PSI - Issue 80

Alok Negi et al. / Procedia Structural Integrity 80 (2026) 203–211 AlokNegi / Structural Integrity Procedia 00 (2023) 000–000

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phenomenon wherein atomic hydrogen, produced through corrosion reactions, di ff uses into the steel matrix, signifi cantly reducing ductility and fracture resistance under tensile stress [Negi et al. (2023); Elkhodbia et al. (2023); Negi et al. (2024)]. SSC poses a major threat to the safe operation of OCTG components, particularly those made from high-strength carbon and low-alloy steels, which are often deployed in deep, high-pressure sour wells [Zhang et al. (2020)]. Failures can occur at stress levels well below the nominal yield strength, making the accurate prediction of performance limits, such as burst pressure, vital for safe design, operational integrity, and e ff ective fitness-for-service (FFS) evaluations. While current industry standards provide essential guidelines for material selection and structural assessment, they often rely on simplified or conservative assumptions. One critical factor often oversimplified or ne glected in standard assessments is the presence of residual stresses introduced during manufacturing processes such as forming, welding, and heat treatment. These as-manufactured residual stresses can reach magnitudes as high as 50% of the material’s yield strength in inner / outer layer of OCTG-grade tubular products [Nawathe et al. (2016); Long and Moore (2018); Elkhodbia et al. (2024)]. By superimposing onto applied loads, residual stresses can locally amplify the stress intensity at geometric features such as notches or defects and influence e ff ective fracture resistance. Traditional analytical and experimental techniques struggle to fully capture the coupled e ff ects of residual stresses, hydrogen transport, and fracture processes. This challenge motivates the use of advanced computational modeling approaches. Among these, the phase-field (PF) method has emerged as a powerful framework for simulating fracture in materials, particularly in scenarios involving complex, multi-physics interactions. This study presents a coupled deformation–di ff usion–fracture phase-field framework to investigate SSC-driven burst failure in API 5CT C110 steel pipes under sour service conditions. The model explicitly incorporates as-manufactured residual stress fields, in troduced via a simplified thermo-mechanical loading approach that replicates realistic stress distributions observed in manufactured pipes. The framework integrates key physical phenomena: elastoplastic deformation, stress-driven hydrogen di ff usion kinetics (calibrated for C110 steel in NACE environments), and hydrogen-sensitive fracture resis tance modeled through a concentration-dependent toughness degradation law. Specifically, we investigate how these stresses alter local stress states, drive hydrogen accumulation, and impact crack initiation and propagation. The pa per is structured as follows: Section 2 presents the theoretical foundation of the modeling framework to model SSC. Section 3 discusses the key results involving full-scale pipe burst simulation. Finally, Section 4 summarizes the main conclusions of this study.

2. Modeling framework

Phase-field methods are particularly well-suited for modeling complex crack phenomena characteristic of SSC, as they regularize sharp crack discontinuities into continuous, di ff use damage zones using a scalar phase-field variable ϕ ∈ [0 , 1] [Miehe et al. (2010)]. Here, ϕ = 0 denotes the intact material, while ϕ = 1 represents complete fracture, with the transition occurring over a characteristic length scale l .

2.1. Phase-field formulation for elastoplastic fracture

The fracture process is modeled within a variational energy minimization framework, where the system’s behavior is governed by minimizing the total potential energy Π = Ψ − W ext . The symbol W ext denotes the external work, and the free energy functional Ψ encompasses elastic energy, plastic work energy, and fracture energy contributions, and is defined as, Ψ ( u ,ϕ, ϵ p , C ) = Ω g e ( ϕ ) ψ e ( ϵ e ) + g p ψ p ( ϵ p ) dV + Ω G c ( C ) γ ( ϕ, ∇ ϕ ) dV (1) where u is the displacement field, ϵ p is the plastic strain tensor, G c is the critical energy release rate, and C is the local hydrogen concentration. The elastic strain energy density follows a quadratic form,

1 2

e : ϵ

ϵ e : C

ψ e ( ϵ e ) =

e , where ϵ e = ϵ − ϵ p

(2)