PSI - Issue 80

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

207

AlokNegi / Structural Integrity Procedia 00 (2023) 000–000 5 Table 1: Material and hydrogen transport parameters for phase-field simulations of C110 steel in sour environments [ANSI / NACE TM0177 (2016); Jun et al. (2019); Trillo et al. (2019); Zhang et al. (2020); Chambers et al. (2021); Cupertino-Malheiros et al. (2024)].

Parameter

Value

Elastic Modulus, E Poisson’s Ratio, ν Yield Strength, σ y 0

207GPa

0.3

800MPa

0.04

Strain Hardening Exponent, n p Critical Energy Release Rate, G c 0

61.21N / mm

4 mm 2 / sec

1 . 2 × 10 − 2000mm 297.15K

Hydrogen Di ff usivity, D app

3 / mol

Partial Molar Volume of Hydrogen, ¯ V H

Temperature, T ref

8314Nmm / mol − 1 K − 1

Ideal Gas Constant, R

Phase-Field Length Scale, l

0.2mm

Fig. 1: (a) Hydrogen-dependent critical energy release rate G c ( C ) for C110 steel [Cancio et al. (2010); Sales et al. (2018); Zhang et al. (2020); Liu et al. (2022)], (b) Time-dependent surface hydrogen concentration C b ( t ) used as Dirichlet boundary condition, derived from hydrogen permeation tests on C110 steel in NACE Solution A (100% H 2 S) [Cupertino-Malheiros et al. (2024)]. The gradual decrease in surface hydrogen concentration over time is attributed to the formation of a protective FeS film.

3.3. Pipe burst simulations

The full-scale burst simulations serve as the primary validation of the coupled framework, aiming to replicate the failure behavior observed in PRAC II pipe burst experiments [API PRAC II (2012)]. These tests involve pressurizing a full-length C110 steel pipe containing a pre-machined longitudinal notch on the outer diameter (OD), while both the inner and outer surfaces are exposed to sour environmental conditions. Fig. 2(a) shows the finite element model geometry, boundary conditions, and mesh discretization. The applied internal pressure history, shown in Fig. 2(b), is representative of staged burst testing, where pressure is increased incrementally and held constant over time to simu late realistic operating conditions. The simulation results for the baseline case (i.e., no residual stresses) are presented in Fig. 2 (c) and (d). Crack progression is visualized through the phase-field variable ϕ , with ϕ = 1 indicating fully fractured regions, while hydrogen di ff usion is visualized using the normalized concentration C . After 672 hours of exposure, no SSC-induced crack initiation or propagation is observed, indicating that the baseline pipe configuration, despite being exposed to highly sour conditions, remains structurally intact. This observation di ff ers from the PRAC II results, where fullscale-pipe exhibited failure at around 13.78 MPa (2000 psi). This suggests that factors such as notch geometry may play a significant role in resisting SSC onset, beyond what is captured in traditional sharp-crack FAD analyses.