PSI - Issue 45

Aditya Khanna et al. / Procedia Structural Integrity 45 (2023) 12–19 Khanna and Young / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 5. Variation in the through-thickness normal stress distribution near the weld toe, adapted from Niemi et al. (2018).

To ensure safe life under constant amplitude loading, the hot-spot stress must remain below experimentally derived constant amplitude fatigue limit (CAFL) for the appropriate weld category. In practice, scatter in the fatigue life due to variations in weld geometry, initial defects, metallurgical effects, residual stress, etc. are accounted for by using the lower bound S-N curve (99.7% survival probability, mean minus two standard deviations). For branch connection at pressure vessels, British Standard BS 7608:2014 recommends a Class D weld detail, for which the allowable design stress is 53 MPa. The European Standard EN 13445-3 (2021) recommends a Class 63 weld detail, which allows a similar design stress value of 63 MPa for test category 3 (limited NDT inspection) nozzle connections. Lower values of CAFL can be adopted when assuming fatigue failure to occur in the very high-cycle fatigue regime. For carbon steels, a more conservative endurance limit at 1E11 cycles can be estimated by dividing the value at 1E7 cycles by 1.3 (Wachel, 1995). Under variable amplitude loading, when some stress cycles are expected to exceed the CAFL, BS 7608 (2014) recommends modifications to the design S-N curve by extrapolating the curve to 5E7 cycles and thereafter a change in inverse slope from m to ( m +2), where m is assumed to be 3.0 for the Class D weld detail. 2. Model setup The FE model comprises of a cylindrical pressure vessel with fixed ends and a single cylindrical nozzle intersecting the vessel radially at mid-height (Fig. 6a). The nozzle is mass-loaded by a flange pair at the free end and the standard Raised Face Long Weld Neck (RFLWN) flange geometry is assumed. A parametric study is performed to cover a practical range of vessel wall thicknesses, nozzle bore size and flange classes, with higher flange classes corresponding to bigger, heavier flanged connections that can withstand greater temperatures and internal pressures. The values of fixed, variable and dependant geometry parameters are provided in Table 3. The various combinations of these parameters resulted in fifty-eight (58) unique geometries covering a wide range of natural frequencies (100 – 1000 Hz). For each geometry, the harmonic response analysis was performed for both the lateral and vertical modes of nozzle vibration. A sinusoidal force of arbitrary amplitude was applied at the flange (free end of the nozzle) and the forcing frequency was set to be equal to the resonant frequency of the nozzle bending mode. The weld leg size is assumed to be 10 mm and the Hot Spot Stress (HSS) at the weld toe is obtained using the surface stress extrapolation method specified in BS 7608 (linear extrapolation of stresses at 0.4 t and 1 t distances away from the weld toe, where t is the component thickness). The maximum nozzle deflection along the bending plane was also obtained fro m the harmonic analysis and the “allowable” displacement amplitude is obtained by multiplying the displacement output by the allowable (design) stress range for Class D welds (53 MPa) and dividing by the obtained value of the HSS. Depending on the wall thickness ratio and other geometric parameters, the critical or hot-spot location occurred either on the nozzle side or on the vessel side of the weld. The resulting vibration limit curve is shown in Fig. 7.