PSI - Issue 80

Alok Negi et al. / Procedia Structural Integrity 80 (2026) 203–211

209

AlokNegi / Structural Integrity Procedia 00 (2023) 000–000

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Fig. 3: (a) Geometry, boundary conditions, and the choice of finite element mesh of the full-scale pipe segment. The complete pipe geometry is modeled to accurately capture the e ff ects of the distinctive double-bottom notch profile observed in PRAC II specimens, (b) Contour plot of the phase-field damage variable ϕ after 672 hours of hydrogen exposure, illustrating the absence of crack initiation from the blunted notch tip under the applied loading conditions.

Fig. 4: Geometry, boundary conditions, and a finite element mesh are used for simulating residual stresses in the pipe segment. A thermal gradient is applied by prescribing a positive temperature T s to the inner surface and a negative temperature − T s to the outer surface, (b) Contour plot showing the resulting normalized hoop stress distribution σ r θ for an applied thermal load of ∆ T = 77 ◦ C. Maximum hoop stresses σ r θ − max reaches up to 20% of the material yield strength (i.e, σ r θ − max /σ y 0 ≈ 0 . 2), (c) Hoop stress variation σ r θ across the pipe wall thickness for di ff erent applied thermal di ff erential ∆ T , indicating a nearly linear stress profile.

et al. (2024)], where a linear distribution of residual hoop (circumferential) stress across the pipe wall thickness is assumed, with tension on the OD and compression on the ID. Fig. 4(c) presents di ff erent magnitudes of residual stress considered in this work by varying the applied temperature di ff erential ∆ T . These residual stress fields are mapped onto the notched pipe geometry. Fig. 5(a) shows a mapped initial residual stress distribution corresponding to the applied temperature di ff erential of ∆ T = 77 ◦ C (20% residual stress levels), clearly showing the interaction between the pre-existing stress field and the stress concentration introduced by the notch. Fig. 5(b) shows crack evolution via the damage variable ϕ at a testing time of t = 18 . 76 hours under the imposed initial residual stress condition in Fig. 5(a). Coupled simulations were conducted for various levels of residual hoop stress (up to 20% of σ y 0 ). These findings are summarized in Fig. 6, which compares experimental failure (burst) pressures with model predictions for di ff erent residual stress scenarios. The results from the numerical simulations indicate that residual stress levels up to a certain magnitude ( ∼ 17.5%of σ y 0 ) do not lead to burst failure within the 672-hour exposure window. However, when the residual stress exceeds this threshold, crack initiation and burst failure occur, as visualized in Fig. 5(b).