3 Orientation'5 Comparison of Applied Loads with ASME Criteria for Level C Loading Conditions and an Axial Flaw ha&.l Criterion Flaw Stabili Criterion USE Applied J Material J Applied Material Criteria Level ~in-1b ~in-1b ini T T Satisfied in'83 10 199 2.6 yes 20 ,183 230 <0.5 3.7 yes 30 183 261 <0.5 7.3 yes 40 183 292 <0.5 13.2 yes 50 183 323 <0.5 18.3 yes 60 183 353 yes, J, cJ<<

70 183 384 yes, J, <J<<

80 183 438 yes, J <Jic 90 183 517 yes, J, <J,c 100 183 yes, J, <J,c

'esults shown are for the most limiting initial flaw over the spectrum of flaws analyzed

USE Level 10

~AIied T Jape JMAx Material T 5-4 Comparison of Applied Loads with ASME Criteria for Level D Loading Conditions and an Axial Flaw Orientation Flaw Stabilit Criterion Satisfied no Criteria

'6'able 20 <0.8 11.0 yes 30 <0.8 18.3 yes 40 yes, J,~<Junc 50 yes, J~<Jic 60 yes'app~rc 70 yes'app~tc 80 yes, Jo~<Jrc 90 yes J <Jrc 100 yes, J, <Jrc

'esults shown are for the most limiting initial flaw over the spectrum of flaws analyzed.

,

~

47 HOOP STRESS DISTRIBUTION FOR LEVEL C TRANSIENT 100 80 co 60 CO U)

LU 40 CO 20 0.0 0.6 1.0 1.5 2.0 CRACK LENGTH (In.)

Figure 5-1 Peak Circumferential Base Metal Stress Distribution for NMP-1 Design Basis 250'F/7.5 Min. Blowdown Transient

48 AXIAL STRESS DISTRIBUTION FOR LEVEL C TRANSIENT 100 80 60

'CO CO UJ 40 CO 20 0

0.0 0.5 2.0 CRACK LENGTH (In.)

Figure 5-2 Peak Axial Base Metal Stress Distribution for NMP-1 Design Basis 250'F/7.5 Min. Blowdown Transient

49 HOOP STRESS DISTRIBUTION FOR LEVEL D TRANSIENT 100 80 60 40 20 0

0.0 0.5 2.0

<3RACK LENGTH (In.)

Figure 5-3 Peak Circumferential Base Metal Stress Distribution for Steam Line Break Transient

gC 50 O'XIAL STRESS DIST RI BUT ION FOR LEVEL D TRAN IENT 100 80 60 CO 03 LLI 40 K

20 0

0.0 0.5 1.0 1.5 2.0 CRACK LEN9TH (ln.)

Figure 5-4 Peak Axial Base Metal Stress Distribution for Steam Line Break Transient

In Small Scale Yield Limits Study Axially Cracked Cylinder {R/t = 10) 4.5 3.5 3

.~ 2.5 2

0.5 0

0 0.5 1.6 -

2 2.5 3.5 Pressure (ksi)

~ J(BSY/ae) ~ Jep(n=5.3) ~ Jep(n=8.4)

Figure 5-5 Comparison Between Small Scale Yielding Solution (J(SSY/ae)) and the Elastic-Plastic Solutions with Hardening Exponents of 5.3 (Jep(n=5.3)) and 8.4 (Jep(n=8.4))

/'

52 6.0 Summary and Conclusions The results of the elastic-plastic fracture mechanics assessment are shown in Table 6-1. As discussed in Reference tMA93], the A302B material model best represents the NMP-1 beltline plates. The A302B material model, applied to the case of an axial flaw orientation, yields the most conservative results. Based on the calculations reported in Reference PvIA93] and herein, it has been concluded that the NMP-1 plate G-8-1 is limiting from a ductile fracture perspective, and the USE must be maintained above 23 ft-lbs. Based on the data reported in Reference

[MA93], none of the NMP-1 beltline plates are expected to fall below the 23 ft-lb level.

Although the Appendix X criteria are satisfied at or above the 23 ft-lb level, it is not clear that the plant should be operated at this ductility level. It is anticipated that future federally funded research and subsequent regulations will address this issue.

fi

~

53 Table 6-1 Minimum Upper Shelf Energy Level for NMP-1 Plates Based on the ASME Draft Appendix X Evaluation Criteria for Service Levels A, B, C and D Minimum USE (Ft-Lbs)

ASME Service Material Plate Level Model Flaw Growth of 0.1 Flaw Stability A&B in. Criterion Criterion

(

Ji Jo.i G-8-1 A&B A302B 13 23 G-307-4 A&B A302B 13 23 G-8-1 A302B 10 10 G-8-1 D A302B 20

54 7.0 References

[ASME92] ASME Draft Code Case N-XXX, "Assessment of Reactor Vessels with Low Upper Shelf Charpy Energy Levels", Revision 11; May 27, 1992.

[CENC] Unit 1 Analytical Report for Niagara Mohawk Reactor Vessel, Report No. CENC 1142, ACC No. 002301187, Appendix B Thermal Analysis.

[FSAR] Updated FSAR Volume IV,Section I, Page I-11.

[HI89], 'iser, A.L., Terrell, J.B., "Size Effects on J-R Curves for A302B Plate",

NUREG/CR-5265, January, 1989.

[MA92] Manahan, M.P., Soong, Y., "Response to NRC General Letter 92-01 for Nine Mile Point Unit 1", NMPC Project 03-9425, June 12, 1992.

[MA93] Manahan, M.P., Final Report to NRC, "Elastic-Plastic Fracture Mechanics Assessment of Nine Mile Point Unit 1 Beltline Plates for Service Level A and B Loadings", February 19, 1993.

[NEDC] NEDC-31446P, NMP-1 SAFER/CORECOOL/GESTR-LOCA Loss of Coolant Accident Analysis.

[NMP1DP] NMP-1 Drywell Pressure Calculation, SO-TORUS-M009, GENE-770-91-34.

[NMP2TC] NMP-2, 762E673, Reactor Vessel Thermal Cycles.

[STRS] Section E9, Emergency'& Faulted Analysis of Recirculation Outlet Nozzle 251" BWR Vessel. STRS 16.010-5039A, page E11, 12. Unit 2 Stress Analysis.

[TA73] Tada, H., Paris, P.C., Irwin, G.R., "The Stress Analysis of Cracks Handbook", Del Research Corp., 1973.

[TCD] Unit 2 Reactor Vessel Thermal Cycles Diagram 762E673.

[TRUMP) Manahan, M.P., 'TRUMP/MPM: Thermal Transient Heat Transfer Analysis Code, Version 1.0, September, 1989.

[USE93] USE' (3.0)Code Package for Elastic-Plastic Fracture Mechanics Assessment of Nuclear Reactor Pressure Vessels, MPM Research & Consulting, 1993.

[WELD3] "WELD3 Computer Code Verification", MPM Research & Consulting, Calculation No. MPM-NMPC-99205, Rev. 0, January 21, 1993.-

~<

55

[WGFE92] ASME Working Group on Flaw Evaluation, Proposed Changes to Article A-3000 entitled, "Method for K, Determination", August, 1992.

56 Acknowledgement Dr. Randall B. Stonesifer of Computational Mechanics, Inc. performed all of the finite element analyses and provided many valuable suggestions related- to the fracture mechanics model.

57 Appendices

58 Appendix A

'SME Draft Appendix X "Assessment of Reactor Vessels with Low Upper Shelf Charpy Energy Levels"

(i DRAFT CODE CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS May 27, 1992 REVISZON 11 DRAFT HISTORY REVISION 0 AUGUST 25 g 1 987 REVISION 1 JANUARY 19, 1988

) REVISION 2 APRIL 19, 1988 REVISION 3 AUGUST 30, 1988 REVISION 4 NOVEMBER 30, 1988 REVISION 5 FEBRUARY 27, 1989 REVISION 6 JANUARY 5i 1990 REVISION .7 APRIL 12, 1990 REVISION 8 JANUARY 10, 1991 REVISION 8 MARKED COPY APRIL 15, 1991 REVISION 9 JANUARY 17, 1992 REVISION 10 APRIL 17 1992 REVISION ll CURRENT

gC

(-

ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS TABLE OF CONTENTS CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS APPENDIX A ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGYLEVELS A-1000 INTRODUCTION A-1100 Scope A-1200 Procedure Overview A-1300 General Nomenclature A-2000 ACCEPTANCE CRITERIA A-3000 ANALYSIS A-3100 Scope A-3200 Applied J-Integral A-3300 Selection of the J-Integral Resistance Curve A-3400 Flaw Stability A-3500 Evaluation Approach for Level A and B Service Loadings r

A-4000 EVALUATION PROCEDURES FOR LEVEL A AND B SERVICE LOADINGS A-4100 Scope A-4200 Evaluation Procedure for the Applied J-Integral A-4210 Calculation of the Applied J-Integral A-4220 Evaluation Using Criterion for Flaw Growth of 0.1 in.

A-4300 Evaluation Procedures for Flaw Stability A-4310 J-R Curve Crack Driving Force Diagram Procedure

r l

A-4320 Failure Assessment Diagram Procedure A-4321 Failure Assessment 'Diagram Curve A-4322 Failure Assessment, Point Coordinates A-4322.1 Axial Flaws A-4322.2 Circumf erential Flaws A-4323 Evaluation Using Criterion for Flaw Stability A-4330 J-Integral/Tearing Modulus Procedure A-4331 J-Integral at Flaw Instability A-4332 Internal Pressure at Flaw Instability A-4333 Evaluation Using Criterion for Flaw Stability A-5000 LEVEL C AND D SERVICE LOADINGS

/i Case N-XXX Assessment of Reactor Vessels Nith Low Upper Shelf Charpy Energy LevelsSection XI, Division 1 Inquiry: Section XI, Division 1, XWB-3730, requires that during reactor operation, load and temperature conditions shall be maintained to 'provide protection against failure due to the presence of postulated flaws in the ferritic portions of the reactor coolant pressure boundary. Under Section XI, Division 1, what procedure may be used to evaluate a reactor vessel with a low upper, shelf Charpy.impact energy level as defined in ASTM E 185-82 to .demonstrate integrity for continued service at upper shelf conditions?

Rep2y: It is the opinion.'f the Committee that a reactor vessel with a low upper shelf Charpy impact energy level may be evaluated to demonstrate integrity for continued service for upper

.shelf conditions in accordance with the following.

1.0 EVALUAT1ON PROCEDURES AND ACCEPTANCE CRITERIA Section XI, Division 1, Appendix G, "Fracture Toughness Criteria for Protection Against Failure", provides analytical procedures based on the principles of linear-elastic fracture mechanics that may be used to define load and temperature conditions to provide protection against nonductile failure due to the presence of postulated flaws in the ferritic portions of the reactor coolant pressure boundary. To prevent ductile failure of a reactor vessel with a low upper shelf Charpy impact energy level the vessel shall be evaluated using the principles 'of elastic-plastic fracture mechanics. Flaws shall be postulated in the reactor vessel at, locations of predicted low upper shelf Charpy impa'ct energy and the applied Z-integral for these flaws shall be calculated and compared with'he J-integral fracture resistance of the material to determine acceptability. Factors of safety on applied load for limited ductile flaw growth, and on flaw stability due to ductile tearing, shall be satisfied. All specified design'transients for the reactor vessel shall be considered. Evaluation procedures and acceptance criteria based on the principles .of elastic-plastic fracture mechanics are given in Appendix A of this Code Case.

The evaluation shall be the responsibility of the Owner and shall be subject to review by the regulatory and enforcement authorities -having jurisdiction at the plant site.

I APPENDIX A TO CODE CASE N-XXX ASSESSMENT OF REACTOR VESSELS WITH LOW UPPER SHELF CHARPY ENERGY LEVELS ARTICLE A-1000 INTRODUCTION A-1100 SCOPE This Appendix provides acceptance criteria and evaluation procedures for determining the acceptability for operation of a reactor vessel when the vessel metal temperature is in the upper shelf range. The methodology is based on the principles of elastic-plastic fracture mechanics. Flaws are postulated in the reactor vessel at locations of predicted low upper shelf Charpy impact energy and the applied J-integral for these flaws is calculated and compared with th'e J-integral fracture resistance of the material to determine acceptability. All specified design transients for the reactor vessel shall be considered.

A-1200 PROCEDURE OVERVIEW The following is a summary of the analytical procedure which may be used.

(a) Postulate flaws in the reactor vessel according to the criteria in A-2000.

(b) Determine the loading conditions at the location of the postulated flaws for Level A, B, C and D Service loadings.

(c) Obtain the material properties, including Z, a~, and the J-integral resistance curve (J-R curve), at the locations of the postulated flaws. Requirements for determining the J-R curve are given in A-3300 Evaluate the postulated flaws according to the acceptance

'd) criteria in 'A-2000. Requirements for evaluating the applied J-integral are given in A-3200, and for determining flaw stability in A-3400 'hree permissible evaluation approaches are described in A-3500. Detailed calculation procedures for Level A and B Service loadings are given in A-4000.

~

A-1

A-1300 GENERAL NOMENCLATURE flaw depth which includes ductile flaw growth (in.)

effective flaw depth which includes ductile flaw growth and a plastic-zone correction (in.)

Be effective flaw depth at flaw instability, which includes ductile flaw growth and a -plastic-zone

. correction (in.)

Bo postulated initial flaw depth (in.)

amount of ductile flaw growth (in.)

dB'mount of ductile flaw growth at flaw instability

, (in.)

C = material constants used to describe CR the power-law fit to the J-integral resistance curve for the material,.

ZR = C,(dB)

= cooldown rate

'CR)

( F/hour)

E'oung's modulus (ksi)

E/(2-VR) (ksi)

Fzr F~r geometry factors used to calculate F~ the stress intensity factor (dimensionless)

Far Fur geometry factors used to calculate Fg the stress intensity factor at flaw instability I (dirtensionless )

J-integral'ue to the applied loads (in.-lb/in.')

+R J-integral fracture resistance for the material (in. ,1b/in.~)

A-2

J-integral fracture resistance for the material at a ductile flaw growth of 0.10 in. (in.-lb/in.~)

Jz applied J-integral at a flaw depth of a, + 0.10 in. (in.-lb/in.')

J-integral at flaw instability (in.-lb/in.~)

Kz mode I stress intensity factor (ksi v'in.)

C Kzp mode I'stress intensity factor due to internal pressure, calculated with no plastic-zone correction (ksi v'in.)

Kzp Kzp ca 1 cu 1 ated with a p 1 astic-zone correction (ksi V'in. )

Kzp Kzp at flaw- instability, calculated with a plastic-zone correcti'on (ksi V'in.)

Kze mode I stress intensity factor due to a radial thermal gradient through the vessel wall, calculated with no plastic-zone correction (ksi V'in.)

Kz K calculated with a plastic-zone 'I correction (ksi Min.)

Kze K at flaw instability, calculated with a plastic-zone correction (ksi Min.)

ordinate of the failure assessment diagram curve (dizransionless) ratio of the stress intensity factor to the fracture toughness for the material (dixransionless) internal pressure (ksi) accumulation pressure as defined in the plant-specific Overpressure Protection Report, but not exceeding l.l times the design pressure (ksi)

A-3

Ps pressure used to calculate the applied J-integral/tearing modulus line (ksi)

P internal pressure at'law instability (ksi)

Po reference limit-load internal pressure (ksi)

Rq inner radius of the (in.)

vessel'bscissa of the failure assessment diagram curve (LQmnsionless )

ratio of internal pressure to reference limit-. load internal pressure (dhransionless)

(SF) = saf ety factor (dhransionless )

vessel wall thickness (in.)

tearing modulus due to the applied loads (diz~nsionless) tearing modulus resistance for the material (dUransionless) parameter used to relate the applied J-integral to the applied tearing modulus (dimensionless)

Poisson's ratio (dirmnsionless) reference flow stress, specified as 85 ksi (ksi) yield strength for the material (ksi)

ARTICLE A-2000 ACCEPTANCE CRITERIA The adequacy of the upper shelf toughness of the reactor vessel shall be determined by analysis. The reactor vessel is.

acceptable for continued service when the criteria of Paragraphs (a), (b), and (c) are satisfied.

(a) Level A and B Service Loadings When evaluating the adequacy of the upper shelf toughness for the weld material for Level A and B Service loadings, postulate an

.interior semi-elliptical surface flaw with a depth one-quarter of the wall thickness and a length six times the depth, with the flaw'.s major axis oriented along the weld of concern and the flaw plane oriented in the radial direction. When evaluating. the adequacy of the upper shelf toughness for the base material, postulate both interior axial and circumferential flaws with depths one-quarter of the wall thickness and lengths six times the depth and use the toughness properties for the corresponding orientation.

Smaller flaw sizes may be used on-an individual case basis when justified. Two criteria shall be satisfied:

(i) The applied J-integral evaluated at a pressure which is 1.15 times the accumulation pressure as defined in the plant-specific Overpressure Protection Report, with a factor of safety of 1.0 on thermal loading for the plant specified heatup and cooldown conditions, shall be shown to be less than the J-integral characteristic of the material resistance to ductile tearing at a flaw growth of 0.10 in.

(2) The flaw shall be shown to be stable, with the possibility of ductile flaw growth, at a pressure which is 1.25 times the accumulation pres'sure defined in Subparagraph (1), with a factor of safety of 1.0 on thermal loading for the plant specified heatup and cooldown conditions.

The J-integral resistance versus crack growth curve shall be a conservative representation for the vessel material under evaluation.

A-5

~ /

(

(b) Level C Service Loadings When e: aluatin g the ade quacy of the upper shelf toughness for the weld material for Level C Service loadings, postulate interior semi-elliptical surface flaws with depths up to 1/10 of the base metal wall thickness, plus the cladding thickness, with total depths not to exceed 1.0 in., and a surface length six times the depth, with the flaw's major axis oriented along the weld of concern and the flaw plane oriented in the radial direction. When evaluating the adequacy of the upper shelf toughness for the base material, postulate both interior axial and circumferential flaws, and use the toughness properties for the corresponding orientation.

Flaws of various depths, ranging up to the maximum postulated depth, shall be analyzed to determine the most limiting flaw depth.

Smaller maximum flaw sizes may be used on an individual case basis when justified. Two criteria shall be satisfied:

(1) The applied J-integral shall be shown to be less than the J-integral characteristic of the material resistance to ductile tearing at a flaw growth of 0.10 in., using a factor of safety of 1.0 on loading.,

(2) The flaws shall be shown to be stable, with the possibility of ductile flaw growth, using a factor of safety of 1.0 on loading.

The J-integral'esistance versus crack growth curve shall be a conservative representation for the vessel material under evaluation.

(c) Level D Service Loadings When evaluating the adequacy of the u'pper shelf toughness for Level D Service loadings, post'ulate flaws as specified for Level C Service loadings 'in Paragiaph b), and use the toughness properties for the corresponding orientation. Flaws of various depths, ranging up to the maximum postulated depth, shall be analyzed to determine the most limiting flaw depth. Smaller maximum flaw sizes may be used on an individual case basis when justified. The flaws shall be shown to be stable, with the possibility of ductile flaw using a factor of safety of 1.0 on loading. The J-integral "'rowth, resistance versus crack growth curve shall be a best estimate representation for the vessel material under evaluation.

The stable flaw depth .shall not exceed 75% of the vessel wall thickness, and the remaining ligament shall be safe from tensile

~ ~ ~ ~

instability.

~ ~ ~

~

A-6

ARTICLE A-3000

\

ANALYSIS A-3100 SCOPE This Article contains a general description of procedures which shall be used to evaluate the applied fracture mechanics parameters, as well as requirements for selecting the J-R curve for the material. References are made to acceptable approaches to apply the criteria.

A-3200 APPLIED J-INTEGRAL The calculation of the J-integral due to the applied loads.

shall account for the full elastic.-plastic behavior of the stress-strain curve for the material. When the conditions fall into the category of elastic fracture mechanics with small-scale yielding, the J-integral may alternately be calculated .by using crack-tip stress intensity factor formulae with a plastic-zone correction.

The method of calculation shall be validated and documented.

A-3300 SELECTION OF THE J-INTEGRAL RESISTANCE CURVE When evaluating the vessel for Level A, B and C Service loadings, the J-integral 'resistance versus crack growth curve (J-R curve) shall be a conservative representation of the toughness of the controlling beltline material at upper shelf temperatures in the operating range. When evaluating the vessel for Level D Service loadings, the J-R curve shall be a best estimate

.representation of the toughness of the controlling beltline material at upper shelf temperatures in the operating range. One of the following optioris: shall be used to determine the J-R curve.

(a) A J-R curve generated for the actual material under consideration by following accepted test procedures may be used. The J-R curve shall be based on the'roper combination of crack orientation, temperature and fluence level.'he crack growth shall include ductile tearing with no occurrence of cleavage.

A-7

S' A J-R curve generated from a J-integral database obtained from the same class. of material under consideration with the same orientation using appropriate correlations for the effects of temperature, chemical composition and fluence level may he used. The crack growth shall include ductile tearing with no occurrence of cleavage.

(c) When the approaches of (a) or (b) are not possible, indirect methods of estimating the J-R curve may be used provided these methods are justified for the material under consideration.

A-3400 FLAW STABILITY The equilibrium equation for stable flaw growth is J= J where J is the J-integral due to- the applied loads for the postulated flaw in the'vessel, and J is the J-integral resistance to ductile tearing for the material.

The inequality for flaw stability due to ductile tearing is QJ dLTg aa da where BJ/Ba is the partial derivative of the applied J-integral with respect to the flaw depth a with load held constant, and d J/da is the slope o f the J-R curve. 'nder a condition o f increasing load, stable flaw growth will continue as long as BJ/Ba remains less than dJ/da.

A-3500 EVALUATION APPROACH FOR LEVEL A AND B SERVICE LOADINGS The procedure given in A-4200 shall be used to evaluate the applied J-integral -for a specified amount of ductile flaw growth.

There are three approaches that are equally acceptable for applying the flaw stability acceptance criteria according to the governing flaw stability rules in A-3400. The first is a J-R curve crack driving force diagram approach. In this approach flaw stability is evaluated by a direct application of the flaw stability rules given in A-3400. Guidelines for using this

~ ~

approach are given in A-4310. The second is a failure assessment diagram approach. A procedure based on this approach for the

~

A-8

t I~

postulated initial one-quarter wall thickness flaw is given in A-4320. The third is a J-integral/tearing modulus approach. A procedure based on this approach for the postulated initial one-quarter wall thickness flaw is given in A-4330.

ARTICLE A-4000 EVALUATION PROCEDURES FOR LEVEL A AND B SERVICE LOADINGS A-4100 SCOPE This Article contains calculation procedures to be used to .

satisfy the acceptance criteria in A-2000 for Level A and B Service loadings. A procedure to be used to satisfy the J-integral criterion for a specified amount of flaw growth of 0.10 in. is given in A-4200. Procedures to satisfy- the flaw stability criterion are given in A-4300. These procedures include the ax'ial and circumferential flaw orientations.

A-4200 EVALUATION PROCEDURE FOR THE APPLIED J-INTEGRAL A-4210 CALCULATION OF THE APPLIED J-INTEGRAL The calculation of. the "applied J-integral consists of two steps: Step 1 is to calculate the effective flaw depth which includes a plastic-zone correction; and-Step 2 is to calculate the J-integral for small-scale yielding based on this effective flaw depth.

~Ste 1 For. an axial flaw with a depth a, calculate the stress intensity factor due to internal pressure with a safety factor (SF) on pressure by using R>> = (SF) p (I + (R,/t) J (na)',

F~ = 0.982 + 1.006(a/t)~

This equation for R>> is valid for 0.20 s a/t s 0 the effect of pressure acting on the flaw faces.

'0, and includes A-9

For a circumferential flaw with a depth a, calculate the

~

stress intensity factor due to internal pressure with a safety

~ ~

factor (SF) on pressure by 'using Kzp = (SF) p (1 + (RE/(2t) ) J (za) .

Fz (2)

F, = 0.885 + 0.233(a/t) + 0.345(a/t)3 This equation for K>> is valid for 0.20 s a/t s 0.50, and includes the effect of pressure acting on the flaw faces.

For an axial or circumferential flaw with a depth a, calculate the stress intensity factor due to radial thermal gradients by using KE0 = ( (CR) /I000) t F3 (3)

F, = .0.584 + 2;647(a/t) - 6.294(a/t)' 2.990(a/t)3 This equation for Kz, is valid for 0.20 c a/t ~ 0.50, and 0 c (CR)

~ 100 F/hour.

Calculate the effective flaw depth for small-scale yielding, aby using a, = a + (I/(6'))((Kzp + KE0)/<yJ

~Ste 2 For an axial flaw, calculate- the stress intensity factor due to internal pressure for small-scale yielding, Kzp, by substituting a, in place of a in equation (1), including the equation for F,.

For a circumferential flaw, calculate Kz py substituting a, in place of a in equation (2), including the equation for F,. For an axial or circumferential. flaw, calculate the stress intensity factor due to ra'dial thermal gradients for small-scale yielding, Kz by substituting a in place of a in equation (3), including the equation for F3. Equations (1), (2) and (3) are valid for 0.20 c a,/t c 0.50.

The J-integral due to the applied loads for small-scale yielding is given by Z = 1000(Kzp + K' /E'

A-4220 EVALUATIONgUSING CRITERION FOR FLAN GRONTH OF 0.1 ZN Calculate the J-integral due to the apple.ed loads, J by following A-4210. Use a flaw depth a equal to 0.25t + 0.10 in.; a pressure p equal to the accumulation pressure for Level A and B Service loadings,' and a safety factor (SF) on pressure equal to 1;Z5. The acceptance. criterion for Level A and B Service loadings based on a ductile flaw growth of'.10 in. in A-2000(a)(1') is satisfied when the following inequality is satisfied.

Js ~ Jo.i where J, = the applied J-integral for a safety factor on

=

pressure of 1.15, and a safety factor of 1.0 on thermal loading, J,, = the J-integral resistance at a ductile flaw growth of 0.10 in.

A-4300 EVALUATION PROCEDURES FOR FLAN STABILITY A-4310 J-R CURVE CRACK DRIVING FORCE DIAGRAM PROCEDURE Zn thxs procedure flaw stabzlzty xs evaluated by a direct

~ ~

application of the flaw stability rules given in A-3400. The applied J-integral is calculated for a series of flaw depths corresponding to increasing amounts of ductile flaw growth. The applied J-integral for Level A and B Service loadings shall be calculated by using the procedures given in A-4210. The appliep pressure p is set equal to the accumulation pressure for Level A and B Service loadings, p; and the safety factor (SF) on pressure is equal to 1.25. The applied J-integral is .plotted against crack depth on the crack driving force diagram to produce the applied J-integral curve, as illustrated in Figure A-4310-1. The J-R curve is also plotted on the crack driving force diagram, and intersects the horizontal axis at the initial flaw depth, a,. Flaw stability at a given applied load is demonstrated when the slope of the applied J-integral curve is less than the slope of the J-R curve at the point on the J-R curve where the two curves intersect.

Jr Material JR

'pplied J Evaluation Point ap FIGURE A-4310-1 COMPARISON OF THE SLOPES OF THE APPLIED J-INTEGRAL CURVE AND THE J-R CURVE ~

I~

A-4320 FAILURE ASSESSMENT DIAGRAM PROCEDURE This procedure is restricted to a postulated depth equal to one-quarter of the wall thickness.

initial flaw A-4321 FAZLURE ASSESSMENT DIAGRAM CURVE The same failure assessment diagram curve shall be used for axial and circumferential flaws, and is given in. Figure A-4320-1.

The coordinates (SR,) of the failure assessment diagram curve are given in Table A-4320-1. This curve is based on material properties which are characteristic of reactor pressure vessel steels.

A-4322 FAILURE ASSESSMENT POINT COORDINATES The flaw depth a for,a ductile flaw growth of h,a is given by a- = 0250 + ha The failure assessment point coordinates (S', K') for a ductile

~

flaw growth of ha shall be calculated by using the following expressions:

~

Kz R~ (I 000/(E J ) )

V where the stress intensity factor shall be calculated using the flaw. depth a without the plastic-zone correction, and is given by K~ = Kzp + R~,

and s: = (sz) p/p.

where (SZ) is the required safety factor on pressure. The procedure for calculating Kz~ Kz and p, for axial flaws is given in A-4322.1, and for. circumferential flaws in A-4322.2.

A-13

-0 A-4322.1 Axial Flaws The stress intensity factor due to internal pressure for axial flaws with a safety factor (SZ) on pressure is given by equation (1'). The stress intensity factor due,to radial thermal gradients is given by equation (3) ~

The reference limit-load pressure is given by H (2/~3 } o [ Q . 905 Q . 379 (h,a/ t) I

[0.379 + (R~/t) + 0.379 (ha/t} 1 For materials with a yield strength o greater than 85 ksi, set a equal to 85 ksi in this equation. This equation for p, is valid for 0 s za/t s 0.10.

A-4322.2 Circumferential Flaws C

The stress intensity factor due to internal pressure for circumferential flaws with a safety factor (SF) on pressure is given by equation ( 2 ) . The stress intensit factor due to radial thermal gradients is> given by equation (3).

The reference limit-load pressure is given by o [1 0.91 (0.25 + (Aa/t} ) ~ ( t!R~) l p [1+ (R/(2t} })

For materials with a yield strength oz greater than 85 ksi, set oy equal to 85 ksi in this equation. This equation for p is valid for 0 s za/'t s 0.25.

A-4323 EVALUATION USING CRITERION FOR FLAN'TABILITY Assessment points shall be calculated for each loading condition according to A-4322, and plotted on Figure A-4320-1 as follows. Plot a series of assessment points for various amounts of ductile flaw growth ba up to the validity limit of the J-R curve.

Use a pressure p equal to the accumulation pressure for Level. A and B Service loadings, p and a safety factor (SF) on pressure equal to 1.25. When one or more assessment points lie inside the failure assessment curve, the acceptance criterion based on flaw stability.

in A-2000(a)(2) is satisfied.

/r TABLE A-4320-1 COORDINATES OF THE FAILURE ASSESSMENT DIAGRAM CURVE OP FIGURE A-4320-1 K

0.000 1.000 0.050 1 F 000 0.100 0.999 0.150 0.998'.996 0.200 0.250 0.993 0.300 0.990 0.350 0.987 0.400 0.981 0.450 0.973 0.500 0.960 0.550 0.939 0.600 0.908 0.650 0.864 0.700 0.807 0.750 0.737 0.800 0.660 0.850 0.581 0.900 0.505 0.950 0 '35 1.000 0.374 1.050 0.321 1.100 0.276

1. 150'. 0.238 A-15

Js 1.2 1.0, 0.8 0.6 K,

0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 S,

FIGURE A-4320-1 FAILURE ASSESSMENT DIAGRAM FOR THE ONE-QUARTER MALL THICKNESS FLAN A-16

J A-4330 J-ZNTEGRAL/TEARZNG MODULUS PROCEDURE This procedure is restricted to a postulated depth equal to one-quarter of the wall. thickness.

initial flaw A-4331 J-ZNTEGRAL AT FLAN ZNSTABZLZTY 1

Referring to Figure A-4330-1, the onset of. flaw instability is the point of intersection of the applied and material curves plotted on a graph of the J-integral versus tearing modulus (J versus T). The expression for the applied J/T curve is given by J = (1000 V t Oi/Z) T (4) where oi is a reference flow stress which is set to 85 ksi in equation (4). For axial flaws p = 0.235(l + (0.083 x 10 ')(CR)t'/((SF)p,)J (5) where p, is the pressure under evaluation. Equation (5) is valid for 6 s t s 12 in.,~ 2.25 s ((SF)p,) s 5.00

~ ksi, and 0 s (CR) 100 ~ F/hour.

For circumferential flaws

~ ~

V = 0.21(1 + (0.257 x 10 ) (CR)t /((SF)p,) J (6)

Equation (6)

ksi, t

is valid for 6 s s 12 in., 2.25 s ((SF)p,) s 9.00 and 0 s (CR) s 100 F/hour. Equations (4), (5) and (6) are based on material properties which are characteristic of reactor pressure vessel steels.

The tearing modulus for the material is determined by differentiation of the J-R curve with respect to flaw depth a.

(Z/(1000 Qi )) dJ/da (7)

The- same values for Z and oi shall be used in equations (4) and (7). The J-integral versus tearing modulus J~/T~ curve for the material is given by plotting J against T~ for a series of increments in ductile flaw growth. Each coordinate for JR is evaluated at the same amount of ductile flaw growth as the coordinate for T~.

/

The'value of the J-integral at the onset of flaw instability,

~

J', corresponds to the intersection of the applied J/T curve given

~ ~ ~

by equation (4) with the material J~/T~ curve, as illustrated in

~ ~ ~

Figure A-4330-1. ~

h The J-integral at the onset of flaw instability may be determined analytically when a power-law curve fit to the J-R curve of the form J- Ci(ha) +

is available. The J-integral at the onset of flaw instability, J, in this case is given by A-4332 ZNTERNAL PRESSURE AT FLAN ZNSTABZLZTY The calculation of the internal pressure at the onset of flaw

~ ~

instability is based on the value of the J-integral at. the onset of

~

flaw instability, J . The ductile flaw growth at the onset. of flaw

~ ~ ~

instability, ha, is taken from the J-R curve. The effective flaw depth at the onset of flaw instability includes the ductile flaw growth b.a', and is given by a = 0.25t + ha + (1/(6n)) fZ'8'/(1000 o~'))

The stress intensity factor due to radial thermal gradients at the onset of flaw instability, Zi for axial:or circumferential flaws is given by .."

Zzi = ((CR)/1000) t~'~ Z'~

= 0.584 + 2. 647(a,'/t) 6.294(a,'/t)~ + 2.990(a,'/t)~

This equation for'Ri, is valid for 0.20 ~ a,/t ~ 0.50,'nd 0 s (CR) s 100'F/hour. The stress intensity factor for small-scale yielding due to internal pressure at the onset of flaw instability, Eppes is given by

,0 For a given value of K,'~, the internal pressure at the onset of flaw instability for axial flaws is given by p = Ksp / ((1 + (R,/t)) (za )o.s F,']

F~ . = 0.982 +,, 2. 006(a,/t)~

and for circumferential flaws by

/

p = Ki ((1 + (Ri/(2t))) (za,) '~ J F' 0.885 + 0.233(a,/t) + 0.345(a,/t)

These equations for p are valid for 0.20 s a,/t s 0.50, and include the effect of pressure acting on the flaw faces.

A-4333 EVALUATION USING CRITERION FOR FLAN STABILITY Calculate the value of the J-integral at the onset of flaw instability, J', by following A-4331 using a pressure p, in equations (5) and (6) equal to the accumulation pressure for Level A and B Service loadings, p and a safety factor (SF) on pressure equal to 1.25. Calculate the internal pressure at the onset of flaw instability, p, by following A-4332. The acceptance criterion based on flaw stability in A-2000(a)(2) is satisfied when the following inequality is satisfied.

p > I 25p, ARTICLE A-5000 LEVEL C AND D SERVICE LOADINGS The possible combinations of loadings and material properties which may be encountered during Level C and D Service loadings are too diverse to allow the application of pre-specified procedures and it is recommended that each situation be evaluated on an individual case basis.

A-19

0 Instability

.Material JR vs TR Jtc Applied J vs T FIGURE A-4330-1 ILLUSTRATION OP THE J-INTEGRAL/TEARING MODULUS PROCEDURE A-20

A 83 Appendix B ASME Working Group on Flaw Evaluation Draft Modification to Article A-3000

ART<.CI,E A.-3OoO NETHOD FOR Es DETERMINATION pg~W CV r iH ABC&

A-3100 SCOPE A-3100 SCOPE Thia Aructe provider a method for calculating atrcaa intcnrity This Atticle provides a method for calculating stress factor K< from the reprerenrartve arreraer at the flaw location intensity factor Kr from the membrane and bending determined from arrear analysis. More aophirticatcd techniques may be stresses determined from stress analysis. used ln determining I4 pmvldcd the methods aed aeatyaea are documented.

f A-3MO h-3200 STQBSES STRE55ES The stresses at the flaw location should be resolved (a) For the caro of a subsurface fiaw, th atromca at the flaw into membrane and bending stresses with respect to the location shall be resolved into membrane and bending atrcrrca with respect to the wall thlcknecr. Rertduat strcasca and applied arrccaca wall thickness. Residual stresses and applied stresses from all fonna of loadmg, including pressure arreaaee and chddag.

from all forms of loading. including pressure stresses, induced atrearor, abaQ be oonrutcred. For nonlinear strcaa varianres thermal stresses. discontinuity stresses. and cladding through the wall, the actual arreaa distributio can be conaervanvely induced stresses. should be considered. ln the case of approximated by the linearization techruque illuarrared in Fig. h-3200-1(b). The bncariaed atrea'e dtrrributton ahoutd rbcn be a nonlinear stress distribution through the wall, the ac- characterised by the membrane atrcaa e'nd the beudurg arreea g aa tual stress distribution should be conservatively ap- rhown in Fig. A-3200.1(b).

proximated using the linearigation technique illustrated in Fig. A-3200-1. The linearized stress distribution (b) For the care of a surface flaw, rhe arrerrca at the flaw location shall be reprerrntrd by a polynornlat fit given by the foUowiag should then be charicterized by the membrane stress relationship:

cr and thc bending stress era, as shown in Fig.

A-3200-1 ~

o - A, ~ A,x ~ A,xa -A,x' where x is the dirrauce through tho wall and AA,. Aand A, are constants. The derermiua6on of codflcteors Ao through + rhall provide a conservative reprrccntation of atrear over rhe crack one 0 c x 4 a for au vat~ of crack dcptha covered by the analysis.

Stresrea from aourcea iMocr&d ln A-3200(a) ahall be coasidcrcd. ln the case whra a nonlinear arrcaa dlarrlbutiou la dlfflcuttto fit be Eq. 1, thc actual dlrrribunon can be coeacrvarlvely appro6rnared by 0>>

hncarizatlon rcchntquo Ulurrrared tn Figure A-3200 t(a) fottowteg the diacuaaion given tn h-3200(a) for aubcuzface flawa.

A-3300 STRESS INTENSITY EQUATION h-3300 SIILESS INTENSITY FACTOR EQUATIONS (a) Stress intensity factors for the Aaw model should be calculated from the membrane and bending stresses The flaw shall be tepteseated by an elGpse that cbcumacdbaa at the flaw location using the following equation: the detected flaw as iilutttated in Fig. A 3300 1. The stress iattosity iactots for the flaw model shall bo detencined ftom the stresses and K/~e NYrr~alQ+ tr>M>Va'Valg (I) flaw geometry as desctibed ia h-3310 for subsurface flaws aad ln h-3320 for sutfaco flaws.

where cr, tre~ membrane and bending stresses. psi. in ac- h-3310 Subsuttace Flaw Equations cordance 'with A-3200 a minor haifdiamcter, in., of embedded (a) Stress attensity factors for subsurface flaw shall be calculated from tho as:mbrane and beading suesses at the fLaw location flaw: flaw depth for surface flaw by the following cquatioa:

Qmflaw shape parameter as determined fmm Fig. A-3300-l using (tr+ rr,)/a, and the Raw geometry a toMm + ob Mbj f~ 0/0 (2)

M =correction factor for membrane stress (sce Fig. A-3300-2 for subsurface flaws; Fig. A-3300-3 for surface flaws) ~

where, factor for bending stress (see

'emcorrcction Fig. A-3300-4 for subsurface laws: Fig. A- ~ 0>> IJg Membrane and beading stresses ia accordance with 3300-5 for surface flaws) A-3200(a)

%here variations in K/ amund thc periphery of

~ ~ a Minor halMmnetes M Conection factor for membrane sttess glvcat in occur. thc maximum value is to be used.

D ~

Fig. A 3200-2

~

(c) The use of Eq. (1) is only a tecomn>>ndation for

~

M, Conection factor for beading stress givtst in determination of A'/. More sophisticated techniques may

~

Pig. h-3200.3 bc used, provided the methods and analyses are doc- Q Flaw sbapo pataateter as given by Eq. 3 urnented. In many cases involving complex geometries The flaw shape panttnctct Q is calculated firom the following equatioa:

and sttess distributions, the methods outlined above may be inadequate.

Q 1 - 4.598 (a/>)' - q whete a/r is the flaw aspect ratio 0 s a/r s'8, aad q, is the ptastic soue cottectioa factor equal to 0.212 I (o + eJ / o)'.

(b) Whete variatioas ia K, around the pcriphetv of tbe flavv occur. the maximum value is to be used ia the delcnniaatioa of tbe ctiticat flaw luuamctcra a, and +.

(c) The uso of Eq.2 is only a tecomaamdatioa foe detenainatioa of Kv Ia some cases iavolviag comptca geometries and sttess distribution. the method outlined above may aot be adequate.

I A.3320 Sur&ce Flaw Equations (a) Stress intensity factors for strrfsce flaws should be calculated from the cubic polyaoaual stress relation by the followieg equstl orv (4)

K QOo'A t3tarAtotat AsOsaj~x Crack depth A, AAs, A, ~ Coefficieats from Eq. 1 that ~utsrtsrts the stress distribution over the crack (0 s.x5a)

Oor Oo Gte Or Free surface correction factors for tbe given stress variation provided ia Tables A-3320 1 and A.3320.2 as a function ot flaw aspeN ratio a/f, crack eaetration s/t, aad crack tip positiott (PTL aad F72)

Q Flaw shape psrstaetcr ss given by Eg. 3 with q, defiaed as 0.212 [A,/trP (b) ~ the Line Iraaen method ls used to convert tho actual stress fieM into tr aad tr, stresses as illustrated ia Hg. A-3200-1(a),

then Eq. 2 shall be Used to calculate )(t with tho followingequations for M, Msrd Q:

M Mi Go 2 (a/t) Gr Q ~ Sq.3whereq,isdefinedas0.212((re+

~/o'e)

%hue variation ia Kr sra the peripher of the fLaw occur, the trLaxitaum value is to be used ia the detertainatlon of a, aad tt (d) The uso of the above methods Is only a recotrutMadatlcsr for determination of Q. ln some cases iavolviag comply geotnesries and stress duuribunons. the methods outlined above may nce be adequate.

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G FUNCTION RESULTS FOR A/L=O.1 CfKK TlP PT1 a Shiratori, o Raju-Newman

+ Extropofated Point 1.4 G2 .

G3 0.4 Q.Q O.Q S.1 0.> 0~ 0.4 u n 0,7 OZ QS u)

Crack Oepth a/t

~e J

. G FUNCTION RESULTS FOR A/L=0.1 2.0 CRACK TlP PT2 0 Shiratori o Raju-Neo<man

+ Extrapolated Point g U

)'

0.6 0.4 G2 0.0 0.1 0.2 03 OA 0.5 0.6 0.7 03 09 IQ Crack Depth a/t

0 G FUNCTiON RESULTS FOR A/L=D.2 CRACK-TlP PT3 Shiratori 0 Raju-Newman' Extrapolated Point Q

Hl CD Og 0.4 0.2

.0 Oo O.~ 0.2 0,3 04 Oa 0.S 07 Oa 09 ]a Crack Depth a/t

0 FUNCTII3N RfSULTS FOR A/L=02 2.0 CRACK TlP PT2 0 Shiratori o Roju-Newman e Extrapolated Point 0.4 G4

. 0,0 0.1 02 03 0.4 0.5 0.6 07 B 09 5 Crack Oapth a/t

f G FUNCTION RESULTS FOR A/L=0.3

'2.0 CRACK TIP PT1 o Shirotori o Raju-Newman 1,6 + Extrapotated Point 1.4 00 1+2 1.0

- 0.8 0,6 0.2

.

0.0 0.1 02 03 0.4 0.5 0.6 0,7 03 0.9 1.0 Crack Depth a/t

G FUNCTION RESULTS FOR A/L=D3 2,0 CRACK TIP PT2 c3 Shiratori 0 Raju-Newman

+ Extrapofated Point G]

0.2 0.0 0,0 0.1 02 03 04 0.5 0.6 07 0,8 09 $ 0 Crack Depth a/t

0 G FUNCTIQN RESULTS FQR A/L=D.5 2.0 I I CRACK TIP PT5 1,8 0 Shiratori o Roju-Newman

+ Extrapoloted Point U

1.0 0,4 0,2 0,0 oa O.~ Oa O,Z a.4 O,S 0.6 0.7 03 09 I Crack Depth a/t

G FUNCTION RESULTS FOR A/L=O.5 2.0 CfIACK Te Pt2 1.8 0 Shirotori 0 Raju-Headman

+ Extrapolated Point GO

.= 1ll 0.6 02

.0 0.0 0.1 02 03 0.4 0.5 (M 0.7 (M 09 5 Crack Depth a/t

G FUNCTION RESULTS FOR AjL=D.D 4.0 CRACK TlP PT1 x Tgdg 3.9 1.0 0.0 00 0.$ 02 03 0.4 0.5 0.6 07 08 09 Ul Crxk Depth a/t

8%

0

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