PSI - Issue 60

D. Sen et al. / Procedia Structural Integrity 60 (2024) 44–59 Deeprodyuti Sen/ Structural Integrity Procedia 00 (2024) 000 – 000

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8

a

b

Figure 6: Comparison of numerical values of threshold peak stress for Debris Fretting Flaw, obtained from the in-house ZIPTAS code with the results of Scarth (2002). The material parameter p c is taken as (a) 450 MPa and (b) 650 MPa 4. Results of 220MWe and 540MWe Indian PHWRs In the previous two sections of this paper, technical details of the process zone model, recommended in CSA standard (2016), for evaluation of DHC initiation from blunt flaws and its numerical implementation in the in house ZIPTAS code were presented. The fitness for service evaluation of pressure tubes used in PHWRs requires estimation of permissible flaw size for a given set of operating conditions. The geometrical details of the pressure tube and the expected service loads are typically available in the design documents. Based on the type of service induced volumetric flaw (Bearing pad fretting flaw/debris fretting flaw), the process zone model (described earlier) provides the threshold peak stress required for initiation of DHC. For a given magnitude of nominal stress in the pressure tube, the peak stress near the vicinity of a volumetric flaw depends on the stress concentration factor ‘ k t ’ which depends upon the flaw geometry. The threshold peak stress, as discussed earlier, is also a function of flaw geometry especially the flaw tip root radius. As a result, the evaluation of maximum permissible size of flaw that will not lead to DHC initiation for the given design loads is not straightforward. An iterative procedure is implemented in the ZIPTAS code to accomplish this task. The technical details of the iterative procedure are as follows, Step-1 : The process zone model, as discussed earlier in section 2, is based on an idealized two-dimensional representation of a hydride lying at the tip of a volumetric flaw. The depth of a flaw ‘ a ’ and its root radius ‘ ρ ’ are the parameters that are used in the evaluation of threshold peak stress. Based on the nominal thickness of pressure tube ( w ) used in 220 and 540 MWe Indian PHWRs, the limits on validity range of ‘ a ’ and ‘ ρ ’ are fixed. Since the stress concentration factor depends also on the length of a volumetric flaw ‘ 2c ’ , this third dimension of a flaw (BPFF/DFF) also enters into the calculations. The validity range of stress concentration factor ‘ k t ’ brings a limit on the flaw length ‘ 2c ’ . Step-2 : Based on the type of a volumetric flaw (BPFF/DFF), the geometry coefficients ‘ f i ’ , ‘ g i ’ and ‘ h i ’ used in the evaluation of stress intensity factor K I and the crack mouth opening displacement ‘ v T ’ (see eq.4 and 5) are selected. Since the geometry parameters such as ‘ h i ’ and ‘ g i ’ are implicit functions of , ‘ s ’ , the evaluation of threshold peak stress becomes an iterative procedure. In the ZIPTAS code, a trial process zone length ‘ s ’ is selected and the iterative procedure continues till eq. 9 is satisfied within the specified tolerance band. Once a converged value of ‘ s ’ is obtained, the threshold peak stress is calculated using eq. 8. Step-3 : For a given value of flaw depth ‘ a ’ and root radius ‘ ρ ’ , the outcome of Step-2 is in the form of process zone length ‘ s ’ and the threshold peak stress. Based on the geometrical details of pressure tube used in 220 and 540 MWe Indian PHWRs and the design internal pressure, the nominal stress inside the pressure tube can be easily calculated. A loop for crack length c is then executed and the corresponding values for stress concentration factor