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Multi-physics microstructural modeling of a carbon steel pipe failure in
sour gas service
M. Elkhodbia, I. Gadala, I. Barsoum, A. AlFantazi, M. Abdel Wahab
PII:
DOI:
Reference:
S1350-6307(25)00210-9
https://doi.org/10.1016/j.engfailanal.2025.109469
EFA 109469
To appear in:
Engineering Failure Analysis
Received date : 4 December 2024
Revised date : 24 February 2025
Accepted date : 27 February 2025
Please cite this article as: M. Elkhodbia, I. Gadala, I. Barsoum et al., Multi-physics microstructural
modeling of a carbon steel pipe failure in sour gas service, Engineering Failure Analysis (2025),
doi: https://doi.org/10.1016/j.engfailanal.2025.109469.
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Multi-Physics Microstructural Modeling of a Carbon Steel Pipe
Failure in Sour Gas Service
M. Elkhodbiaa , I. Gadalab , I. Barsouma,c,∗, A. AlFantazid , M. Abdel Wahabe,f
a
Department of Mechanical and Nuclear Engineering, Khalifa University, Abu
Dhabi, 127788, United Arab Emirates
b
Department of Materials Engineering, The University of British Columbia, 309 Frank Forward
Bldg, 6350 Stores Rd, Vancouver, BC V6T 1Z4, Canada
c
Department of Engineering Mechanics, Royal Institute of Technology – KTH, Teknikringen
8, Stockholm, 100 44, Sweden
d
Department of Chemical and Petroleum Engineering, Khalifa University, Abu
Dhabi, 127788, United Arab Emirates
e
Laboratory Soete, Faculty of Engineering and Architecture, Ghent University, Ghent, 9000, Belgium
f
College of Engineering, Yuan Ze University, Taoyuan City, 32003, Taiwan
Abstract
∗
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This study presents a comprehensive failure analysis of an ASTM A106B steel pipe
exposed to sour natural gas, focusing on degradation and cracking mechanisms. A
range of experimental methodologies, including visual inspection, chemical spot tests,
XRD analysis, SEM-EDS examination, metallographic analysis, and hardness testing,
were employed to identify critical material deficiencies. The findings indicate that environmentally assisted cracking (EAC) initiated at the pipe’s outer diameter (OD) and
propagated inward. The experiments also revealed a hardness gradient across the pipe’s
thickness and a non-uniform distribution of microstructural inclusions. Additionally, a
coupled chemo-mechano-damage finite element analysis (FEA) was conducted to simulate crack propagation driven by hydrogen embrittlement. The FEA used a phase-field
approach to model interactions between hydrogen diffusion, mechanical stresses, and
microstructural features such as non-uniform inclusion distribution and varying hardness across the pipe wall. The simulations successfully mimicked the crack growth path
under sulfide stress cracking (SSC) conditions, demonstrating the influence of material
inhomogeneity. The results confirmed that failure initiated at the OD and propagated inward due to hydrogen accumulation at inclusions. These inclusions caused
higher gradients of hydrostatic stress, accelerating hydrogen accumulation and crack
initiation in regions with a higher inclusion density. Regions of higher hardness were
particularly susceptible to failure, as they exhibit lower fracture toughness, which is
further degraded by hydrogen diffusion, accelerating the failure process. This study
highlights the critical role of microstructural heterogeneities and hydrogen embrittleCorresponding author
Email address: imad.barsoum@ku.ac.ae (I. Barsoum)
March 8, 2025
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ment in pipeline failure and suggests that the methods presented can be applied to
pipelines in hydrogen blending or pure hydrogen transmission, offering key insights
for improving material selection and design for pipelines in sour gas and hydrogen
environments.
Keywords: Failure Analysis, SSC, Finite element analysis, Phase field, Hydrogen
embrittlement, Microstructural modeling
1. Introduction
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The structural integrity of pipelines transporting sour natural gas is a major concern in the oil and gas industry due to the corrosive nature of sour gas, primarily
composed of hydrogen sulfide (H2 S) and carbon dioxide (CO2 ) [1]. H2 S, in particular,
induces severe corrosion and embrittlement in carbon steel pipelines, causing failures
through sulfide stress cracking (SSC), a form of hydrogen embrittlement [2, 3, 4]. Research shows that hydrogen embrittlement occurs when atomic hydrogen, produced
by H2 S corrosion, diffuses into steel, reducing its ductility and toughness. Hydrogen
accumulates at stress concentrators, such as notches and grain boundaries, leading to
crack initiation and propagation, especially under tensile stresses [5, 6]. The susceptibility of carbon steels to hydrogen embrittlement is influenced by their microstructural
characteristics, including grain size and inclusions. Studies indicate that finer grain
structures and uniform inclusion distribution enhance resistance to hydrogen embrittlement [7]. The bainitic microstructure in medium carbon steels shows higher strength
and lower susceptibility compared to ferrite-pearlite structures [8]. Reduction in mechanical properties are caused by larger grains and hydrogen-induced cracks, through
the recombination of atomic hydrogen within the steel matrix forming pocket of hydrogen gas, creating a fissure in the material [9]. Moreover, varying hydrogen pressures
with H2 S presence intensify embrittlement [10].
Experimental methodologies like visual inspection, X-ray diffraction (XRD), energydispersive spectroscopy (EDS), scanning electron microscopy (SEM), metallographic
analysis, and hardness testing are essential for investigating hydrogen embrittlement
and SSC mechanisms [11, 12, 13, 14]. However, challenges remain in predicting and
preventing failures in sour gas pipelines due to the complex interplay of microstructural
characteristics, environmental conditions, and mechanical stresses.
Despite significant advancements in understanding and mitigating SSC and hydrogen embrittlement, challenges remain in predicting and preventing failures in sour gas
pipelines [15]. The complex interplay between microstructural characteristics, environmental conditions, and mechanical stresses necessitates ongoing research to develop
more robust predictive models and effective mitigation techniques. Additionally, the
variability in field conditions and the presence of multiple degradation mechanisms require comprehensive approaches that integrate material science, corrosion engineering,
and structural analysis [16].
Computational methods play a crucial role in predicting material behavior under
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extreme conditions, particularly in understanding hydrogen-induced degradation in
metals, such as steels. Research in this area has spanned multiple scales and employed
a variety of modeling approaches, often informed by the dominant proposed degradation mechanisms, namely Hydrogen-Enhanced Decohesion (HEDE) and HydrogenEnhanced Localized Plasticity (HELP) [17]. Some researchers utilized cohesive zone
modeling, governed by traction-separation laws tailored for hydrogen embrittlement
[18, 19, 20, 21, 22]. Others employed gradient damage models [23, 24, 25]. Subsequently, multiphysics models, particularly those leveraging phase-field damage approaches, have emerged to provide a more holistic understanding by coupling chemical
reactions and mechanical stresses. For instance, Martinez-Paneda et al. [26] applied a
phase-field model to simulate hydrogen-assisted cracking. This trend continued with
chemo-mechanical phase-field models capable of simulating hydrogen embrittlement
under both HEDE and HELP assumptions [27], coupled chemo-mechanical frameworks
for hydrogen embrittlement in metals introducing tension-compression split of strain
energy [28], and considering fatigue [29]. Other studies have numerically simulated
hydrogen diffusion and trapping in materials like carbon steels [30]. The advantages
and capabilities of phase-field modeling in this context have been comprehensively reviewed in [31, 6]. Specific to SSC, phase-field modeling has been successfully applied.
Negi et al. [32] developed a coupled deformation-diffusion phase-field framework to
predict SSC onset and growth in pipes with pre-existing defects in sour environments.
Cupertino-Malheiros et al. [33] modeled H2 S-driven hydrogen embrittlement in singleedge notch tension (SENT) specimens, incorporating plasticity and a phenomenological
degradation function. A key strength of phase-field-based approaches lies in their ability to capture microstructural effects. Early work by Nguyen et al. demonstrated the
capability of phase-field methods to simulate crack initiation and propagation in highly
heterogeneous materials [34], and to model the interaction between interfacial damage
and bulk brittle cracking in complex microstructures [35]. More recently, researchers
have explicitly incorporated microstructural features, such as grain boundaries and
precipitates, into phase-field models of hydrogen embrittlement, demonstrating their
influence on crack initiation and propagation [30, 28]. This focus on microstructure is
further exemplified by recent work by Wijnen et al. [36] which introduced a computational framework to predict microstructural phase fractions in weld regions, enabling
the evaluation of the effects of welding parameters on hydrogen damage.
In this study, we conduct a comprehensive failure analysis and phase-field numerical
modeling of a cracked ASTM A106B steel pipe used for sour natural gas transport. The
objective is to identify the root causes of the pipe failure and understand the underlying mechanisms that led to the observed degradation and cracking. Key experimental methodologies include visual inspection, chemical spot tests, XRD-EDS analysis,
SEM-EDS examination, metallographic analysis, and hardness testing. Furthermore, a
coupled chemo-mechano-damage phase-field model is developed to simulate the failure
mechanisms, considering the effects of hydrogen embrittlement and microstructural
features on crack propagation.
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2. Background of Failure
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The incident involves a failure in a 12-inch ASTM A106 Grade B steel pipe at a
compressor station, which transported sour natural gas. A leak, identified by an added
sour odourant, led to the excision and testing of a 1.5-meter pipe segment with a girth
weld about 1 meter upstream from the crack (Fig. 1(a)). The pipe had a non-standard
nominal wall thickness (WT) of 17.45 mm, an outer diameter (OD) of 323.85 mm, and
had been in service for 25 years in a 100-meter horizontal run.
The pipe operated at a maximum operating pressure (MOP) of 10.6 MPa and
a normal operating pressure (NOP) of 7 MPa, and a temperature of 70°C. The gas
contained 42.5% H2 S and 6.6% CO2 . Corrosion control measures of the aboveground
pipe were absent, with no internal inhibitors, pigging, chemical programs, external
coatings, or cathodic protection.
3. Experimental Methodology and Results
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3.1. Visual Examination and Inspection
The failed pipe was systematically examined to determine the root cause of failure.
Initially, both external and internal surfaces were inspected visually. The external
surface was first examined in its as-received condition. The internal surface was then
inspected after longitudinally splitting the pipe. A detailed examination followed after
blasting with aluminum oxide (Al2 O3 ) and performing a liquid penetrant inspection
(LPI) to detect surface-breaking defects. Finally, the fracture faces were inspected
after separating the cracked section.
Key observations included two linear cracks on the external surface, each about 2-3
cm long and less than 0.5 mm wide (Fig. 1(b)). The external surface also showed
scattered reddish-brown corrosion and localized pitting (Fig. 1(c)). The internal surface exhibited dark brown scale with lighter rust-colored staining and a single crack
corresponding to the external cracks (Figs. 1(d, e, f)). Post-blasting examination revealed localized corrosion along the axis of cracking on the external surface, with cracks
reaching 20 cm in length (Fig. 2(a)). The LPI test confirmed a 3 cm crack on the
internal surface (Fig. 2(b, c)). The fracture faces displayed evidence of corrosion, with
cracks initiating from the external surface and propagating inward, since that larger
crack length was found on the OD in comparison to the internal diameter (ID) (Fig.
2(d)).
3.2. Corrosion and Composition Analysis
3.2.1. Chemical Spot Tests
Chemical spot tests were conducted to assess material composition and potential
corrosion products. Tests were performed on the internal and external surfaces near
the cracking location (Fig. 1(b, c, e)). The surfaces were cleaned with a solvent before
testing to ensure accuracy. The spot test results (Table 1) indicated the presence
of sulphides at the cracks, suggesting H2 S corrosion, and carbonates at all locations,
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Fig. 1: (a) The pipe in its as-received condition, (b) external surface showing two linear cracks, (c)
localized corrosion and pitting, (d) internal surface after longitudinal split, (e) single linear crack-like
indication on the bottom internal surface, and (f) evidence of previous liquid phase presence.
indicating CO2 corrosion. Chloride tests were negative, suggesting no produced water
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Fig. 2: Post-blasting examination and LPI results: (a) OD surface after Al2 O3 blasting showing
localized corrosion, (b) ID surface after Al2 O3 blasting and LPI testing showing a single crack, (c)
zoomed view of the ID surface after Al2 O3 blasting and LPI testing, and (d) fracture faces showing
cracks propagating from the external surface towards the internal diameter.
presence. The copper sulfate test was negative, indicating protection against general
corrosion by the scale.
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Table 1: Chemical spot analysis results.
Compounds
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Sulphides
Carbonates
Chlorides
Copper Sulfate
External Surface
Adjacent to the crack Localized corrosion
Positive
Negative
Positive
Positive
Negative
Negative
N/A
N/A
Internal Surface
At bottom surface
Positive
Positive
Negative
Negative
3.2.2. XRD Analysis Near Cracking Location
XRD technique was used to analyze the corrosion product and scale from the internal bottom surface near the crack face. XRD data was collected using a PANalytical
Aeris X-ray diffractometer, which identified several crystalline components in the corrosion product, including pyrite, marcasite, magnetite, hematite, wustite, mackinawite,
troilite, greigite, sulphur, manganese oxide, and quartz. The high percentage of sulphide products such as pyrite, marcasite, greigite, mackinawite, and troilite indicated
that wet H2 S corrosion had occurred. These compounds might have also originated
from downhole mineral formations upstream. Elemental sulphur was also present,
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likely deposited from the process gas stream due to pressure and temperature changes,
or resulting from various chemical and microbial processes in the reservoir or surface
equipment. Iron oxides like magnetite and wustite were identified, which are typical
products of aqueous corrosion. Mn3 O4 was also present, consistent with manganese
being a primary alloying element in ASTM A106 Grade B steel. Quartz (SiO2 ) was
detected, likely originating from trace sand in the internal media of the pipe.
Table 2: Quantitative XRD results of removed scale from the bottom surface (in weight %).
Compound
Pyrite (FeS2 )
Marcasite (FeS2 )
Magnetite (Fe3 O4 )
Hematite (Fe2 O3 )
Wustite (FeO)
Mackinawite (FeS)
Troilite (Fe0.714 S)
Greigite (Fe3 S4 )
Sulphur (S)
Manganese Oxide (Mn3 O4 )
Quartz (SiO2 )
XRD (wt. %)
38.0
19.7
11.8
10.2
6.0
2.5
2.1
1.5
0.9
0.8
0.7
3.2.3. Overall Bulk Composition
The overall bulk chemical composition of the pipe was determined using an optical
emission spectrometer per ASTM E415-17 [37], showing that the material of the pipe
met ASTM A106 Gr. B specifications as shown in Table 3.
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Table 3: Chemical composition of the pipe sample.
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Element
Carbon (C)
Manganese (Mn)
Phosphorous (P)
Sulphur (S)
Silicon (Si)
Copper (Cu)
Nickel (Ni)
Chromium (Cr)
Molybdenum (Mo)
Niobium (Nb)
Titanium (Ti)
Vanadium (V)
Boron (B)
Composition [wt.%]
0.08
0.77
0.011
0.004
0.19
0.02
0.03
0.04
0.001
0.039
0.013
0.002
0.0004
Steel Specification
Max 0.30
0.29 – 1.06
Max 0.035
Max 0.035
Min 0.10
Max 0.40
Max 0.40
Max 0.40
Max 0.15
Not Specified
Not Specified
Max 0.08
Not Specified
3.2.4. EDS of Fracture Face and Local Composition
The fracture face (FF) was divided into three regions (Fig. 3(a)): Region 1, a
through-wall cracked part (6 cm) covered with light rust-colored scale; Region 2, a
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partial thickness cracked part (3 cm) with dark corrosion scale/product; and Region 3,
another partial thickness cracked part (5 cm) with lighter colored scale. The FF was
examined in its original state and cleaned near the boundary between Regions 1 and
2 for EDS analysis and SEM imagery, as will be shown in section. 3.3).
EDS analysis of the FF at multiple locations as shown in Fig. 3 identified iron,
oxygen, and sulphur as major constituents, indicating the presence of iron sulphide and
oxide scales. Elements like calcium, potassium, magnesium, and aluminum suggested
contamination or mineral presence from the external environment or the internal media.
In the uncleaned sample, three locations, shown in the the red boxes in Fig. 3(a), near
the ID and OD were analyzed (ID 1-3 and OD 1-3), showing significant variation in
composition as seen in Table 4, reflecting the complex nature of the corrosion processes.
The cleaned sample was analyzed at two locations, shown in the the red boxes in Fig.
3(b), near the ID and OD (ID 4, OD 4), indicating the base metal composition in
Table 4. In general, the results show iron as the main constituent, with oxygen and
sulphur present in significant amounts, consistent with the corrosion products identified
by XRD analysis. The presence of elements such as calcium, potassium, magnesium,
and aluminum, which are not typical alloying elements in ASTM A106 Grade B steel,
suggests contamination from external sources or minerals in the aqueous phase.
Inclusions and embedded cracks were also analyzed, revealing higher concentrations
of elements such as silicon and sulphur compared to the overall bulk material. The
inclusion and crack areas were iron-deficient and oxygen-rich, indicating the presence of
non-metallic inclusions, likely oxides. The presence of aluminum, calcium, and silicon in
the inclusions suggests the presence of aluminates and silicates, possibly from external
contamination.
ID 1
42.56
42.26
7.21
2.80
2.78
0.68
0.57
0.43
0.41
0.31
Excl.
ID 2
63.16
28.71
2.04
0.64
2.14
0.36
1.65
0.45
0.21
0.44
0.09
0.07
0.05
Excl.
ID 3
33.92
26.31
22.44
0.06
0.40
0.42
0.13
0.29
16.03
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Element
Iron (Fe)
Oxygen (O)
Sulphur (S)
Calcium (Ca)
Sodium (Na)
Potassium (K)
Magnesium (Mg)
Nickel (Ni)
Silicon (Si)
Manganese (Mn)
Chlorine (Cl)
Phosphorous (P)
Aluminum (Al)
Zinc (Zn)
Chromium (Cr)
Titanium (Ti)
Carbon (C)
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Table 4: Combined EDS results on FF and localized compositions (all elements, wt.%).
ID 4
98.32
0.51
0.27
0.84
0.06
Excl.
OD 1
29.21
46.19
1.57
7.92
1.69
0.95
8.53
0.20
1.71
0.50
0.13
1.24
0.14
Excl.
OD 2
32.54
33.35
23.14
2.30
1.50
0.84
4.49
0.20
0.94
0.45
0.05
0.21
Excl.
OD 3
49.51
19.72
28.67
0.09
0.12
0.20
0.51
0.58
0.27
0.24
Excl.
OD 4
98.34
0.52
0.21
0.88
0.05
Excl.
Inclusion
73.73
21.28
0.47
0.38
0.44
0.66
2.95
0.09
Excl.
Embedded crack
67.69
31.38
0.12
0.46
0.36
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3.3. SEM Analysis of the Fracture Face
SEM examination captured high-resolution images of the cleaned fracture surfaces
(Fig. 3(b)), providing insights into fracture modes and differentiating between ductile
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Fig. 3: (a) Macroscopic view of the fracture before cleaning, showing different regions, with red boxes
indicating EDS analysis locations, (b) macroscopic view after cleaning, with red and black boxes
indicating EDS and SEM analysis locations, respectively, (c-d) SEM images of the FF at various
magnifications for region 1, (e-f) SEM images showing cracks coalescing between regions 2 and 3.
and brittle fractures.
SEM analysis revealed detailed fracture morphology and mechanisms. Region 1
near the OD edge (Fig. 3(c)) showed a flat fracture surface with minimal plastic deformation, indicating cleavage-type brittle cracking with some intergranular cracking.
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Region 2 (Fig. 3(d)) showed more plastic deformation, indicating hydrogen embrittlement near the OD. At the boundary between Regions 2 and 3, a diagonal ridge
consistent with the coalescence of two cracks was observed, indicating brittle cracking.
A secondary crack along the ridge further evidenced brittle cracking in these regions.
3.4. Metallographic Analysis
A metallographic cross-section was prepared for microscopic and microstructural
examination to assess the pipe material condition at the failure location. The crosssection was taken from Region 1 (Fig. 3(a)), exposing the cross-section of the WT at
the crack initiation site. The sample was cold-mounted, metallographically prepared,
and etched in a 3% Nital solution to reveal its microstructure following ASTM E3
[38]. Fig. 4(a) shows the sample after mounting and etching, with the locations of the
microscopic images indicated by black boxes.
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3.4.1. Microscopic Examination
The microscopic examination revealed several critical observations. Inclusions were
visible near the OD edge and FF (Fig. 4(b-d)). Both edges exhibited signs of corrosion and irregular metal loss. Despite corrosion altering the FF, crack propagation
appeared intergranular, confirmed by secondary cracking near the FF. Additional crack
initiation points were observed on the OD near the main through-wall crack initiation
point and associated FF. The ID edge showed more corrosion and metal loss than
the OD, attributed to exposure to corrosive media while the OD was exposed to the
atmosphere. Fig. 4(e) shows a crack initiating from the OD and growing towards
inclusions, indicating that inclusions significantly influence crack propagation. The
presence of inclusions creates stress concentration, facilitating hydrogen accumulation,
crack initiation and propagation, especially in corrosive environments.
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3.4.2. Microstructural Evaluation
The microstructural evaluation revealed a uniform ferrite-pearlite microstructure
(Fig. 4(f)). Polygonal ferrite was the dominant grain structure, with pearlite formations at grain boundaries. No banding or stringers were observed, indicating isotropic
mechanical behavior, consistent with ASTM A106 Gr. B carbon steel. Despite the
uniformity in the ferrite-pearlite microstructure, there was a noted lower uniformity in
the distribution of inclusions in the microscopic level of the sample, which influenced
the cracking behavior.
3.5. Hardness Testing
Hardness testing evaluated the mechanical properties of the pipe material at various locations, providing insights into the differences between cracked and uncracked
regions. Macrohardness measurements were taken on the OD and ID surfaces using
a Wilson Rockwell Tester, with results converted to Vickers Hardness (HV) using the
ASTM E140-5 conversion table. Notably, The OD had higher hardness than the ID.
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Fig. 4: (a) Metallographic cross-section after mounting and etching, (b-d) microscopic images showing
inclusions near OD edge and fracture face (FF), (e) crack initiating from OD and growing towards
inclusions and (f) ferrite-pearlite microstructure.
Microhardness measurements on the metallographic cross-section were performed
using a Shimadzu Hardness Tester, with a 500 g load (HV500g). The highest hardness
was at the intersection of the OD and FF, around 181 HV, consistent with the crack
initiation point. The OD showed the highest hardness, followed by identical hardnesses
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of the mid-wall and ID, supporting the macrohardness results. This distribution suggests that cracking began on the OD and propagated inward. The highest drop in
hardness was between the OD and the adjacent mid-wall along the FF, consistent with
the crack initiation point.
Table 5: Brinell and Vickers hardness results.
Location
ID Surface
OD Surface
Mid-Wall
Macrohardness
HRB(W) HV (equivalent)
76 ± 1
139
84 ± 1
162
-
Microhardness
(HV500g)
141
177
141
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3.6. Sequence of Events
The failure sequence of the ASTM A106 Grade B steel pipe began with SSC initiating at the OD, despite the corrosive environment being more prominent at the ID.
Several factors contributed to this failure, as identified through experimental characterization. Hardness testing revealed a significant gradient across the pipe wall, with
the highest hardness at the OD and the lowest at the ID (Table 5). Harder regions
are more susceptible to SSC due to increased brittleness, and this effect was compounded by the metallographic analysis, which showed a higher density of inclusions
near the OD (Figs. 4(b-d)). These inclusions acted as stress concentrators, facilitating
hydrogen accumulation. Furthermore, the operating temperature of 70 °C accelerated
hydrogen diffusion, allowing hydrogen to permeate faster through the steel and concentrate at the OD. This combination of high hardness, faster hydrogen diffusion, and
inclusions created localized stress fields that triggered crack initiation. Microscopic
examination confirmed that cracks propagated towards inclusions (Fig. 4(e)), further
supporting their role in crack growth. Over time, these cracks coalesced, leading to
through-wall failure and leakage of the internal media. This sequence highlights the
critical interaction between mechanical stresses, hydrogen embrittlement, and material
inhomogeneities—particularly at the OD—as the primary drivers of failure.
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4. Coupled Multi-Physics Modeling of the Microstructure
The experimental results collectively suggest that the combination of higher hardness at the OD and the non-uniform distribution of inclusions played a crucial role
in the cracking process, contributing to the unusual observation of failure propagation
from the OD to the ID. To further investigate this hypothesis and explore the key
contributing factors, a numerical simulation using a coupled chemo-mechano-damage
phase-field finite element model is employed. This simulation provides a valuable tool
to analyze the failure process within a representative domain, incorporating a nonuniform distribution of inclusions and a hardness gradient based on the observed material characteristics. The model considers the influence of hydrogen transport and the
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resulting damage, arising from the interplay between mechanical , hardness gradients,
and microstructural features. While more comprehensive models incorporating multitrap mechanisms for hydrogen exist [39, 40], the current model focuses on elucidating
the primary factors believed to be responsible for the observed OD-to-ID failure in this
specific case.
4.1. Numerical Methodology
4.1.1. Governing Equations for the Mechanical Problem
The phase-field fracture model, initially introduced by Francfort and Marigo [41] to
address the limitations of the classical Griffith theory, employs a variational approach
to fracture. This method formulates brittle fracture as a problem of minimizing the
total energy potential functional ψ associated with a cracked structure. For a solid
body with an internal discontinuity Γd , the total potential energy functional includes
terms for the surface energy dissipated during cracking and the elastic strain energy,
Z
Z
e
Gc dV
(1)
ψ (ϵ(u))dV +
ψ(u, Γd ) =
Γd
Ω
where ϵ represents the infinitesimal strain tensor, ψ e is the elastic strain energy density,
and Gc denotes the critical energy release rate. Bourdin et al. [42, 43] extended this
model by proposing a regularized formulation as
Z
Z
ψ(u, ϕ) =
g(ϕ)ψ0 (ϵ(u))dV + Gc
γ(ϕ, ∇ϕ)dV
(2)
Ω
Ω
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In this formulation, ψ0 represents the elastic strain energy of the intact material, γ is a
crack density functional per unit volume, and g(ϕ) is a degradation function describing
material damage through a scalar phase-field variable ϕ. The phase-field ϕ varies
smoothly from 0 (intact) to 1 (fully damaged). The chosen degradation function in
this study is given by
g(ϕ) = (1 − ϕ2 ) + k
(3)
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where k is a numerical stability parameter, chosen to be as small as possible to avoid
singularities in the numerical simulations. Under linear elastic loading conditions, the
elastic strain energy density ψ0 in Eq. 2 is expressed as,
1
ψ0 (ϵ(u)) = ϵ : C0 : ϵ
2
(4)
where C0 is the stiffness tensor for the uncracked material. The second term in Eq.
2, γ, is defined as a crack density function involving an internal length scale l that
regulates the width of the diffused crack and includes the phase-field ϕ and its gradient
∇ϕ,
1
l
γ(ϕ, ∇ϕ) = ϕ2 + |∇ϕ|2
(5)
2l
2
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Minimizing ψ and introducing a history variable H yields the following set of coupled
governing equations,
g(ϕ)∇ · σ0 = 0
(6)
1
ϕ − l∆ϕ − 2(1 − ϕ)H = 0
(7)
Gc
l
where σ0 is the undamaged Cauchy stress tensor,
σ0 = C0 : ϵ
(8)
and H ensures the irreversibility of the phase-field ϕ evolution, preventing healing,
H = max [ψ0 (ϵ(u))]
(9)
Eq. 6 guarantees mechanical equilibrium, while solving the PDE in Eq. 7 provides the
spatial and temporal evolution of the phase-field ϕ.
4.1.2. Governing Equations for Hydrogen Transport
Hydrogen transport in SSC involves the diffusion of atomic hydrogen into the material when exposed to environments with high H2 S content and tensile stresses. Atomic
hydrogen results from corrosion processes, with reactions between acidic aqueous components and the metal surface. The generation of hydrogen ions is described by the
following electrochemical reactions, where H2 S dissolves and dissociates in an aqueous
medium [44, 45],
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H2 S(g) + H2 O(l) ⇐⇒ H2 S(aq)
H2 S ⇐⇒ H+ + HS−
−
HS
+
⇐⇒ H + S
(10)
2−
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Simultaneously, metal atoms, such as iron, oxidize and leave electrons on the metal
surface, which then form free atomic hydrogen via proton reduction,
Fe(s) ⇐⇒ Fe(aq) 2+ + 2 e−
(11)
H+ + e− ⇐⇒ Hads
(12)
In most cases, atomic hydrogen recombines to form hydrogen gas (H2 ), which bubbles
off the metal surface,
Hads + Hads = H2(g)
(13)
However, certain species like bisulfide ions (HS− ) inhibit recombination, increasing
the absorption of atomic hydrogen into the metal lattice [46]. The modified Fickian
diffusion model describes hydrogen transport, considering both concentration and hydrostatic stress gradients. The local mass balance equation for hydrogen transport
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dC
+∇·J=0
(14)
dt
The hydrogen flux J relates to the gradient of the chemical potential ∇µ through a
linear Onsager relationship,
DC
J=−
∇µ
(15)
RT
where D is the hydrogen diffusivity, R is the gas constant (R = 8.314 Jmol−1 K−1 ), T is
the absolute temperature, and µ is the chemical potential driving hydrogen diffusion,
µ = µ0 + RT ln
θL
− V̄H σH
1 − θL
(16)
Here, µ0 is the reference chemical potential, and σH is the hydrostatic stress (σH =
(σ11 + σ22 + σ33 )/3). Assuming low site occupancy θL << 1 so that θL /(1 − θL ) ≈ θL ,
and constant hydrogen trapping density ∇N = 0, the hydrogen diffusion flux J is given
by
DC
J = −D∇C +
V̄H ∇σH
(17)
RT
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4.1.3. Hydrogen-Induced Fracture Energy Degradation
Hydrogen embrittles metallic materials by lowering the bond energy between metal
atoms, thereby reducing fracture resistance. This effect is particularly pronounced in
iron. Studies using Density Functional Theory (DFT) have shown that the presence
of hydrogen at grain boundaries significantly decreases the material’s fracture energy
(e.g., [47, 48]). Following the work by Martı́nez-Pañeda et al [26], the critical energy
release rate Gc can be expressed as a function of hydrogen coverage θ, assuming a linear
relationship:
Gc (θ)
= 1 − χθ
(18)
Gc (0)
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where Gc (0) is the critical energy release rate without hydrogen, and the value of χ
can be estimated for different materials by fitting DFT data from the literature. For
example, Jiang and Carter [48] provided the damage coefficient values for iron as 0.89.
Next, the Langmuir-McLean isotherm [49] is used to estimate hydrogen coverage from
bulk hydrogen concentration C:
θH =
C
−∆G0
C + exp RT b
(19)
where ∆G0b is the binding energy of the hydrogen trap, and C is the bulk hydrogen
concentration in mole fraction.
For the purposes of this model, the degradation of fracture energy in iron due to
hydrogen coverage will be used to simulate the impact of hydrogen embrittlement on
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4.2. Numerical Simulation
4.2.1. Numerical Implementation
This section outlines the implementation of the proposed coupled chemo-mechanical
phase-field damage model in COMSOL Multiphysics. The software’s built-in finite
element method is employed for spatial discretization, and a backward Euler scheme
is used for time integration. All material properties are assumed to be isotropic. The
Solid Mechanics (solid) interface node governs the mechanical sub-problem, defining
the displacement field as the primary unknown. A Linear Elastic Material model is
used, modified to include damage. The phase-field evolution is implemented using
the Coefficient Form PDE (cpt) interface node. The history variable H is introduced
to ensure crack irreversibility and is implemented as a state variable using the ‘State
Variables of Variable Utilities‘. The Transport of Diluted Species (tds) interface node
handles the hydrogen diffusion sub-problem. The hydrogen flux is defined based on Eq.
17. Similar to the approach of Chen et al. [50], the Domain ODEs and DAEs (dode)
interface node is also employed to solve for the hydrostatic stress, which is needed for
the hydrogen flux calculation.
A staggered, iterative solution scheme solves the coupled system. First the mechanical equalibrium, hydrogen diffuison and the hydrostatic stress auxilary equations
are solved simulatneously for their respective degrees of freedom, namely, displacement,
hydrogen concentration, and the hydrostatic stress with fixed damage dof. Then, keeping these fixed, the damage dofs are solved. A solution is reached that meets a specified
criterion based on a relative tolerance of 0.0001.
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4.2.2. Geometry, Boundary Conditions, and Mesh
The numerical simulation focuses on a representative volume element (RVE) of
the pipe wall to capture the critical aspects of crack initiation and propagation under
the influence of hydrogen embrittlement. We assume a hypothetical scenario where
a square slice with a 1 mm length is modeled in plane strain. The chosen boundary
conditions for the RVE are inspired by the works of Nguyen et al. [35, 34], which utilized
displacement boundary conditions in their microstructure models. The geometry and
boundary conditions are depicted in Fig. 5. The top part of the section is modeled to
represent the properties of the OD, while the bottom part simulates the properties of
the material near the ID. The entire section is subjected to specific boundary conditions
to replicate the operational stresses experienced by the pipe in service. The left and
right edges of the domain are subjected to horizontal tensile loading, as indicated
by the blue arrows, simulating the hoop stresses. The bottom edge of the domain
is constrained vertically, preventing vertical displacement, while allowing horizontal
movement to simulate the support provided by the pipe wall. The top edge of the
domain is free to move in both horizontal and vertical directions, allowing the material
to deform under the applied tensile load. By allowing horizontal movement at the ID,
we accurately capture the hoop stress, which is the primary driver of crack growth
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Fig. 5: (a) Schematic representation of the geometry and boundary conditions for the numerical simulation, showing the displacement and initial crack locations, (b) micrograph showing the distribution
and size of inclusions within the material inspired from, (c) histogram showing the frequency of the
size of inclusions from, and (d) finite element mesh used for the simulation, highlighting the refined
mesh around the inclusion areas.
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in our model. Constraining vertical movement at the ID simplifies the simulation by
concentrating on the critical horizontal stresses. This assumption allows us to reduce
unnecessary complexity in the model, while still ensuring the most relevant stress
behaviors, essential for crack propagation analysis, are accurately represented. The
green line shown in Fig. 5(a) represents the hydrogen concentration assumed on the
ID. We modeled 10 inclusions, assuming sizes between 0 µm and 15 µm. This size
range was determined by inspecting both the micrographs in Fig. 4 and those from
[51], as shown in Fig. 5(b). The inclusion sizes were based on the data from [51], with
selected sizes ranging from 0 to 15 µm. Fig. 5(c) presents a histogram of the inclusion
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sizes found in [51, 52], demonstrating that most inclusions fall within our chosen range.
The simulation was made for four different cases. The cases are described as follows: Case 1 uses the distribution shown in Fig. 6(a), where there is a linear gradient of
hardness from the OD to the ID. Case 2 is similar to Case 1, except that the hardness
is uniform throughout the entire domain, with the properties of the ID (141 HV). Case
3 is similar to Case 1, except that the OD and ID inclusion distributions are geometrically flipped while maintaining a linear gradient of hardness. Case 4 is similar to Case
2 but with a geometrically flipped distribution of inclusions. Each case was simulated
three times with different initial bulk hydrogen concentrations, Cini = 0, 1, and 2 wt
ppm. Given the reported operating environment of 42.5% H2 S at 70◦ C, high hydrogen
ingress is not expected. While more sophisticated models incorporating both dynamic
and moving chemical boundary conditions exist [53, 33], adding this complexity was
deemed unnecessary for the qualitative investigation of the primary failure mechanisms
in this specific case, particularly given the inherent limitations of post-failure analysis which make precise experimental replication for boundary condition determination
infeasible. Thus, these values were chosen for investigative purposes, assessing sensitivity to plausible hydrogen concentrations. The mesh used in the simulation consists
of linear 4-node quadrilateral elements, with a very fine resolution of 175,179 elements.
Assuming a phase-field length scale of l = 0.0025 mm, an element size of l/2 was used.
The choice of element size is justified in Section 4.2.4, where a mesh sensitivity analysis demonstrates its adequacy for capturing the mechanical response accurately while
maintaining computational efficiency. Fig. 5(d) shows an example mesh that was used
for simulating Case 1 of the four randomized cases.
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4.2.3. Material Properties
In this study, we are modeling two distinct components: the steel matrix and
the inclusions within the material. The inclusions are assumed to be linear elastic
materials without consideration for phase field damage. Typical for inclusions found
in the material, their elastic properties are characterized by an elastic modulus of 300
GPa and a Poisson’s ratio of 0.2. The choice of this Young’s modulus value was based
on studies of aluminates, silicates, and carbides, which report typical modulus values
in the range of 200-400 GPa. Given this range, we chose a Young’s modulus of 300 GPa
as an average value, which is supported by several studies [54, 55, 56]. For the steel
matrix, the mechanical properties used in the model are a Young’s modulus (E) of 210
GPa and a Poisson’s ratio of 0.3. Determining the precise initial fracture toughness
values (Gc (0)) for the steel matrix is challenging due to the specific conditions of the
pipe. Therefore, we propose establishing a relationship between hardness and fracture
toughness based on data collected from the literature. This was done to effectively
capture the effect of the hardness gradient on the initial fracture toughness (Gc (0)).
We introduce tensile strength as an intermediate link in this relationship. The HV
hardness values obtained from Rockwell microhardness testing across the thickness,
shown in Table 5, were used to determine tensile strength (Sut ) using the relationship
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from [57, 58]:
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Fig. 6: Schematic showing the chosen cases to be simulated. (a) Case 1: randomized inclusion
distribution with a linear gradient of hardness. (b) Case 2: randomized inclusion distribution with
uniform hardness. (c) Case 3: flipped inclusion distribution of Case 1 with a linear gradient of
hardness. (d) Case 4: flipped inclusion of Case 1 distribution with uniform hardness.
Sut = 3.15Hv
(20)
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Subsequently, the tensile strength (Sut ) was used to estimate the initial fracture toughness (KIC ) by fitting a power law to extensive experimental data on steels from the
literature [59], as shown in Fig. 7. The expression of this fitted power law is:
−0.8141
KIC (Sut ) = 29540Sut
(21)
These relationships were verified to fall within the actual ranges of fracture toughness
and tensile strength for ASTM A106 Grade B steel [60], where Sut is greater than 413.7
√
MPa (specified minimum tensile strength), and KIC ranges from 151 to 284 MPa m.
To convert KIC to Gc (0), the following relation is used:
Gc (0) =
19
2
KIC
E′
(22)
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Fig. 7: Correlation between KIC and Sut in steels, illustrated with a fitted power law derived from
extensive experimental data [59].
E
where E ′ is the plane strain modulus, defined as E ′ = 1−ν
2 for plane strain conditions.
Table 6 summarizes the hardness, equivalent Vickers hardness, tensile strength, and
initial fracture toughness values across the pipe thickness:
Table 6: Hardness, tensile strength, and fracture toughness across the pipe thickness.
Location
ID
OD
HV hardness
141
177
√
Sut (MPa) KIC (MPa m)
444.2
206.5
557.6
171.6
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The hardness of the simulated sample will be modeled to have a linear distribution
across the domain length, with the highest hardness (177 HV) at the face labeled OD
and the lowest (141 HV) at the face labeled ID. Points in between will have a linear
distribution of hardness based on their distance from the OD to the ID.
For hydrogen transport, the material properties used include a binding energy of
30 kJ/mol and a partial molar volume of V̄H = 2000 mm3 /mol [26]. The diffusion
coefficient used is D = 5.27 × 10−4 mm2 /s which is calculated based on a working
temperature of 70 °C using the formula:
1120
−4
(23)
D(T ) = 1.379 × 10 exp −
T
where T is the temperature in Kelvin. This formula, derived from atomistic calculations, provides the hydrogen diffusion coefficient for bcc-iron as determined in [61].
4.2.4. Mesh Convergence Study and Effect of RVE Size
To ensure the robustness of the numerical results, a mesh convergence study and an
analysis of the effect of RVE size on the mechanical response were conducted. These
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analyses aimed to confirm the reliability of the phase-field model used in this study.
The analyses were performed using Case 1 with a hydrogen boundary condition of
C = 2 wt ppm.
A mesh sensitivity analysis was performed for a single phase-field length scale to
determine the optimal mesh size. The maximum load was compared across different
mesh configurations, as shown in Fig. 8(a), which plots the results in terms of the
number of elements. For reference, a mesh size equal to half of the phase-field length
scale (l/2) corresponds to approximately 170,000 elements, while a mesh size that
is 5 times smaller (l/5) corresponds to approximately 485,000 elements. The results
demonstrate that the maximum load stabilizes with increasing refinement, with no
differences observed between the l/2 and l/5 configurations. To balance computational
efficiency with accuracy, the l/2 configuration, corresponding to a mesh size of 2.5×10−3
mm, was selected for this study, as shown in Fig. 5(d). This choice ensures accurate
resolution of damage gradients while maintaining computational feasibility.
Fig. 8: (a) Mesh convergence study showing peek stress vs. number of elements, and (b) effect of RVE
size, illustrating the numerical robustness and representativeness of the selected mesh and RVE size.
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The effect of RVE size on the mechanical response was analyzed by varying the
size of the RVE while maintaining the same inclusion density across all configurations.
Fig. 8(b) compares the stress-strain curves for different RVE sizes, showing that the
mechanical response becomes independent of the RVE size once it is sufficiently small,
as achieved with the selected 1 mm x 1 mm RVE used in this study.
These analyses confirm that the chosen mesh size and RVE dimensions result in a
mesh- and size-independent response, ensuring the reliability of the phase-field simulations presented in this study.
5. Numerical Results
The simulation results offer valuable insights into the mechanisms of crack initiation and propagation, emphasizing the influence of inclusions and hardness variations.
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The primary objective is to validate the hypothesis that higher hardness at the OD,
combined with the presence of inclusions, significantly increases susceptibility to SSC.
This condition is expected to result in failures initiating at the OD and propagating
towards the ID, despite the corrosive environment being more prominent at the ID and
hydrogen diffusion occurring towards the OD.
Figs. 9-12 show the progression of damage for each case at three stages: damage
initiation, halfway damaged, and fully damaged. Each figure also differentiates between
the initial hydrogen concentrations: Cini = 0, Cini = 1, and Cini = 2. These figures
illustrate the crack propagation paths and the phase-field parameter ϕ contours for the
four cases with varying initial hydrogen concentrations. In Case 1 (Fig. 9), damage
starts at the OD and progresses towards the ID for all concentrations. This is due
to hydrogen migrating to areas of high hydrostatic stress and accumulating there, as
shown in Fig. 13. In this case, inclusions act as stress concentrators, which results
in a high gradient of the hydrostatic stress, leading to a higher diffusion potential as
shown in equation 17. Additionally, higher hydrogen concentrations lead to higher
hydrogen coverage, θ, which significantly degrades fracture energy, especially on the
ID due to the hardness gradient. This leads to the observed failure patterns. In Case
2 (Fig. 10), cracks propagate more uniformly through the domain when Cini = 0.
For Cini = 1, damage initiates uniformly but concentrates more around the areas with
high inclusions density, especially near the OD. At Cini = 2, damage starts directly
near the OD, indicating that higher initial hydrogen concentration makes the effect of
non-uniform inclusion distribution more apparent, even without a hardness gradient.
Case 3 (Fig. 11) shows similar behavior to Case 1, despite higher inclusion density
near the ID. This suggests that the hardness gradient has a dominant effect, driving
crack propagation from the OD to the ID. In Case 4 (Fig. 12), with uniform hardness
and higher inclusion density near the ID, the crack propagates from the ID to the OD
in all Cini . Here, the inclusion density biases crack initiation near the ID, leading to
failure. These observations demonstrate that both the hardness gradient and the nonuniform distribution of inclusions influence crack propagation from the OD to the ID
in actual pipes. The hardness gradient has a more significant impact on crack behavior
compared to inclusion distribution. However, inclusion distribution still plays a crucial
role, especially in models with uniform hardness, where it is the primary determinant
of crack direction and behavior.
The time to failure for each case and hydrogen concentration is summarized in
Table 7. This table demonstrates that the time to failure decreases significantly with
the presence of hydrogen and the increase in its initial concentration. Moreover, the
simulations show that the presence of a hardness gradient affects the extent of the
impact of the initial hydrogen concentration. As shown in Table 7, in Cases 1 and 3,
where the hardness gradient is present, the failure time is more significantly affected
by the hydrogen concentration compared to Cases 2 and 4. This observation indicates
that the hardness gradient plays a crucial role in determining the susceptibility of
the material to hydrogen-induced failure. The results highlight the importance of
considering material heterogeneity when assessing the durability and reliability of steel
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Fig. 9: FEA results showing ϕ contours for Case 1 at three stages of damage: (1) damage initiation, (2)
halfway damaged, and (3) fully damaged domain. Each subfigure represents different initial hydrogen
BC: (a) C ini = 0 , (b) C ini = 1, and (c) C ini = 2 wt ppm.
pipes exposed to sour environments.
Discussion
The coupled chemo-mechano-damage FEA provided valuable insights into how material properties, hydrogen ingress, and microstructural features contributed to SSC in
the ASTM A106 Grade B steel pipe. The simulation confirmed that higher hardness at
the OD, which was measured at 177 HV compared to 141 HV at the ID (Table 5), com23
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Fig. 10: FEA results showing ϕ contours for Case 2 at three stages of damage: (1) damage initiation,
(2) halfway damaged, and (3) fully damaged domain. Each subfigure represents different initial
hydrogen BC: (a) C ini = 0, (b) C ini = 1, and (c) C ini = 2.
Table 7: Time to failure (in seconds) for the various cases with different initial hydrogen concentrations.
Case
Case 1
Case 2
Case 3
Case 4
C ini = 0 wt ppm
52240 s
48752 s
53692 s
47842 s
C ini = 1 wt ppm C ini = 2 wt ppm
8226 s
8011 s
9487 s
8905 s
8154 s
7815 s
9477 s
8990 s
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Fig. 11: FEA results showing ϕ contours for Case 3 at three stages of damage: (1) damage initiation,
(2) halfway damaged, and (3) fully damaged domain. Each subfigure represents different initial
hydrogen BC: (a) C ini = 0, (b) C ini = 1, and (c) C ini = 2 wt ppm.
bined with a non-uniform inclusion distribution, played a crucial role in initiating crack
growth. Harder regions are typically more susceptible to hydrogen embrittlement due
to lower ductility and fracture toughness,
as shown by the significant √
drop in fracture
√
toughness at the OD (171.6 MPa m) compared to the ID (206.5 MPa m). This, coupled with the stress concentration caused by inclusions, created localized areas highly
prone to crack initiation and propagation. The experimental findings, where cracks
were observed propagating toward inclusions near the OD, were consistent with the
simulation results, as shown in Fig. 4(e). The combination of high hardness and dense
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Fig. 12: FEA results showing ϕ contours for Case 4 at three stages of damage: (1) damage initiation,
(2) halfway damaged, and (3) fully damaged domain. Each subfigure represents different initial
hydrogen BC: (a) C ini = 0, (b) C ini = 1, and (c) C ini = 2 wt ppm.
inclusions near the OD led to faster crack initiation and propagation, confirming that
both factors worked together to drive the failure mechanism. This highlights the need
for careful control of hardness levels and inclusion content in material manufacturing
to reduce susceptibility to SSC in sour service environments.
The results also showed that the introduction of hydrogen significantly reduced
the time to failure, emphasizing its role as a critical factor in SSC progression. For
instance, in the simulation with an initial hydrogen concentration of 1 wt ppm, the
time to failure decreased from 52,240 s to 8,226 s (Table 7) compared to the case with
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Fig. 13: Hydrogen concentration C contours for Case 1 with Cini = 2 wt ppm prior to crack propagation.
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no hydrogen. However, when the initial hydrogen concentration was increased to 2
wt ppm, the time to failure further reduced, but at a slower rate (8,011 s), indicating
that the effect of hydrogen on failure time is not linear. This suggests that while
the presence of hydrogen is a key contributor to accelerating crack growth, its impact
diminishes as the concentration increases, highlighting the importance of controlling
even low levels of hydrogen ingress to prevent embrittlement. Even small amounts of
hydrogen can drastically reduce the material’s time to failure. Nonetheless, at higher
concentrations, hydrogen continues to pose a significant risk, reinforcing the need for
effective corrosion control measures to limit its penetration into the steel.
The findings of this study assumes brittle material behavior, which aligns with conditions of high hydrogen ingress where materials are known to transition from ductile
to brittle failure. Such an assumption is valid for a lot of SSC cases in sour natural gas
environments, where significant hydrogen ingress reduces ductility and fracture toughness. The specific conditions studied included a sour gas composition of 42.5% H2 S.
These conditions are typical of SSC-prone environments and justify the model’s applicability in capturing the dominant mechanisms under such scenarios. Although the
model does not account for plastic deformation, it effectively captures the dominant
crack growth mechanisms under these conditions. This makes the model particularly
applicable to scenarios where hydrogen penetration reaches levels sufficient to induce
brittle failure, as commonly observed in SSC.
Furthermore, the results underscore the importance of a holistic approach to failure
prevention in pipelines exposed to sour service environments. Material properties, such
as hardness and inclusion distribution, must be controlled in conjunction with effective environmental management to minimize the risk of SSC. The FEA demonstrated
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that localized hydrogen embrittlement, driven by inclusions and hardness gradients, is
a major factor in reducing pipeline integrity, as confirmed by the significant damage
initiation and crack propagation near the OD in the simulation (Fig. 9). Therefore,
proper corrosion control strategies, regular inspections, and material quality management are essential to ensure long-term durability and safety in sour gas pipelines.
6. Conclusions
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This study analyzed the failure of an ASTM A106B steel pipe in a sour natural
gas environment, revealing that SSC initiated at the OD and propagated inward due
to a higher hardness (177 HV at the OD vs. 141 HV at the ID) and the presence
of inclusions. Experimental methods, including SEM-EDS, XRD, and metallographic
analysis, identified a higher inclusion density near the OD as a critical factor facilitating hydrogen accumulation and crack initiation. Phase-field FEA simulations on a
hypothetical RVE incorporated the effects of hardness gradient and non-uniform inclusion distribution, confirming their role in promoting crack initiation. The simulations
also demonstrated that hydrogen embrittlement significantly accelerated crack growth,
reducing the time to failure from 52,240 s without hydrogen to 8,226 s with 1 wt ppm
of hydrogen, and further decreasing to 8,011 s at 2 wt ppm. The model assumes brittle material behavior, which is valid under conditions of high hydrogen ingress, such
as those encountered in the studied sour gas composition (42.5% H2 S). These findings emphasize the importance of controlling hydrogen ingress and managing material
properties to mitigate SSC susceptibility. The methods presented in this study could
also prove useful for hydrogen blending or pure hydrogen transmission pipelines, given
the similar embrittlement mechanisms involved. The success of phase-field modeling
in capturing SSC crack growth under material inhomogeneity underscores its potential
value in failure prediction and understanding. Future work should focus on improving
material resistance to SSC, refining predictive models to incorporate additional complexities, and implementing effective corrosion control measures and regular inspections
to prevent similar failures.
Acknowledgements
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The authors acknowledge the financial support provided by Abu Dhabi National
Oil Company (ADNOC) under grant no. S.O. 9100000617 / KUX 8434000453. The
authors are thankful for the assistance of Mr. Wesley Latimer and Mr. Prakash Dodia
at Acuren and SEMx Materials Analysis Laboratories in Calgary, Canada, with the
experimental analyses.
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Highlights
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Conducted experimental failure analysis of ASTM A106B steel pipe exposed to sour gas.
Identified EAC initiation at the outer diameter due to hardness gradients and inclusions.
Simulated failure mechanisms using a hypothetical RVE in FEA, integrating phase-field modeling
with hydrogen diffusion, mechanical stresses, and microstructural features.
Provided insights for pipeline integrity in sour and hydrogen environments.
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CRediT author statement
M. Elkhodbia: Conceptualization; Methodology; Software; Validation; Formal analysis; Investigation;
Data Curation; Writing - Original Draft; Writing - Review & Editing; Visualization.
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I. Gadala: Conceptualization; Methodology; Validation; Formal analysis; Investigation; Resources; Data
Curation; Writing - Review & Editing; Visualization; Supervision.
I. Barsoum: Conceptualization; Methodology; Software; Validation; Formal analysis; Investigation;
Resources; Data Curation; Writing - Review & Editing; Visualization; Supervision; Project administration;
Funding acquisition.
A. AlFantazi: Writing - Review & Editing; Visualization; Supervision.
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M. Abdel Wahab: Writing - Review & Editing; Visualization; Supervision.
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Declaration of interests
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☒ The authors declare that they have no known competing financial interests or personal relationships
that could have appeared to influence the work reported in this paper.
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☐ The authors declare the following financial interests/personal relationships which may be considered
as potential competing interests: