PSI - Issue 80

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

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

where G c 0 is the fracture toughness without hydrogen, G min c

is the minimum toughness at saturation, and α controls

the degradation rate.

2.3. Incorporation of residual stresses

A representative initial residual stress field σ r is generated numerically by solving a steady-state heat conduction equation,

2 T

k th ∇

= 0

(9)

where k th is the thermal conductivity. Imposed thermal gradients induce thermal strains ϵ th = α th ( T − T ref ) I and resulting thermo-elastic stress field σ r = C e : ( ϵ − ϵ th ). The residual stress field σ r is mapped onto the main simulation mesh as an initial condition.

3. Numerical results

This section presents the key numerical findings obtained from the numerical simulations, benchmarked against full-scale laboratory burst tests performed under the Multi-Phase Piping Research and Application Council (PRAC) II Joint Industry Project (JIP), sponsored by the American Petroleum Institute [API PRAC II (2012)]. The modeling focuses on capturing the influence of sour environment (NACE solution A with 100% H 2 S exposure) and the presence of residual stresses on the transient evolution of hydrogen-assisted crack growth. A two-dimensional (2D) plane strain formulation is adopted to model the pipe geometry. The coupled deformation–di ff usion–fracture framework is implemented in COMSOL Multiphysics. A staggered scheme sequentially solves the mechanical equilibrium, phase-field evolution, and hydrogen di ff usion equations at each time step. The implementation utilizes several physics interfaces. 3.1.1. Residual stress generation and mapping The residual stress field is generated in a preliminary step using the predefined “Thermal Stress, Solid” multiphysics interface that couples heat transfer and solid mechanics to simulate stresses from a prescribed thermal gradient. The resulting stress field is then mapped from the generation geometry to the main simulation mesh using “General Ex trusion” coupling operator. This mapped field is applied as an initial condition to the solid mechanics model in the main coupled simulation via the “Initial Stress and Strain” feature, which generates an initial stress field that is self equilibrated with respect to the boundary conditions provided in the main coupled simulation. More details on the residual stress generation methodology can be found in Ref. Negi and Barsoum (2025). Table 1 summarizes the calibrated parameters used for API 5CT C110 steel under NACE A conditions, extracted from published experimental studies [ANSI / NACE TM0177 (2016); Zhang et al. (2020); Cupertino-Malheiros et al. (2024)]. The fracture toughness degradation with increasing hydrogen concentration is modeled using a concentration dependent G c ( C ) relationship, depicted in Fig. 1(a), reflecting empirical data for C110 steel exposed to sour environ ments [Cancio et al. (2010); Sales et al. (2018); Zhang et al. (2020); Liu et al. (2022)]. The fitting parameters in Fig. 1(a) are set to α = 0 . 75, and G c min = 1 . 0 N / mm, with the experimental G c data points calculated through the fracture toughness measurements, K Ic values (or K ISSC in sour conditions), through the linear elastic fracture mechan ics relationship for plane strain conditions, K Ic = EG c / 1 − ν 2 . To accurately represent hydrogen ingress, Fig. 1(b) shows a time-dependent boundary condition C b ( t ) applied on exposed surfaces, derived from experimental permeation measurements under NACE A solution [ Cupertino-Malheiros et al. (2024)]. 3.2. Choice of model parameters and hydrogen boundary conditions 3.1. Numerical implementation