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# Investigating the influence of strain rate on hydrogen embrittlement in steel sub-size tensile specimens using 3D X-ray tomography

L.M. Santana a,c,d,*, V. Okumko a,b, A. King b, T.F. Morgeneyer a,b, J. Besson a,b, Y. Madi a,b

## ARTICLE INFO

### Keywords:

Gaseous hydrogen embrittlement

Mini-specimen

3D X-ray tomography

Rupture

Plasticity

Damage quantification

## ABSTRACT

This study investigates the effect of strain rate on hydrogen embrittlement in ferritic-pearlitic E355 steel sub-size tensile specimens. Micrometer-scale damage analysis was performed using 3D X-ray tomography. Tests were conducted using an optical extensometry at varying strain rates in air and a 100 bar gas hydrogen atmosphere, including interrupted tests before rupture to capture damage states. Hydrogen reduces ductility, with losses reaching up to 62.8% at slower strain rates. At moderate strain rate, $5 \times 10^{-4}$ s$^{-1}$, surface damage manifests as brittle, flat ellipsoidal cracks perpendicular to the tensile axis, while the bulk retains ductile damage with prolate voids aligned longitudinally. Hydrogen-enhanced internal shearing leads to damage coalescence via slant fracture of the ligament between surface cracks and internal voids. At low strain rates ($1 \times 10^{-5}$ s$^{-1}$), deeper hydrogen diffusion induces brittle flat ellipsoidal cracks both at the surface and in the bulk.

## 1. Introduction

There is growing interest in the potential of hydrogen produced from renewable resources as a means of decarbonizing the energy sector. One approach to integrating hydrogen into the energy matrix is to transport it through existing natural gas pipelines, which reduces the initial investment [1–4].

However, a challenge arises from hydrogen’s ability to diffuse through metals and interact with their crystal lattice, rendering them less ductile and more susceptible to cracking. This complex phenomenon, known as Hydrogen Embrittlement (HE), has been the subject of investigation over the years [5,6].

Hydrogen diffusion in metals is governed by concentration-driven transport, interaction with microstructural trapping sites, and the influence of mechanical stress. The sub-surface hydrogen concentration, $C_0$, follows Sieverts’ law, assuming hydrogen behaves as an ideal gas [7]:

$$C_0 = K \sqrt{P}, \quad K = K_0 \exp \left( -\frac{\Delta H}{RT} \right) \qquad (1)$$

where K represents solubility, dependent on temperature but independent of pressure.

Microstructural defects such as vacancies, dislocations, and grain boundaries serve as hydrogen trapping sites, significantly altering diffusion kinetics. Traps are classified as reversible or irreversible based

on their binding energy $E_b$, which dictates hydrogen retention [8]. For reversible traps, Oriani’s equilibrium model expresses trap occupancy as [9]:

$$\frac{\theta_T}{1 - \theta_T} \cdot \frac{1 - \theta_L}{\theta_L} = \exp \left( -\frac{E_b}{RT} \right) \qquad (2)$$

where $\theta_T$ and $\theta_L$ are the occupancies of trap and lattice sites, respectively. Trapping reduces the effective diffusivity, and at critical concentrations, trapped hydrogen can contribute to crack initiation.

Mechanical stress further influences diffusion by modifying the chemical potential of hydrogen. In regions of tensile hydrostatic stress, hydrogen migrates toward stress-concentrated zones such as crack tips, even in the absence of a concentration gradient [10]. This stress-driven diffusion modifies the transport equation by introducing an additional flux term:

$$\frac{\partial C}{\partial t} = D_L \nabla^2 C + \nabla \cdot \left( -\frac{D_L C}{RT} \cdot \overline{V_H} \nabla \sigma_m \right) - \frac{\partial C_1}{\partial t} - \frac{\partial C_2}{\partial t} \qquad (3)$$

where $\overline{V_H}$ is the partial molar volume of hydrogen, and $\sigma_m$ is the hydrostatic stress. These effects are crucial for understanding hydrogen embrittlement mechanisms in metals exposed to mechanical loading and hydrogen environments [8].

<footnote>a Centre des Matériaux, MINES Paris, Université PSL, CNRS UMR, 7633, France</footnote>

<footnote>b Synchrotron SOLEIL, France</footnote>

<footnote>c Air Liquide, Innovation Campus Paris, France</footnote>

<footnote>d Mannesmann Precision Tubes France SAS, France</footnote>

<footnote>* Corresponding author at: Centre des Matériaux, MINES Paris, Université PSL, CNRS UMR, 7633, France. E-mail address: luciano.meirelles_santana@minesparis.psl.eu (L.M. Santana).</footnote>
Several mechanisms have been proposed to elucidate the phenomenon of HE, including Hydrogen Enhanced Localized Plasticity (HELP) [11–13], Hydrogen Enhanced Decohesion (HEDE) [14,15], Adsorption-Induced Dislocation Emission (AIDE) [16], and Hydrogen Enhanced Strain-Induced Vacancy (HESIV) [17].

The HELP mechanism proposes that hydrogen enhances the mobility of dislocations near the tips of cracks, which subsequently increases local plastic deformation. This localized increase in plasticity may lead to a greater vulnerability to overall brittle fracture in the material. On the other hand, the HEDE mechanism involves a reduction in cohesive energy at grain boundaries and interfaces, which intensifies their susceptibility to decohesion and facilitates crack growth. The AIDE mechanism describes how hydrogen adsorption weakens interatomic bonds, making it easier for dislocations to be emitted from crack tips. In contrast, the HESIV mechanism emphasizes how hydrogen atoms promote the formation of lattice vacancies in metals, resulting in reduced strength and increased fracture susceptibility.

Moreover, various researchers propose that HE may arise from the interplay of several mechanisms. For instance, Novak et al. [18] argue that hydrogen significantly affects dislocations by becoming trapped within them. This trapped hydrogen decreases the critical stress for dislocation movement and lowers the energy required for decohesion at dislocation pile-ups at the carbide/matrix interface. Their proposed model suggests that the combined effects of the HELP and HEDE mechanisms explain the observed behaviors. Additionally, Martin et al. [19] examined quasi-cleavage surfaces on API X80 and X60 grade HIC pipeline steels using techniques such as Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM), and Transmission Electron Microscopy (TEM). Their findings showed that these surfaces are not uniform but feature large-scale undulations. TEM analysis revealed a high density of dislocation lines and loops just beneath the surface, indicating that hydrogen contributes to the development of this dislocation substructure and increases the local concentration of hydrogen, thereby enhancing the risk of cracking in these regions. This evidence reinforces the view that the HELP mechanism, rather than HEDE, is responsible for the observed flat quasi-cleavage fractures.

The utilization of sub-size specimens, machined from coupons extracted from pipelines, has been proposed as a method for monitoring the effect of hydrogen on mechanical properties during operational life [20]. Sub-size specimens allow mechanical testing of pipeline materials without interrupting gas production, making the process more practical and efficient. Additionally, their use in a small-volume chamber eliminates the need for explosion-proof facilities, enabling laboratory-scale testing and reducing costs. The Slow Strain Rate Tensile Tests (SSRT) has been used for investigation of HE by several authors [21–25], as it enables controlled exposure of materials to hydrogen while progressively straining them at low rates. The slow deformation allows the diffusion of hydrogen atoms into the material's microstructure to proceed over a longer period of time, thereby increasing the probability of embrittlement phenomena, including crack initiation, propagation and ductility loss.

3D X-ray Tomography is an effective tool for exploring damage micro-mechanisms qualitatively and quantitatively at the micrometer scale [26,27]. This technique proves particularly useful in studying HE [28–35]. In particular, Shibata et al. [30] used X-ray tomography combined with FIB-SEM serial sectioning to investigate hydrogen-related intergranular crack propagation in martensitic steel, highlighting the role of prior austenite grain boundary (PAGB) segments in crack arrestability. Depraetere et al. [31,32] employed X-ray tomography to investigate the impact of hydrogen on damage observed in tensile samples of X56 and X70 grade steels pre-charged with hydrogen. Their observations revealed that while the presence of hydrogen accelerates fracture mechanisms in X56 grade steel, it alters void shape ratios in X70 grade steel. Konert et al. [33] studied the impact of hydrogen on the mechanical properties of an API 5L X65 pipeline steel tested in gaseous hydrogen atmosphere using the hollow specimen technique

and X-ray tomography. They noted a significant change in crack orientation and the nucleation of secondary cracks in hydrogen-tested samples compared to those in a reference atmosphere. Wang et al. [34] observed the particle debonding and fracture behavior of H-charged 7075 Al alloy during tensile testing. Their findings indicated that while hydrogen influences the debonding of Mg₂Si particles, its effect on ductile fracture appears to be limited. The study of void size and spatial distribution is crucial in understanding hydrogen embrittlement because these factors directly influence the initiation and propagation of microcracks. Using transmission X-ray microscopy during SENT testing under in-situ electrochemical hydrogen charging, Lee et al. [35] observed that hydrogen charging results in void formation concentrated within approximately 10 µm of the crack tip. Near the crack tip, the voids are smaller and elongated in the crack direction, contrasting with the larger voids found in samples without hydrogen charging.

It is also important to emphasize that most hydrogen studies are conducted in an electrolyte environment, even though the intended applications involve pressurized gaseous conditions. Limitations in laboratory hydrogen charging methods — often performed under conditions harsher than those in service — can complicate the transferability of experimental data to real-world applications. This necessitates an effective correlation (e.g., via hydrogen fugacity) between electrochemical and gaseous charging methods [36]. The present study proposes an analysis within a gas environment, offering a refined methodology to examine the interplay between mechanical behavior, damage evolution, and hydrogen exposure. In a previous study, Madi et al. [20] demonstrated the feasibility of characterizing the mechanical tensile properties of pipeline steel using sub-size tensile specimens with diameters of 1.2 mm and 2.4 mm. The findings obtained in air demonstrated that the acquired data were identical to those from standard-sized specimens with a diameter of 4.0 mm, particularly when examining the stress-radial strain curve behavior. It was shown that the localized plastic deformation (radial strain in the necking region) was consistent across the different specimen geometries. Madi et al. further advanced their research by testing sub-size specimens (1.2 mm and 2.4 mm) in a gaseous H₂ environment under pressures of 100 bar and 200 bar, applying a strain rate of 5 × 10⁻⁴ s⁻¹. The results demonstrated that even with strain rates higher than those typically recommended by the standards, it was possible to observe distinct responses to the HE effect for different specimen geometries and H₂ pressures. This approach enabled the development of a new methodology for obtaining data useful for material screening, through the calculation of distinct Hydrogen Embrittlement Indices (HEI), and even for use as input data for Finite Element Analysis (FEA) simulations of hydrogen embrittlement.

In addition to experimental efforts, modeling of HE serves as an indispensable tool for interpreting results obtained from experimental campaigns [37–40]. In particular, in [40], Santana et al. demonstrated an excellent agreement between experiments and simulations during Disk Pressure Tests (DPT) on the same E355 modified steel of the present study, where numerical simulations using the Kumnick et al. model [41] for the evolution of hydrogen trap density with accumulated plastic strain corroborated the experimental. Pinto et al. [42] further advanced the field by employing a modified non-local Gurson–Tvergaard–Needleman (GTN) model coupled with hydrogen diffusion. The simulations of tensile tests revealed that crack initiation predominantly occurs from the surface for specimens tested at moderate strain rates. However, at low strain rates, when hydrogen has sufficient time to diffuse, material embrittlement occurs within the bulk. Therefore, damage becomes more pronounced at the center of the specimen, where triaxiality is higher after the onset of necking. However, the experimental dataset used in their study [43] lacked direct evidence of this damage evolution, making it impossible to experimentally validate the predictions made by Pinto et al.

This study complements the work of Madi et al. by investigating lower strain rates and offering a more detailed characterization of hydrogen embrittlement through 3D X-ray Tomography. This technique
<figure><img src="image_3.png" /><figcaption>(a) Ferritic matrix with elongated pearlite bands. Average grain diameter is 15.9 µm.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) SEM analysis of unetched specimens reveal few globular inclusions, averaging 0.25 µm in diameter,</figcaption></figure>

<caption>Fig. 1. Microstructure of the studied steel 1(a) obtained by metallographical analysis using Nital etching, and globular inclusions 1(b) revealed by SEM without etching.</caption>

provides an advanced characterization that enables the study of the damage volume, distribution, morphology and orientation. Sub-size tensile specimens were taken from the same modern ferritic-pearlitic steel used by Madi et al. E355 mod., which was selected for its isotropic behavior, excellent ductility, and high toughness, making it well-suited for hydrogen embrittlement studies. Its composition, microstructure, and mechanical properties closely resemble those of pipeline steels used for natural gas transportation, particularly X52 steel. Tests under a gaseous hydrogen environment at various strain rates were interrupted before rupture to pinpoint the origin of damage. The goal is to investigate the distinct damage evolution for various strain rates, thereby refining the analysis and interpretation of mechanical tests in hydrogen environments. This will help to deepen our understanding of the underlying damage mechanisms.

## 2. Experimental procedures

### 2.1. Material

For this study, a modern E355 modified steel grade (referred to as E355 mod. steel) was utilized. It was obtained in the form of a seamless hot-rolled tube, manufactured by the Thermo-Mechanical Controlled Process (TMCP). The chemical composition (in at%) of the material is 0.15% C, 1.38% Mn, 0.19% Si, 0.04% Cr, 0.02% Ni, 0.01% Mo, 0.002% S, 0.015% P, with the balance being Fe.

The microstructure comprises a ferritic matrix containing elongated pearlite bands in both longitudinal and transverse directions, as observed in Fig. 1(a). The average grain size was determined using the intercept method according to the ASTM E112 standard. The studied material has a grain size number of 9.0, corresponding to an average grain diameter of 15.9 µm.

Scanning Electron Microscopy (SEM) observations and Energy Dispersive Spectroscopy (EDS) analyses were performed on the unetched specimens to assess their inclusion content, morphology, and composition. A few globular inclusions were observed (Fig. 1(b)), with an average diameter of 0.25 µm. These inclusions were identified as CaS and (Al, Mg) oxides through EDS analysis. The volume fraction of inclusions in the studied steel is 0.06%.

### 2.2. Tensile test

Sub-size tensile specimens with a diameter ($\Phi_0$) of 1.2 mm and a gauge length ($L_0$) of 2 mm, denoted as mST-$\Phi_0$ = 1.2 mm, were extracted parallel to the longitudinal (L) direction of the tube, ensuring that the loading direction during the tensile test corresponds to the L-direction of the tube. The machining process ensured the surface

roughness was strictly kept below 0.35 µm Ra. Madi et al. [20] demonstrated that this specimen geometry does not affect the mechanical properties in a test campaign comparing standard and sub-size specimens. Across all specimen geometries, the Engineering Stress ($F/S_0$) versus radial strain ($\Delta\Phi/\Phi_0$) plots exhibited consistent results, indicating that local plastic behavior remains unaffected by specimen geometry and the machining processes, even in the post-necking stage.

The tensile tests were conducted using a dynamic MTS servo-hydraulic machine, a high-precision testing system, equipped with a high-pressure chamber designed for non-ATEX conditions, meaning there was no significant risk of explosive atmosphere, and specialized explosion-proof equipment was not required. This chamber is equipped with four sapphire windows, enabling the utilization of the Edge Tracing (ET) technique for extensometry as previously described in the literature [20,44]. The test setup includes a precise displacement sensor capable of controlling very slow displacement rates as low as to 0.3 µm/min and an internal load cell for direct measurement of the specimen's mechanical load. A major technical advance in this test setup is the real-time communication between the optical measurement system and the test machine controller, which allows the displacement rate to be adjusted based on the radial contraction of the specimen. This high-precision control enables the test to be halted just before rupture, preserving the specimen intact and allowing for the detailed study of hydrogen-induced damage evolution via 3D X-ray tomography.

For further details about this tensile test methodology, please refer to the previous work of Madi et al. [20].

The tests were performed at strain rates ($\dot{\epsilon}$) of $5 \times 10^{-4} \text{ s}^{-1}$, to replicate the results obtained in the previous study by Madi et al. and ensure comparability across studies, and $1 \times 10^{-5} \text{ s}^{-1}$, which was selected based on the recommendations of the ANSI/CSA CHMC 1-2014 standard [45], Test Methods for Evaluating Material Compatibility in Compressed Hydrogen Applications - Metals, for slow strain rate tensile testing of smooth specimens in hydrogen environments. Both strain rates were tested under air and gaseous $H_2$ environments.

The stated strain rate corresponds to the local longitudinal strain rate in the necking region of the specimen. For the specimen geometry employed in this work, a local longitudinal strain rate of $5 \times 10^{-4} \text{ s}^{-1}$ corresponds to a global longitudinal strain rate of $4 \times 10^{-4} \text{ s}^{-1}$, while a local strain rate of $1 \times 10^{-5} \text{ s}^{-1}$ corresponds to a global strain rate of $8 \times 10^{-6} \text{ s}^{-1}$. Four tests were interrupted before the specimens reached final rupture, preserving the damage induced by plastic deformation and the $H_2$ interaction within the material. Three tests were conducted until the fracture of the specimen.

A field emission SEM operated at 15 kV was used to observe the lateral surfaces and cross sections of the interrupted tensile test specimens, as well as the surface fractures of the specimens from completed tensile tests.
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Illustration of the methodology for reconstructing a volume representing the deformed specimen without the damage. 2(a) shows a cross-sectional view of the XY plane, where the surface crack is indistinguishable from the surrounding background. 2(b) demonstrates the manual segmentation process, extending the specimen bulk to incorporate the surface crack. This segmentation is performed at intervals of 20 voxels along the Z-axis, as depicted in 2(c). Interpolation of these segments generates the reconstructed volume shown in 2(d).</figcaption></figure>

## 2.3. 3D X-ray tomography

X-ray tomography was performed at SOLEIL Synchrotron<fnref n="1" /> to obtain 3D images of the specimens following the interruption of the tensile tests. Contrast between steel and damage (voids and cracks) was achieved using a white beam with a peak energy of 65 keV and an exposure time of 20 ms. The volume of interest was 2.36 mm³ (2048 × 2048 × 2048 voxels) with a voxel size of 0.275 µm³ (0.65 × 0.65 × 0.65 µm³). A total of 1500 projections of each specimen were acquired to enable the 3D segmentation and reconstruction.

As previously characterized in Refs. [20,40], the steel in question exhibits isotropic behavior in terms of plasticity. Accordingly, no specific effort was made to align the S and T orientations of the specimen with the X and Y coordinates of the tomography data. However, it is guaranteed that the Z-axis of the tomography data correlates with the longitudinal (L) direction of the tensile specimens.

The tomography data were processed using Pymicro [46], an open-source Python package for working with material microstructures and 3D datasets, and with Thermo Scientific™ Avizo™ Software.<fnref n="2" />

A non-local means filter was applied to enhance local contrast in the tomography data, allowing for a clearer distinction between porosities and the surrounding matrix. Hydrogen-induced damage in

steel specimens manifests both on the surface (surface cracks) and internally (bulk damage). However, distinguishing surface cracks from the free surface proves to be a significant challenge, as their volumetric opening makes it difficult to identify the initiation sites. This problem is compounded by the similarity in grey-level values between surface cracks and the surrounding air, as illustrated in Fig. 2(a), leading to errors in threshold-based segmentation. To address this issue, it is crucial to generate a mask that represents the deformed specimen while excluding any contribution from surface damage.

For specimens without surface cracks, a simple fill-holes operation on the raw data suffices. However, when surface cracks are present, this method fails to distinguish cracks from the surrounding air due to their similar grey-level values and connectivity with the surroundings. To resolve this, a specialized workflow was developed in Avizo. Specifically, the specimen is manually segmented along XY planes, creating a mask that integrates surface cracks into the bulk (Fig. 2(b)). This segmentation is repeated at regular intervals along the Z-axis for accuracy (Fig. 2(c)) and then interpolated to produce a volumetric representation, called the Initial Seed (Fig. 2(d)).

The methodology refines the Initial Seed through erosion and inversion operations, generating two distinct elements: an Internal Seed (representing the specimen's interior) and an External Seed (representing the surrounding background). These seeds are then used in a watershed segmentation, where their expansion is tightly guided by the gradient of the targeted surface (derived from the grayscale values acquired via X-ray tomography).

<footnote n="1">¹ https://www.synchrotron-soleil.fr</footnote>

<footnote n="2">² https://www.thermofisher.com</footnote>
<table><caption>**Table 1**
Summary of results for interrupted tensile tests and for tests to failure.</caption><thead><tr><th>Test ID</th><th>Environment</th><th>ε<br>s<sup>-1</sup></th><th>YS<br>MPa</th><th>UTS<br>MPa</th><th>ΔΦ/Φ<sub>0</sub>|<sub>s</sub></th><th>F/S<sub>0</sub>|<sub>s</sub><br>MPa</th></tr></thead><tbody><tr><td>AIR-V4-0.51</td><td>Air</td><td>5 × 10<sup>-4</sup></td><td>318</td><td>506</td><td>0.514</td><td>226</td></tr><tr><td>H<sub>2</sub>-V4-0.17</td><td>100 bar H<sub>2</sub></td><td>5 × 10<sup>-4</sup></td><td>336</td><td>505</td><td>0.169</td><td>467</td></tr><tr><td>H<sub>2</sub>-V4-0.30</td><td>100 bar H<sub>2</sub></td><td>5 × 10<sup>-4</sup></td><td>321</td><td>500</td><td>0.301</td><td>221</td></tr><tr><td>H<sub>2</sub>-V5-0.17</td><td>100 bar H<sub>2</sub></td><td>1 × 10<sup>-5</sup></td><td>306</td><td>473</td><td>0.169</td><td>402</td></tr><tr><td>AIR-V4-Full</td><td>Air</td><td>5 × 10<sup>-4</sup></td><td>301</td><td>506</td><td>0.562</td><td>-</td></tr><tr><td>H<sub>2</sub>-V4-Full</td><td>100 bar H<sub>2</sub></td><td>5 × 10<sup>-4</sup></td><td>316</td><td>502</td><td>0.288</td><td>-</td></tr><tr><td>H<sub>2</sub>-V5-Full</td><td>100 bar H<sub>2</sub></td><td>1 × 10<sup>-5</sup></td><td>324</td><td>483</td><td>0.209</td><td>-</td></tr></tbody></table>

Importantly, no explicit convexity constraint is added: the manner in which the watershed expands from the internal and external seeds (ignoring internal cracks where gradients are not sufficiently pronounced) naturally induces a continuous or “convex” envelope of the specimen.

This approach yields a high-fidelity mask closely matching the specimen's boundaries, even in regions where the surface is interpolated. Derived from the segmented Internal Seed, the final mask effectively isolates voids and cracks, enabling reliable and accurate damage analysis in steel specimens. A schematic illustration of these steps is provided in Appendix A

## 3. Results

### 3.1. Tensile tests

Table 1 contains the tensile test parameters and the nomenclature of the tests discussed in this work. The identification is divided into three parts: the first denotes the environment (AIR or H₂), the second the strain rate $\dot{\epsilon}$ (V4: 5 × 10⁻⁴ s⁻¹ or V5: 1 × 10⁻⁵ s⁻¹) and the third term is the value of the radial deformation at the moment the test was interrupted (ΔΦ/Φ₀|s, where the subscript s denotes “stop”). The table also includes the final engineering stress (F/S₀|s) of each test. It is observed that all tests conducted with a $\dot{\epsilon}$ of 5 × 10⁻⁴ s⁻¹ presented similar Yield Strength (YS) (around 301–336 MPa) and Ultimate Tensile Test (UTS) (around 500–506 MPa). However, it is noticeable that the test conducted with a $\dot{\epsilon}$ of 1 × 10⁻⁵ s⁻¹ presented comparable YS (306–324 MPa) and lower UTS (473–483 MPa). This discrepancy in UTS is mainly attributed to the influence of $\dot{\epsilon}$ effect on the viscoplastic behavior of the material, as already discussed by Santana et al. [40]. For similar tensile tests conducted in air at the strain rate of 1 × 10⁻⁵ s⁻¹, UTS values of 477 and 482 MPa were obtained, which fall within the same range as those measured in a gaseous H₂ environment.

It was demonstrated by Santana et al. [40] that the strain rate has no significant influence on the radial strain for this same material. Since the radial strain in air serves in this work as the baseline for comparing the severity of Hydrogen Embrittlement, and this parameter is not significantly influenced by strain rate, the author chose to report only the tests in air conducted at $\dot{\epsilon}$ = 5 × 10⁻⁴ s⁻¹. All the results obtained from tensile tests conducted in a hydrogen gas environment are compared with these air results, despite the distinct strain rates.

Fig. 3 presents the F/S₀ – ΔΦ/Φ₀ plot for the seven different tensile tests. The dashed lines represent the tests conducted until the specimen rupture: AIR-V4-Full (black line), H₂-V4-Full (blue line), and H₂-V5-Full (red line). These tests achieved a final ΔΦ/Φ₀|s values of 0.56, 0.29 and 0.21, respectively. The two tests to failure conducted at strain rate $\dot{\epsilon}$ = 5 × 10⁻⁴ s⁻¹ are the same previously presented by Madi et al. [20].

The curve with white squares corresponds to the F/S₀ – ΔΦ/Φ₀ plot from the AIR-V4-0.51 test. This test was halted at ΔΦ/Φ₀|s = 0.51, corresponding to 91.4% of the final radial strain achieved by the specimen AIR-V4-Full, which was tested under identical conditions until rupture. The interruption occurred just after the inflection point marking the onset of rupture. The interruption point, indicated by a

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Engineering Stress (F/S₀) – Radial Strain (ΔΦ/Φ₀) plot for specimens tested under different environments and strain rates. The solid and dashed curves represent full and interrupted tests, respectively. The data correspond to tests conducted in air ($\dot{\epsilon}$ = 5 × 10⁻⁴ s⁻¹) and in gaseous H₂ at 100 bar with strain rates of $\dot{\epsilon}$ = 5 × 10⁻⁴ s⁻¹ (green and blue) and $\dot{\epsilon}$ = 1 × 10⁻⁵ s⁻¹ (red). The cross markers (X) indicate the point at which the interrupted tests were terminated, followed by unloading. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

cross on the plot, corresponds to a load reduction of 55.3% relative to the UTS.

The curve with green diamonds illustrates the F/S₀ – ΔΦ/Φ₀ plot for the test H₂-V4-0.17. This test was interrupted at ΔΦ/Φ₀|s = 0.17, corresponding to 56.9% of the final radial strain achieved by the specimen H₂-V4-Full, which was tested under the same conditions until fracture. At the point of interruption, the stress was F/S₀|s = 467 MPa, indicating a load decrease of approximately 7.5% relative to the UTS.

The curve with blue circles exhibits the F/S₀ – ΔΦ/Φ₀ plot for the H₂-V4-0.3 test. This test was interrupted at approximately the same stress level as the specimen AIR-V4-0.51 (F/S₀|s = 221 MPa), corresponding to a load decrease of 55.8% relative to the UTS. The interruption occurred at a ΔΦ/Φ₀|s of 0.30, slightly higher than the ΔΦ/Φ₀ of 0.288 observed for the H₂-V4-Full test. This slight difference can be attributed to the natural variability in experimental results, further confirming that the specimen was in a state of imminent rupture.

The curve with red triangles presents the F/S₀ – ΔΦ/Φ₀ plot for the H₂-V5-0.17 test, which was halted at ΔΦ/Φ₀|s = 0.17, just after the onset leading to failure. This ΔΦ/Φ₀|s corresponds to 80.9% of the final radial strain achieved by the specimen H₂-V5-Full, tested until fracture until the same conditions. Although this test was interrupted in the same radial strain level as the H₂-V4-0.17 test, the load decrease was equivalent to 15% of the UTS, which was sufficient to induce the onset of failure in this test.

With these results, a Hydrogen Embrittlement Index can be calculated, using Eq. (4):

$$HEI_{Z} = \left(1 - \frac{Z(H_{2})}{Z(Air)}\right) \times 100 \qquad (4)$$

where Z is the ratio ΔΦ/Φ₀ at the moment of the specimen rupture.

The results clearly show that lowering the strain rate significantly affects embrittlement. There was a notable increase in HEI<sub>Z</sub> from 48.7% at $\dot{\epsilon}$ = 5 × 10⁻⁴ s⁻¹ to 62.8% at $\dot{\epsilon}$ = 1 × 10⁻⁵ s⁻¹. Notably, the HEI<sub>Z</sub> value of 62.8% obtained under 100 bar H₂ at $\dot{\epsilon}$ = 1 × 10⁻⁵ s⁻¹ being comparable with the 59.2% reported by Madi et al. [20] for tests performed at 200 bar H₂ and strain rate of $\dot{\epsilon}$ = 5 × 10⁻⁴ s⁻¹. These
<figure><img src="image_7.png" /><figcaption>Fig. 4. Scanning Electron Microscopy (SEM) observations of the lateral surfaces of interrupted test specimens after unloading. The symbols in the upper left corner of each subfigure correspond to the markers used in Fig. 3. (a) Air-tested specimen ($\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$), showing significant plastic deformation without surface cracking. (b) Specimen tested in 100 bar H₂ at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$ and interrupted at $\Delta\Phi/\Phi_0|_s = 0.17$, exhibiting numerous small surface cracks. (c) Specimen tested in 100 bar H₂ at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$ and interrupted at $\Delta\Phi/\Phi_0|_s = 0.30$, displaying extensive surface cracks, with major cracks oriented at approximately 45° to the tensile axis. (d) Specimen tested in 100 bar H₂ at $\dot{\epsilon} = 1 \times 10^{-5} s^{-1}$, showing relatively fewer secondary cracks compared to (c).</figcaption></figure>

findings highlight the significant impact of strain rate on the severity of hydrogen embrittlement.

Fig. 4 presents Scanning Electron Microscopy (SEM) observations of the lateral surfaces of the interrupted test specimens once the unloading phase is complete.

Fig. 4(a) presents the lateral view from the central zone of the AIR-V4-0.51 specimen as observed before testing. It can be observed that

the surface has undergone significant plastic deformation, and that no surface cracks have formed.

The lateral view of the H₂-V4-0.17 specimen is presented in Fig. 4(b). It is notable that numerous small surface cracks are present.

Fig. 4(c) displays the central zone of the lateral of the H₂-V4-0.30 specimen. There is a substantial presence of extensive surface
<figure><img src="image_8.png" /><figcaption>Fig. 5. 2D slices (XY, XZ, and YZ planes) extracted from the center of the tomography data (1024, 1024, 1024 voxel) of the four specimens tested under different conditions. (a) Air-tested specimen ($\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$, $\Delta\Phi/\Phi_0|_x = 0.51$), displaying significant striction and central void formation. (b) Specimen tested in 100 bar $H_2$ at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$, interrupted after a 15% decrease in UTS ($\Delta\Phi/\Phi_0|_x = 0.17$), showing no evident central damage but with visible surface cracks along the gauge length. (c) Specimen tested in 100 bar $H_2$ at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$, interrupted just prior to rupture ($\Delta\Phi/\Phi_0|_x = 0.30$), exhibiting extensive surface cracks, some propagating internally, along with round voids in the central region. (d) Specimen tested in 100 bar $H_2$ at a lower strain rate ($\dot{\epsilon} = 1 \times 10^{-5} s^{-1}$, $\Delta\Phi/\Phi_0|_x = 0.17$), showing fewer surface cracks but extensive central damage characterized by penny-shaped voids normal to the loading direction, suggesting a different failure mechanism compared to the air-tested specimen.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. XZ plane views of the striction zone for each specimen, highlighting damage mechanisms. (a) Air-tested specimen (AIR-V4-0.51) with significant striction and central voids. (b) Specimen H₂-V4-0.17 with surface cracks but no evident central damage. (c) Specimen H₂-V4-0.30 with extensive surface cracking and central voids. (d) Specimen H₂-V5-0.17 with severe central damage and penny-shaped voids.</figcaption></figure>

cracks, with the larger ones oriented at a 45° angle to the specimen's longitudinal axis.

Fig. 4(d) depicts the lateral view of the central part of the H₂-V5-0.17 specimen after testing. In comparison with Fig. 4(c), it is clear that there is a relatively low amount of secondary cracks.

Hydrogen-induced surface cracks in tensile specimens are strongly influenced by the surface finish and machining defects introduced during fabrication. Indeed, surface defects (machining scratches, steps, etc.) favor crack initiation in the presence of hydrogen [47]. These defects serve as sites for hydrogen adsorption and facilitate crack initiation by localizing deformation and weakening the protective oxide layer, enabling hydrogen ingress into the steel [48].

Interestingly, surface cracks oriented at approximately 45° to the tensile direction were observed in specimens tested in hydrogen environments, tearing the material independently of machining traces, as it can be seen in the details in Figs. 4(b), 4(c) and 4(d). These 45° cracks appear to be favored by hydrogen, as will be discussed later. Similar findings were reported by Moro [49], who noted that non-polished tensile specimens (Ra ≈ 0.5 µm) tested under 300 bar H₂ exhibited numerous external cracks perpendicular to the tensile axis, along with fracture surfaces comprising two distinct zones: one perpendicular to the tensile direction and another inclined at 40–45°.

## 3.2. 3D X-ray tomography

Fig. 5 shows the 2D sections XY, XZ, and YZ of the tomography data obtained from the four specimens. These slices were extracted from the center of the specimen (1024, 1024, 1024 voxel) to reveal the damage. Fig. 6 illustrates a detailed view of the plane XZ of the striction zone for each specimen.

As illustrated in Fig. 5(a), the specimen AIR-V4-0.51 displays a considerable degree of local strain, evidenced by the striction in the center of the specimen. It is also worth noting the presence of substantial voids at the center of the structure, as illustrated in Fig. 6(a).

The specimens tested in a 100 bar gaseous hydrogen atmosphere are depicted in Figs. 5(b), 5(c) and 5(d).

The specimen H₂-V4-0.17, whose tensile test was interrupted after a decrease of 15% relative to the UTS, is depicted in Fig. 5(b). At this point, no discernible damage is observed at the center of the specimen. However, the presence of surface cracks distributed along the gauge length is evident. These features are illustrated in greater detail in Fig. 6(b).

The specimen H₂-V4-0.30, tested at the same $\dot{\epsilon}$ as the specimen H₂-V4-0.17 but interrupted just prior to rupture, exhibits a high number of surface cracks, as illustrated in Fig. 5(c) and shown in greater detail in Fig. 6(c). It is noteworthy that certain surface cracks propagated further into the specimen, which may ultimately result in rupture. Furthermore, as illustrated in Fig. 6(c), the specimen displays the presence of round voids in the center, which may be indicative of residual ductility in the central part of the specimen.

In contrast, specimen H₂-V5-0.17, tested under a slower $\dot{\epsilon}$ ($1 \times 10^{-5} s^{-1}$) and interrupted just prior to rupture, exhibits a reduced number of surface cracks in comparison to the sample H₂-V4-0.30. Fig. 6(d) illustrates the presence of extensive damage in the center of the specimen, evidenced by numerous voids that are penny shaped and normal to the loading direction. This differs from the typical round shape observed in dimples found in the sample tested in air. Similar voids were observed by Depraetere et al. [31] for grade X70 pipeline steel tested after hydrogen pre-charging. However, they attributed this void geometry to the presence of elongated MnS inclusions, which are not present in the steel studied in the present work. The combination of the surface cracks and the internal voids may ultimately result in a fully brittle fracture.

Fig. 7 shows a 3D visualization where the sample surface is semi-transparent and the bulk is completely transparent. The damage is represented following the colormap legend in each image's lower left quadrant. Blue indicates damage near the surface, while red indicates damage closer to the center. These observations facilitate a more precise spatial assessment of the damage. Supplemental materials, including videos of the results for each specimen, are provided to enhance comprehension (see Appendix C).

It is possible to observe in Fig. 7(a) that the majority of the damage is developed in the center for the AIR-V4-0.51 specimen. In contrast, the specimen H₂-V4-0.17 exhibits a predominance of damage on the surface, as can be seen in Fig. 7(b). The specimens H₂-V4-0.30 and H₂-V5-0.17, depicted in Figs. 7(c) and 7(d) shows a distribution of damage both in the surface and in the bulk of the specimen.

Each void detected in the specimen was individually labeled, and its barycenter position, volume, and distance from the closest outer surface were determined. Fig. 8 presents the results of this analysis. The histograms show the volumetric distribution of the voids in relation to their distance from the surface. The y-coordinate, indicating the normalized damage volume, is in logarithmic scale to allow better visualization of the data. The distance from the surface was normalized
<figure><img src="image_10.png" /><figcaption>Fig. 7. Three-dimensional visualization of the interrupted test specimens, where the specimen surface is semi-transparent, and the bulk is fully transparent. Damage is color-coded according to the colormap in the lower left quadrant, with blue indicating surface damage and red representing damage near the center. This visualization enables a spatial assessment of damage distribution, highlighting differences between air- and hydrogen-tested specimens. Supplementary videos are available for further analysis. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

by taking into account the diameter of the specimen in the height (Z-axis) where the damage was detected. The x-coordinate ranges from 0 (surface) until 1 (center) of the specimen.

On the right side of each histogram, an orthogonal projection is shown, where the damage is projected onto the XY plane. This projection provides insights into the spatial distribution of damage by distinguishing between surface and bulk regions of the specimen. These projections help visualize the extent and localization of damage, revealing whether it is primarily concentrated at the surface or extends into the bulk.

It can be observed that the specimen tested in air (AIR-V4-0.51) has a high amount of damage in the center, while the specimens tested in gaseous H₂ have a predominance of damage in the surface, regardless of the strain rate or the moment at which the test was interrupted.

Fig. 8(a) depicts the results obtained from the AIR-V4-0.51 specimen. Interestingly, it reveals a high concentration of damage volume at 0.7 from the surface, which is not precisely at the center of the specimen as one might expect. This anomaly is due to the presence of a substantial void that developed in the center of the specimen, although its barycenter is displaced. This void is clearly discernible in Fig. 6(a) and the orthogonal projection of the damage.

Fig. 8(b) depicts the results obtained for the H₂-V4-0.17 specimen. It indicates that on this specimen, nearly 100% of the damage volume is

located at the surface. The damage projection was used to estimate the average penetration of surface damage, yielding a value of 84 µm, which is approximately five times the material's average grain diameter.

Similar to the H₂-V4-0.17 specimen, most of the damage of the specimen H₂-V4-0.30 is concentrated on the outer surface, as depicted in Fig. 8(c). The damage progressed from the external surface toward the center, although the damage in the center remains relatively low, as clearly indicated in the orthogonal damage projection. For this specimen, the average penetration of the surface damage was estimated at 260 µm, which is approximately 16 times the material's average grain diameter.

The results of the specimen H₂-V5-0.17 are presented in Fig. 8(d). It is evident that there is a predominance of cracks on the surface of the specimen, but these coexist with a considerable quantity of voids in the bulk of the specimen. It is noteworthy that the damage is distributed more evenly between the surface and the bulk. However, unlike the other specimens tested under H₂, the surface damage is not uniformly distributed around the circumference. As seen in the orthogonal damage projection, the surface damage is concentrated on one side of the specimen, with the maximum penetration in this region reaching approximately 300 µm.

Table 2 shows the quantification of the damage volume found in the interrupted tensile tests. The higher volume of damage is observed
<figure><img src="image_11.png" /><figcaption>Fig. 8. Histograms illustrating the volumetric distribution of voids relative to their normalized distance from the specimen surface. The y-axis represents the normalized damage volume on a logarithmic scale, while the x-axis ranges from 0 (surface) to 1 (center of the specimen). The distance from the surface is normalized by the specimen diameter at the location where the damage was detected. On the right side of each histogram, an orthogonal projection onto the XY plane is shown, providing insights into the spatial distribution of damage by distinguishing between surface and bulk regions of the specimen. These projections help visualize the extent and localization of damage, revealing whether it is primarily concentrated at the surface or extends into the bulk. The histograms reveal that the specimen tested in air (AIR-V4-0.51) exhibits a high concentration of damage in the center, while specimens tested in gaseous H₂ show surface-dominant damage regardless of the strain rate or interruption time.</figcaption></figure>
<table><caption>**Table 2**
Summary of damage volume found by X-ray tomography analysis from interrupted tensile tests.</caption><thead><tr><td>Test ID</td><td>Damage volume (mm<sup>3</sup>)</td></tr></thead><tbody><tr><td>AIR-V4-0.51</td><td>8.0 × 10<sup>-4</sup></td></tr><tr><td>H<sub>2</sub>-V4-0.17</td><td>1.8 × 10<sup>-3</sup></td></tr><tr><td>H<sub>2</sub>-V4-0.30</td><td>3.6 × 10<sup>-2</sup></td></tr><tr><td>H<sub>2</sub>-V5-0.17</td><td>4.9 × 10<sup>-3</sup></td></tr></tbody></table>

in the specimen AIR-V4-0.51 (8.0 × 10⁻⁴ mm³). The specimen H₂-V4-0.30 shows higher damage volume than the specimen H₂-V4-0.17 (3.6 × 10⁻² mm³ and 1.8 × 10⁻³ mm³, respectively) as expected. Interestingly, the specimen H₂-V5-0.17 presents a significantly lower damage volume (4.9 × 10⁻³ mm³) in comparison with the specimen H₂-V4-0.30, although both are close to the rupture. However, it is consistent with the reduced plastic strain to fracture.

### 3.3. Analysis of damage shape and orientation

In order to analyze the voids shape and orientation within the material, a systematic approach was employed that included the calculation of the center of mass, moments of inertia, Euler angles, and adimensional moments of inertia. Detailed methodologies for these calculations are provided in Appendix B, which outlines the theoretical framework utilized in this analysis. The analysis of damage orientation and morphology is important in order to understand the various damage mechanisms that occur in the specimens. This analysis enables the identification of ductile and H-induced brittle damages.

Fig. 9 presents the orientation and shapes of the 50 largest voids identified in the bulk (red) and on the surface (blue) of the specimens. Each line containing a series of diagrams corresponds to one specific specimen, as indicated in the upper left corner.

The angle $\gamma$ is one of the Euler angles and is shown in the first column. It represents the orientation of the void's principal axis relative to the Z axis (the tensile loading direction). A polar plot is used to display this orientation, where the radial component corresponds to the void volume.

The calculation of the moments of inertia allows to determine the shape of each void by evaluating the ratios of the principal moments of inertia vectors. This enables classification into categories such as spherical, flat ellipsoid, prolate ellipsoid, or oblate ellipsoid (Refer to Appendix B for three-dimensional illustrations of these geometries as well as their dimensional relationships). These classifications are depicted in the second column.

The third and fourth columns illustrate the typical damage observed in the bulk and on the surface, respectively, for each of the analyzed specimens.

The analysis of the AIR-V4-0.51 sample revealed damage volumes ranging from 1.30 × 10⁻⁶ to 4.76 × 10⁻⁴ mm³, which corresponds to an equivalent diameter ranging from 13.5 to 96.9 µm. A large void with a shape that approximates an oblate ellipsoid was identified, its principal axis is oriented at approximately 45° relative to the loading axis, as indicated in Figs. 9(a) and 9(b). The remaining voids exhibit shapes ranging from flat ellipsoids to prolate ellipsoids. Fig. 9(c) shows the bulk damage in the sample AIR-V4-0.51, forming a necktie morphology in the neck region, typical of ductile fracture.

The analysis of specimen H₂-V4-0.17 reveals distinct characteristics of surface cracks and internal voids. Surface cracks, with damage volumes ranging from 6.89 × 10⁻⁶ to 1.22 × 10⁻⁴ mm³, corresponding to equivalent diameters between 23.6 and 61.6 µm. These dimensions are equivalent to approximately 1–4 times the average grain size of the material of 15.9 µm. The cracks are oriented perpendicularly to the loading axis and predominantly exhibit flat ellipsoidal shapes, as indicated by the blue markers in Figs. 9(d) and 9(e). These surface

cracks can be observed by 3D X-ray tomography, as depicted in Fig. 9(g). In contrast, internal voids show smaller damage volumes, ranging from 1.19 × 10⁻⁷ to 5.36 × 10⁻⁶ mm³, with equivalent diameters between 6.1 and 21.7 µm. These dimensions are significantly larger than the average diameter of the inclusions found in this material, which is approximately 0.25 µm. These voids are primarily prolate ellipsoids, aligned parallel to the loading axis (red markers in Figs. 9(d) and 9(e)), and display a necktie morphology characteristic of ductile fracture processes, as it can be seen in Fig. 9(f).

The analysis of the largest damage features in specimen H₂-V4-0.30 revealed surface cracks with damage volumes ranging from 2.14 × 10⁻⁵ to 1.67 × 10⁻² mm³ and equivalent diameters between 34.4 and 317.3 µm. These cracks include two prominent examples oriented at approximately 70° to the loading axis, predominantly exhibiting a flat elliptical shape, as highlighted by the blue markers in Figs. 9(h) and 9(i). One of these surface cracks, illustrated in Fig. 9(k), exemplifies a general trend observed in this specimen: the crack initially aligns parallel to the loading axis but deviates to approximately 45° as it propagates into the bulk, a behavior discussed further in subsequent section. In contrast, the bulk voids are smaller, with damage volumes ranging from 6.99 × 10⁻⁷ to 8.67 × 10⁻⁶ mm³ (equivalent diameters of 11.0 to 25.5 µm). These voids are preferentially oriented parallel to the loading axis and predominantly exhibit a prolate ellipsoidal morphology, as indicated by the red markers in Figs. 9(h) and 9(i). A representative bulk void, shown in Fig. 9(j), displays a prolate ellipsoid morphology, aligned with the tensile axis, characteristic of microvoid coalescence.

The analysis of the largest surface cracks in the specimen H₂-V5-0.17 revealed damage volumes ranging from 8.40 × 10⁻⁶ to 1.52 × 10⁻³ mm³, corresponding to equivalent diameters of 25.2 to 142.8 µm. These values are equivalent to 2–10 times the average grain size of the material, which is 15.9 µm. These cracks were oriented perpendicularly to the loading axis and exhibited a predominantly flat ellipsoidal shape, as illustrated by the blue markers in Figs. 9(l) and 9(m), and shown in detail in Fig. 9(o). For the largest bulk voids in specimen H₂-V5-0.17, damage volumes ranged from 2.89 × 10⁻⁶ to 8.59 × 10⁻⁵ mm³, with equivalent diameters between 17.7 and 54.7 µm. Unlike the voids observed in specimens tested in H₂ under a strain rate of $\dot{\epsilon} = 5 \times 10^{-4}$ s⁻¹, these internal voids are aligned perpendicularly to the loading direction and predominantly exhibited an oblate ellipsoid shape, as indicated by the red markers in Figs. 9(l) and 9(m), and detailed in Fig. 9(n).

An analysis of over 50 major damage sites, both on the surface and within the bulk of H₂-V5-0.17 (Fig. 10(b)) and H₂-V4-0.17 (Fig. 10(a)) specimens, was performed. The study examined the relationships between Volume (left side vertical axis), Equivalent Diameter (right side vertical axis), and Shape Factor, obtained by the division $\lambda_2/\lambda_1$. Regarding volume the damages in the H₂-V5-0.17 specimens (low strain rate) were slightly larger, which aligns with expectations since they are closer to rupture. Interestingly, low-strain-rate specimens exhibited more ellipsoidal internal damage, while higher-strain-rate specimens tended to show spherical damage.

### 3.4. Microstructural analysis of damage in hydrogen-exposed specimens

To investigate the damage in specimens H₂-V4-0.30 and H₂-V5-0.17, each was mounted in bakelite resin, ground to expose the central L-S cross section, and polished to a colloidal silica finish (0.1 µm). Nital etching was applied to reveal the microstructure. Scanning electron microscopy (SEM) images were obtained to evaluate surface and internal damage characteristics.

Figs. 11(a) and 11(b) illustrate the damage in the specimen H₂-V4-0.30. Surface cracks, shown in Fig. 11(a), were transgranular, traversing ferrite and pearlite phases with minimal deformation, consistent with hydrogen-induced cracking. Internal voids, depicted in Fig. 11(b), were ellipsoidal and aligned along the L-direction, often nucleating
$$ \text{Air} - \dot{\varepsilon} = 5 \times 10^{-4} s^{-1} - \Delta\Phi/\Phi_0|_s = 0.514 $$

<figure><img src="image_12.png" /><figcaption>(a) γ orientation of voids.</figcaption></figure>

<caption>(b) Principal moments of inertia.</caption>

<caption>(c) Bulk Damage.</caption>

$$ 100 \text{ bar H}_2 - \dot{\varepsilon} = 5 \times 10^{-4} s^{-1} - \Delta\Phi/\Phi_0|_s = 0.169 $$

<figure><img src="image_13.png" /><figcaption>(d) γ orientation of voids.</figcaption></figure>

<caption>(e) Principal moments of inertia.</caption>

<caption>(f) Bulk Damage.</caption>

<caption>(g) Surface Crack.</caption>

$$ 100 \text{ bar H}_2 - \dot{\varepsilon} = 5 \times 10^{-4} s^{-1} - \Delta\Phi/\Phi_0|_s = 0.301 $$

<figure><img src="image_14.png" /><figcaption>(h) γ orientation of voids.</figcaption></figure>

<caption>(i) Principal moments of inertia.</caption>

<caption>(j) Bulk Damage.</caption>

<caption>(k) Surface Crack.</caption>

$$ 100 \text{ bar H}_2 - \dot{\varepsilon} = 1 \times 10^{-5} s^{-1} - \Delta\Phi/\Phi_0|_s = 0.169 $$

<figure><img src="image_15.png" /><figcaption>(l) γ orientation of voids.</figcaption></figure>

<caption>(m) Principal moments of inertia.</caption>

<caption>(n) Bulk Damage.</caption>

<caption>(o) Surface Crack.</caption>

<caption>**Fig. 9.** Orientation and morphology of the largest voids in the bulk (red) and on the surface (blue) of specimens. Specimen identifiers are provided in the upper left corner. First column (a,d,h,l) shows void orientation (γ) relative to tensile axis. Second column (b,e,i,m) classifies void morphology. Third (c,f,j,n) and fourth (g,k,o) columns show typical bulk and surface damage. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</caption>
<figure><img src="image_16.png" /><figcaption>**Fig. 10.** Analysis of the largest surface and bulk damage in H₂-V5-0.17 (low strain rate) and H₂-V4-0.17 (higher strain rate) specimens revealed larger damage volumes in the low strain rate condition. Additionally, bulk damage morphology shifted from ellipsoidal shapes at low strain rates to spherical shapes at higher rates, emphasizing strain rate effects.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Fig. 11.** Microstructural analysis of specimens H₂-V4-0.30 and H₂-V5-0.17 reveals transgranular surface cracks with minimal deformation and internal damage. H₂-V4-0.30 internal voids align with the loading direction, while H₂-V5-0.17 internal cracks are perpendicular to the longitudinal axis.</figcaption></figure>

at ferrite-pearlite grain boundaries. Occasionally, voids appeared to originate within the bulk of the ferrite grains.

Surface cracks in the specimen H₂-V5-0.17, visible in Figs. 11(c), were transgranular with minimal deformation, similar to the behavior observed in H₂-V4-0.30. Internal cracks, presented in Fig. 11(d), were located within the bulk of the material and oriented perpendicular to the longitudinal axis, as confirmed by tomography analysis. Both surface and internal damage exhibited an absence of significant plastic deformation.

### 3.5. Fracture surface observations

Fracture surface analysis of the specimens revealed distinct behaviors depending on the testing conditions and hydrogen exposure.

In the AIR-V4-Full specimen, the fracture surface exhibited ductile characteristics, with spherical voids forming around inclusions, leading to a ductile fracture mode (Fig. 12(a)).

In contrast, the fracture surface of H₂-V4-Full (Fig. 12(c)) specimen showed a mixed behavior: quasi-cleavage fracture near the surface, indicative of hydrogen embrittlement. The center of the fracture displayed Microvoid Coalescence (MVC) as pointed by the red arrows, indicating ductile fracture behavior as shown in Fig. 12(d).

For H₂-V5-Full (Fig. 12(e)), the fracture surface showed a more homogeneous appearance, with quasi-cleavage features observed consistently from the surface to the center, reflecting a brittle fracture behavior. Figs. 12(f) and 12(g) highlight the presence of decohesion around inclusions, with minimal plastic deformation, further supporting the brittle nature of the fracture.
<figure><img src="image_18.png" /><figcaption>**Fig. 12.** Fracture surface observations of specimens AIR-V4-Full (Figs. 12(a) and 12(b)), H₂-V4-Full (Figs. 12(c) and 12(d)), and H₂-V5-Full (Figs. 12(e), 12(f) and 12(g)) reveal distinct behaviors: AIR-V4-Full exhibits ductile fracture, while H₂-V4-Full shows a mix of quasi-cleavage in the surface and Microvoid Coalescence in the center. H₂-V5-Full presents consistent quasi-cleavage, indicating brittle fracture.</figcaption></figure>

# 4. Discussion

## 4.1. Analysis of the specimen tested at air

The specimens tested in air at a strain rate of $\dot{\epsilon} = 5 \times 10^{-4} \text{ s}^{-1}$ (AIR-V4-0.51 and AIR-V4-FULL) exhibited significant local strain at the

center and no surface cracks, as shown in Fig. 4(a). The damage volume in these specimens was notably high, reaching up to $8.0 \times 10^{-4} \text{ mm}^3$. This damage was exclusively located in the bulk, with a pronounced concentration at the center, as extensively demonstrated in Figs. 5(a), 6(a), 7(a) and 8(a). This internal damage distribution contrasts with the surface-dominant damage observed in hydrogen-exposed specimens.
Analysis of the shape and orientation of bulk voids (Figs. 9(a), 9(b), and 9(c)) revealed that microvoid coalescence (MVC) in the AIR-V4-0.51 specimen originates primarily from voids nucleating around inclusions, carbides, and other local imperfections. Under tensile stress, particles aligned in clusters along the rolling direction led to elongated voids, producing a “necktie-like” morphology characteristic of ductile fracture under localized strain, as discussed in [26]. Furthermore, observations of the fracture surface confirmed that the material underwent a ductile fracture mode, as evidenced by the presence of dimples along the entire surface.

## 4.2. Analysis of the specimen tested at 100 bar H₂ with moderate strain rate ($\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$)

Two tensile tests were conducted under 100 bar H₂ at strain rate of $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$ and interrupted prior to fracture, designated as H₂-V4-0.17 and H₂-V4-0.30. The first test was halted at $\Delta\Phi/\Phi_0|_s = 0.17$, corresponding to a load decrease of approximately 7.5% relative to the UTS. The second test was interrupted at $\Delta\Phi/\Phi_0|_s = 0.30$, just before specimen fracture. Additionally, a test under identical environmental conditions and strain rate was performed to complete rupture and is referred to as AIR-V4-FULL.

SEM observations of the interrupted specimens revealed a significant amount of surface cracks. For H₂-V4-0.17 (Fig. 4(b)), incipient surface crack nucleation was observed. These cracks were aligned along slip bands oriented at approximately 45° to the loading axis. For H₂-V4-0.30 (Fig. 4(c)) the surface cracks had propagated into larger, well-developed cracks, maintaining the same 45° orientation relative to the loading axis. For both specimens, no significant localized strain (necking) was observed, suggesting limited plastic deformation.

3D X-ray tomography revealed that the majority of the damage in these specimens is localized at the surface, as illustrated by the slices in Figs. 5(b), 5(c), 6(b), and 6(c). The 3D visualization provides a comprehensive view of the damage morphology, demonstrating that under these conditions, cracks predominantly initiate at the surface (Fig. 7(b)) and propagate into the bulk of the specimen (Fig. 7(c)). This observation is further supported by data from the histograms (Figs. 8(b) and 8(c)), which confirm the predominance of surface damage.

The damage analysis of these specimens revealed distinct damage mechanisms in the surface and bulk regions. In specimen H₂-V4-0.17, damage was primarily concentrated on the surface, where cracks exhibited flat ellipsoidal shapes oriented perpendicular to the loading axis (Z-axis). Furthermore, it was evidenced in Fig. 11(a), that these surface cracks propagates with negligible plastic deformation. This crack morphology and orientation suggest a damage mechanism dominated by Hydrogen Enhanced Decohesion (HEDE), likely driven by elevated hydrogen concentrations at the surface. In contrast, internal voids exhibited prolate ellipsoidal geometries aligned parallel to the loading axis, indicating the early stages of microvoid nucleation and growth, as further evidenced in Fig. 11(b). These internal features resemble ductile failure mechanisms observed in specimens tested in air, suggesting limited hydrogen penetration into the bulk material. In summary, it can be inferred that two distinct fracture mechanisms are simultaneously active in this specimen: hydrogen-induced brittle fracture at the surface and ductile fracture in the bulk.

Further insights into crack propagation in specimen H₂-V4-0.17 can be obtained by examining specimen H₂-V4-0.30, which was subjected to identical testing conditions but allowed to undergo further deformation, stopping just before rupture.

The propagation paths of surface cracks in specimen H₂-V4-0.30 are shown in Fig. 9(k). Initially aligned parallel to the loading axis, these cracks deviate and form angles close to 45° relative to the loading direction. This deviation is a characteristic feature of shearing fracture, driven by the orientation of maximum shear stress, which in a tensile test is inclined at 45°.

The fracture surface of specimen H₂-V4-FULL, tested to rupture under 100 bar H₂ at a strain rate of $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$, is shown in Fig. 12(c). The surface exhibits a quasi-cleavage (QC) fracture morphology, a characteristic signature of hydrogen embrittlement. This aligns with the brittle surface cracks observed in the tomography scans of specimens H₂-V4-0.17 and H₂-V4-0.30, where high hydrogen concentrations near the surface promoted brittle crack propagation via the HEDE mechanism. In the central region of the specimen, the fracture surface is dominated by dimples, which correspond to the internal voids aligned with the loading axis (Z-axis) observed in H₂-V4-0.17 and H₂-V4-0.30.

The progression of the initially brittle surface crack into a slant fracture oriented at 45° is clearly depicted in Figs. 13(a), which display a slice of the tomography data, and 13(b), which display the L-S cross-section of the specimen observed via SEM after polishing and etching.

Figs. 13(c) and 13(d) provide magnified views of the regions highlighted in Fig. 13(b). Numerous small voids, indicated by red arrows, are visible near the main crack. Green arrows highlight deformation bands aligned with the primary crack direction of propagation, corresponding to the axis of maximum shear stress. Yellow arrows point to microvoids formed along one of these deformation bands, suggesting localized plastic deformation in the vicinity of the 45°-oriented crack.

Based on the results, hydrogen-assisted crack propagation in the sub-size tensile specimen tested at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$ is proposed to proceed as follows: once the ultimate tensile strength (UTS) has been reached, the formation of hydrogen-induced surface cracks and microvoids in the material bulk occurs simultaneously. Along the evolution of the test, intense shear deformation develops in the ligaments separating the surface crack from the internal microvoids. This shear deformation causes the main crack to deviate to an orientation of 40–50 degrees relative to the loading axis. Eventually, the ligaments fail due to localized shear deformation, leading to the linkage of the surface crack and internal microvoids.

This sequential process of surface crack propagation, ligament shear deformation, and microvoid coalescence culminates in the observed slant fracture. The proposed mechanism is schematically illustrated in Fig. 14(a).

The occurrence of hydrogen-induced crack surfaces can be explained by a critical combination of hydrogen concentration and maximum principal stress at the surface, as proposed in several studies [40, 50–52]. Malheiros et al. [50] studied this phenomenon using smooth and notched tensile specimens. They performed tensile permeation tests and incorporated the experimental results into finite element modeling. Their approach considered hydrogen diffusion and trapping, coupled with hydrostatic stress, to assess the local conditions leading to quasi-cleavage fracture. Their results showed that the stress required to initiate quasi-cleavage cracks decreases with increasing hydrogen concentration, consistent with the Hydrogen-Enhanced Decohesion (HEDE) mechanism.

In the present study, the test conducted at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$ showed H-induced surface cracks just after reaching the ultimate tensile strength (UTS), as observed in Figs. 7(b) and 8(b). A simple diffusion estimate, using $x = \sqrt{Dt}$ (where x is the Diffusion depth, D is the Diffusion Coefficient and t is time), gives a diffusion depth of 390 µm. This calculation assumes an effective diffusion coefficient $D_{\text{eff}}$ of $5 \times 10^{-10} s^{-1}$ (determined experimentally by electrolytic permeation tests for a similar steel) and diffusion time of 300 s which was the time required to reach UTS. At first glance, this result appears to be inconsistent with the experimentally measured average surface damage penetration depth of 84 µm for this specimen, as discussed in Fig. 8(b). However, as proposed by several authors [40,50–52], H-induced QC fracture is triggered when a critical combination of maximum principal stress and hydrogen concentration is reached. In this test, these critical conditions appear to have been reached only at the outer surface of the specimen. As there was insufficient diffusion time for hydrogen to reach
<figure><img src="image_19.png" /><figcaption>**Fig. 13.** Detailed views of the cross section LS of the H₂-V4-0.30 specimen obtained by SEM, showing voids near the main crack (red arrows) and deformation bands (green arrows) aligned with the crack's propagation direction. Microvoids along a deformation band (yellow arrows) suggest substantial plastic deformation during the 45°-oriented crack's propagation. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 14.** Schematic illustration of damage mechanisms in specimens tested at 100 bar H₂ under two different strain rates. (a) At a moderate strain rate ($\dot{\epsilon} = 5 \times 10^{-4} \text{ s}^{-1}$), Surface cracks form due to high hydrogen concentration, while bulk microvoids grow in lower hydrogen regions. Internal shearing leads to a slant fracture at 45°. (b) At a slow strain rate ($\dot{\epsilon} = 1 \times 10^{-5} \text{ s}^{-1}$), hydrogen diffuses deeply into the bulk, causing brittle cracking throughout and resulting in a flat fracture perpendicular to the specimen's longitudinal axis.</figcaption></figure>

the centre of the specimen, microvoid coalescence (MVC) was initiated in the bulk material.

The remaining ligament shear deformation observed in the H2-V4-0.30 specimen aligns with ductile failure mechanisms driven by void nucleation, growth, and coalescence. Pineau et al. [53] categorized void coalescence into three modes: internal necking failure, internal shearing failure, and link-up along void lengths. The microstructural features observed in the present study suggest a failure mode dominated by internal shearing, which is characterized by diagonally aligned microvoids that connect through shear band rupture.

Furthermore, the formation of slip bands and microvoids aligned with the maximum shear stress direction suggests a potential association with the Hydrogen Enhanced Localized Plasticity (HELP) mechanism. The presence of hydrogen in solid solution enhance dislocation mobility, leading to localized plastic deformation in the region adjacent

to the fracture surface [54]. This localized plasticity could result in the formation of slip bands oriented along the maximum shear stress direction. Additionally, the presence of hydrogen can influence the growth and coalescence of microvoids along the slip bands. In the present context, hydrogen would facilitate the internal shearing failure.

Experimental evidence supporting this hydrogen-induced internal shearing has been documented in the literature. Somerday et al. [55] studied hydrogen-assisted crack propagation in austenitic stainless steel welds and reported a sequence of microcrack formation in the weld ferrite, intense shear deformation in the ligaments between these microcracks, and subsequent ligament fracture. They attributed this behavior to inhomogeneous hydrogen distribution at dislocations, creating a gradient in local flow stress that facilitates localized shear deformation. Similarly, Lee et al. [56] identified hydrogen's role in promoting plastic instability along characteristic slip bands during fracture
of spheroidized AISI 1095 steel. Onyewuenyi et al. [57] observed a significant reduction in critical strain for shear instability onset in spheroidized AISI 1090 steel under the influence of hydrogen.

Park and Thompson [58] studied hydrogen effects on ductile fracture in spheroidized steel using electrolytically charged tensile specimens. The specimens were electroplated with copper after the H-charging, to minimize hydrogen desorption during testing in air. Their results contrast with the present study, as cross-section analysis showed no change in void initiation due to hydrogen, with both charged and uncharged specimens exhibiting higher void density at the center and no H-induced surface cracks. This suggests that continuous hydrogen exposure during testing is crucial for surface crack formation. They also observed that hydrogen-charged specimens had wider voids and that initial crack propagation occurred via micro-crack coalescence linked by localized shear. Additionally, hydrogen increased the shear lip area, indicating a possible influence on final shear deformation.

Matsuo et al. [59] investigated the effects of hydrogen on the tensile properties and fracture surface morphology of 316L stainless steel specimens. To achieve uniform hydrogen distribution, specimens were gas-charged at 100 bar and 250 °C for 192 h. All specimens exhibited cup-cone fracture, but hydrogen exposure increased the presence of small-dimple areas formed by local shear strain. The authors suggested that hydrogen may accelerate void nucleation and the formation of void sheets by potentially enhancing shear deformation localization.

The influence of hydrogen on the observed fracture features is also supported by numerical studies [60-62]. Yu et al. [62] conducted simulations based on HELP mechanism. A new form of hydrogen softening law, differently from the monotonic linearly decreasing function of $\sigma_0$ (initial yield stress) with $c$ (hydrogen concentration), was adopted in their study to account for the experimental observation that hydrogen promotes lateral void growth in the early necking stage of axisymmetrical tensile test [63]. A sigmoidal hydrogen softening law is applied, supported by the experimental results reported by Zhang et al. [64]. The numerical study demonstrated that the effect of hydrogen depends on both stress state and hydrogen trapping. At low trapping levels, hydrogen predominantly enhances internal necking failure, whereas at high trapping levels, internal shearing failure becomes dominant under low triaxiality stress conditions, such as those observed in smooth tensile specimens.

The HELP mechanism proposes softening due to hydrogen in solid solution, although macroscale evidence remains inconsistent. Some studies report an increase in flow stress with hydrogen, while others observe a lack of effect or softening. From the studies cited above, Park and Thompson [58] observed that hydrogen elevated the flow stress in the early deformation stages, whereas Lee et al. observed a 20 MPa reduction (representing 4%) on flow stress due to hydrogen, and Matsuo et al. [59] plots demonstrated a modest decrease in flow stress for hydrogen pre-charged specimens.

The modeling conducted by Somerday et al. [55] considered that the flow stress of the material varies with the amount of hydrogen trapped at dislocations, using a linearly decreasing monotonic function $\sigma_0(c)$. However, it is assumed by the authors that while the simulations demonstrate that hydrogen-induced plastic softening can promote intense shear deformation in the ligaments, it is recognized that micro-cracking alone may alter the stress state and impact shear localization, which is strongly influenced by hydrostatic constraint.

Our interpretation aligns with the concept of H-induced internal shearing but does not necessarily imply material softening or a direct effect of the HELP mechanism. Instead, the simultaneous development of H-induced surface cracks and ductile voids at the specimen's center reduces triaxiality, as also discussed by Somerday et al. [55]. This reduction in triaxiality increases the prominence of shear stresses, facilitating the linkage of surface cracks to internal voids along the maximum shear stress plane at 45°, ultimately leading to slant fracture. Although microscopic observations, such as microvoids aligned in slip bands, are generally associated with the HELP mechanism, our study

lacks strong macroscopic mechanical evidence of hydrogen-induced material softening (particularly at $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$). Therefore, we conclude that the HELP mechanism is not a dominant factor in explaining the observed slant fracture.

### 4.3. Analysis of the specimens tested at 100 bar $H_2$ with slow strain rate ($\dot{\epsilon} = 1 \times 10^{-5} s^{-1}$)

The test $H_2$-V5-0.17 was conducted under 100 bar $H_2$ at a strain rate of $\dot{\epsilon} = 1 \times 10^{-5} s^{-1}$ and interrupted at $\Delta\Phi/\Phi_0|_s = 0.17$, just before fracture. Another test under identical environmental and strain rate conditions, AIR-V5-FULL, was carried out until rupture.

SEM lateral observations of specimen $H_2$-V5-0.17 revealed numerous surface cracks aligned parallel to the loading direction. Detailed observations showed deformation slip bands and cracks that initiated approximately at a 45° angle relative to the loading axis. As illustrated in Figs. 5(d), 6(d), and 7(d), most of the damage was concentrated near the surface, a common characteristic of hydrogen embrittlement. However, this specimen exhibited more extensive damage in the bulk compared to other specimens tested under hydrogen at higher strain rates.

The flat, elliptical shape and perpendicular orientation of the surface cracks (Figs. 9(l) and 9(m)) strongly suggest they were caused by embrittlement from high hydrogen concentrations near the surface, consistent with the HEDE mechanism. Transgranular cracks with minimal plastic deformation, depicted in Fig. 11(c), further corroborate this interpretation and closely resemble those surface cracks observed in specimens tested at a strain rate of $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$.

In contrast, the internal voids in $H_2$-V5-0.17 exhibited a markedly different morphology if compared with the other tests. These voids were predominantly oblate ellipsoids aligned perpendicular to the loading direction, as shown in Figs. 9(l) and 9(m). Fig. 11(d) highlights internal cracks with a transgranular morphology and minimal plastic deformation, characteristic of a brittle damage mechanism driven by HEDE. The similarity in morphology and orientation between internal damage in $H_2$-V5-0.17 and surface damage in both $H_2$-V5-0.17 and $H_2$-V4-0.17 suggests a shared hydrogen embrittlement mechanism. The presence of brittle cracks deep within the bulk further implies that the lower strain rate allowed hydrogen to diffuse extensively, reaching concentrations sufficient to activate the HEDE mechanism.

The fracture surface of specimen $H_2$-V5-FULL, tested until rupture, is shown in Figs. 12(e) and 12(f). The quasi-cleavage features observed from the surface to the center indicate a homogeneous brittle fracture morphology. A notable inclusion decohesion (Fig. 12(g)) further supports the brittle nature of the fracture, as only minimal plastic deformation was observed around the inclusion. This finding provides strong evidence of the HEDE mechanism.

Compared to specimens tested at a higher strain rate of $\dot{\epsilon} = 5 \times 10^{-4} s^{-1}$, $H_2$-V5-FULL exhibited significantly more brittle behavior.

For this specimen, using the simple formulation $x = \sqrt{Dt}$ and maintaining the same effective diffusion coefficient $D_{eff}$ as before, the calculated diffusion depth is 2.55 mm, considering the 13,000 s (approximately 3.6 h) required to reach UTS (with an uniform axial elongation of 15 %). Given that the initial specimen diameter $\Phi_0$ is 1.2 mm, it is reasonable to assume that the hydrogen concentration in the bulk will be significantly elevated by the time UTS is reached. Furthermore, at the onset of necking, a region of high triaxial stress develops at the specimen's center, which is known to enhance hydrogen diffusion toward this zone, further increasing the local hydrogen concentration. This suggests that the critical combination of stress and hydrogen concentration necessary to trigger quasi-cleavage (QC) fracture is achieved in this central region. Consequently, the brittle fracture observed in the bulk of the specimen aligns with the HEDE mechanism.

The lower strain rate facilitated deeper hydrogen diffusion, promoting simultaneous hydrogen-induced cracking on the surface and in the bulk. This observation is consistent with tomography analyses and is schematically illustrated in Fig. 14(b).
## 4.4. Contextualizing current results with literature

Depraetere et al. [32] investigated the damage evolution of an API 5L X56 pipeline steel using X-ray computed tomography. The steel, produced via normalizing rolling, exhibited a banded microstructure. Ex-situ tensile tests were conducted on notched specimens pre-charged with hydrogen via electrolytic methods to achieve a concentration of 0.33 wppm, verified by hot extraction. The relatively old manufacturing method resulted in significant void formation upon fracture. However, hydrogen embrittlement (HE) in this material was mild, with ductility losses ranging from 4% to 25% across all geometries. Interestingly, void distribution, size, and shape were unaffected by hydrogen, suggesting that hydrogen slightly accelerated existing fracture micromechanisms without altering their nature. This contrasts with their earlier findings for API 5L X70 steel [31], where higher hydrogen concentrations caused significant changes in void distribution.

In their study of API 5L X70 steel, which had been in service for around 30 years, Depraetere et al. [31] used a similar approach. This steel, produced via a Thermo-Mechanical Controlled Process (TMCP), exhibited a banded ferritic-pearlitic microstructure with elongated MnS inclusions along the longitudinal (L) and transverse (T) directions. Pre-charged specimens, achieving a hydrogen concentration of 0.89 wppm (measured via hot extraction), underwent tensile testing with loading along the L direction. Hydrogen caused considerable ductility loss but did not affect macroscopic plasticity or anisotropy. X-ray micro-CT revealed two primary effects of hydrogen: (1) void nucleation occurred at lower strains, likely before the maximum load was reached, and (2) hydrogen-induced voids were more oriented perpendicular to the loading direction, although void volume growth was not accelerated.

The findings for X70 steel share some similarities with the results of this study but also exhibit key differences. The E355 mod. steel used in this study was produced using a modern TMCP process, resulting in a low inclusion content (0.06% by volume) and no elongated MnS inclusions. In contrast, the X70 steel contained significant MnS inclusions, which likely contributed to hydrogen-induced damage. Depraetere et al. used ex-situ electrolytic charging, which primarily promotes internal hydrogen embrittlement (IHE) and favors internal damage nucleation, especially near MnS inclusions. In contrast, the present study employed in-situ gaseous hydrogen charging during tensile tests, simulating external hydrogen embrittlement (EHE) and promoting surface cracking. This methodological difference explains the contrasting damage distributions: Depraetere observed more damage in the bulk, while this study found damage concentrated at the surface. Additionally, in-situ charging typically results in more severe ductility loss, aligning with the slightly higher Hydrogen Embrittlement Index (HEI) observed in smooth tensile specimens in this study. Depraetere et al. used larger specimens (initial diameter $Φ_0$ = 6 mm, gauge length $L_0$ = 40 mm) and a lower strain rate ($\dot{\epsilon}$ = $2.5 \times 10^{-4} s^{-1}$) compared to the specimens in this study ($Φ_0$ = 1.2 mm, $L_0$ = 2 mm, $\dot{\epsilon}$ = $5 \times 10^{-4} s^{-1}$). These differences may have further influenced the damage evolution and embrittlement mechanisms. Both studies observed cracks oriented perpendicular to the loading axis. Depraetere et al. attributed this morphology to the presence of MnS inclusions, with hydrogen enhancing lateral void growth through the HELP and HESIV mechanisms, aligning with the hydrogen induced internal necking mediated by HELP, reported by other authors [65-67]. In contrast, the present study found cracks oriented perpendicular to the loading axis arising from the HEDE mechanism. This interpretation is supported comparing bulk cracks with the surface cracking observed in the H₂-V4-0.17 and H₂-V4-0.30 specimens, where sufficient hydrogen concentration likely triggered HEDE.

This comparison demonstrates how material properties, hydrogen charging methods and testing conditions affect the mechanisms of hydrogen embrittlement. Advanced characterization techniques, such as 3D X-ray tomography, provide detailed insights into the micromechanical processes at play.

Moreover, the results of the effect of strain rate from this study are supported by the experimental observations of other researchers in the field. In their study, Wang et al. [68] investigated the impact of hydrogen in a X65 carbon steel through tensile tests conducted under both ex-situ and in-situ hydrogen charging conditions. Similarly, the specimen loaded to fracture under in-situ hydrogen charging condition with $\dot{\epsilon}$ of $1 \times 10^{-4} s^{-1}$ presented a markedly reduced number of surface cracks compared to the specimen loaded under the same conditions but with $\dot{\epsilon}$ of $1 \times 10^{-3} s^{-1}$. A combination of brittle and microvoid coalescence ductile fracture was observed in the center of the surface fractures of both specimens. These observations align with the findings reported for specimen H₂-V4-0.30. Likewise, the increase in the number of surface cracks with an elevated $\dot{\epsilon}$ was also observed in the application of the Slow Strain Rate Tensile test (SSRT) method for the development of alloys resistant to sulphide stress cracking [69]. This was also observed in the application of cathodic potentials on X-65 pipeline steel specimens tested under distinct strain rates [70].

The effects of varying $\dot{\epsilon}$ presented here are in strong agreement with the predictions made by Pinto et al. [42], who developed a numerical framework for simulating HE using a modified nonlocal Gurson-Tvergaard-Needleman (GTN) model coupled with hydrogen diffusion, incorporating hydrogen-enhanced decohesion (HEDE). Their numerical results correctly predicted that failure initiation occurs predominantly at the surface of the specimen at high $\dot{\epsilon}$, and transitions to initiation at the center of the specimen after necking at low $\dot{\epsilon}$, based on the experiments conducted by Briottet et al. [43]. The study conducted by Pinto et al. also correctly predicted the occurrence of higher amount of surface cracks at higher $\dot{\epsilon}$, in contrast with the low amount of surface cracks on specimens tested under lower $\dot{\epsilon}$. However, the experimental dataset used in their study lacked direct evidence of this damage evolution. Our work not only confirms these numerical trends but advances the state of the art by providing the first direct, quantitative experimental validation of these mechanisms in hydrogen-embrittled specimens.

The effect of varying $\dot{\epsilon}$ is also observed for others steel alloys and microstructures. Momotani et al. [22] investigated the effect of strain rate on hydrogen embrittlement in low-carbon martensitic steel. They found that the elongation of hydrogen-charged specimens decreased significantly as the strain rate decreased. Likewise, the characteristics of hydrogen-related fracture behavior were influenced by the strain rate, a change that was also observed in the present work. At lower strain rates, hydrogen tended to accumulate primarily at prior austenite grain boundaries, whereas at higher strain rates, micro-cracks mainly formed within prior austenite grains, leading to transgranular fracture. This difference is likely due to insufficient time for hydrogen to migrate to grain boundaries during higher strain rate tensile tests. Song et al. [71] examined the impact of gaseous H₂ on the fracture behavior of pipeline steel X70 and austenitic stainless steels 304L and 316L using notched tensile tests conducted at 10 MPa H₂ gas pressure and various test speeds. In X70 steel, hydrogen embrittlement became more pronounced as the test speed decreased, whereas test speed had minimal impact on embrittlement in 304L and 316L steels. In X70, the width of the shear lip region, which exhibited quasi-cleavage fracture, increased with decreasing test speed. Conversely, in the austenitic stainless steels, the entire fracture surface transformed to a brittle mode.

The present work investigated the influence of strain rate on hydrogen embrittlement (HE) in steels using tensile specimens. The findings show that variations in strain rate can significantly affect ductility and the global fracture mechanism, consistent with observations reported by other authors [69,70,72]. As a result, careful consideration of specimen geometry and test strain rates is crucial to avoid comparing potentially incompatible global fracture mechanisms. Ideally, strain rates recommended by established standards, such as $1 \times 10^{-6} s^{-1}$ from NACE TM0198 or $1 \times 10^{-5} s^{-1}$ from ANSI/CSA CHMC 1, should be adopted. These standards provide a favorable balance between observing HE phenomena and conducting a feasible slow strain rate
test (SSRT). Tests of reasonable duration, which can reveal perfor-
mance differences between alloys, are especially important for material
screening, ensuring good repeatability and reproducibility.

It is imperative to reiterate that the findings presented in this inves-
tigation are exclusively applicable to the specific material, specimen
geometry, and test parameters under investigation. In particular, the
use of sub-size tensile specimen with Φ₀ = 1.2 mm offers signifi-
cant advantages. Even at a strain rate approaching the upper limit
recommended by standards, these specimens can exhibit total cross-
section embrittlement. This work further explores the effect of strain
rate on hydrogen embrittlement of sub-size tensile specimens, including
new results and advanced characterization that build upon the find-
ings of Madi et al. [20], who demonstrated the distinct responses of
different sub-size geometries and hydrogen pressures. This reinforces
that sub-size tensile specimens are sensitive to different test condi-
tions under hydrogen, making them viable for use in finite element
simulations, which is an essential tool for modeling hydrogen embrittle-
ment phenomena and understanding their effects, ultimately leading to
technological advances. This feature, combined with the low material
consumption associated with this specimen geometry, makes the sub-
size tensile specimen an excellent choice for monitoring hydrogen
embrittlement in repurposed natural gas pipelines.

This study relies exclusively on classical hydrogen diffusion for-
mulations and established theoretical models from the literature to
interpret the experimental results. No modifications or new diffusion
theories were introduced; rather, the analysis is grounded in well-
accepted principles governing hydrogen transport and embrittlement
mechanisms. The experimental findings, which combine mechanical
response characterization with advanced damage analysis, provide a
valuable dataset for finite element (FE) simulations. The integration of
the presented methodology with FE modeling may be explored in future
studies.

Additionally, X-ray tomography is a powerful technique for inves-
tigation of HE in tensile specimens due to its non-destructive nature.
This technique allows for the comprehensive assessment of internal
and external damage at a resolution limited only by the equipment's
capabilities, enabling detailed analysis of the distribution, volume,
shape, and orientation of voids associated with hydrogen-induced dam-
age. Unlike destructive methods such as metallography or fracture
surface analysis, which provide only limited information on surface
characteristics and often overlook subsurface defects, 3D X-ray tomog-
raphy offers a holistic view of the material's integrity. Moreover, while
cross-sectional analysis is limited to two-dimensional views, tomog-
raphy provides a full volumetric representation of damage, serving
as a complementary tool for elucidating the mechanisms of hydrogen
embrittlement. In combination with image analysis, it allows for a
quantification of damage features in terms of size, distribution and
shape that can serve as input and validation data for damage modeling.

5. Conclusions

This study examined the effect of strain rate on hydrogen embrittle-
ment in ferritic-pearlitic E355 steel sub-size tensile specimens, which
allow the mechanical testing of pipeline steel without the necessity
of interrupting gas production. X-ray 3D tomography was employed
to observe micrometer-scale damage. Tensile tests were carried out at
strain rates of 5 × 10⁻⁴ s⁻¹ and 1 × 10⁻⁵ s⁻¹ in both air and a 100 bar
hydrogen atmosphere, with additional interrupted tests prior to rupture
to capture intermediate damage states.

Under air, the radial strain at rupture reached 56.2% with no surface
cracks. By contrast, at 5 × 10⁻⁴ s⁻¹ in 100 bar H₂, ductility dropped
to 28.8% (HEIz = 48.7%) alongside multiple surface cracks. At the
lower strain rate of 1 × 10⁻⁵ s⁻¹, the radial strain at rupture was 20.9%
(HEIz = 62.8%), although fewer surface cracks were observed.

Analysis of the size, morphology, distribution, and orientation of
damage via X-ray 3D tomography provided key insights. In air, the

dominant feature was a large void (96.9 µm equivalent diameter),
shaped as an oblate ellipsoid oriented at approximately 45° to the
loading axis. Under 100 bar H₂ at 5×10⁻⁴ s⁻¹, surface cracks displayed a
flat ellipsoid morphology perpendicular to the loading axis, consistent
with the HEDE mechanism, while internal voids ranged from prolate
to oblate ellipsoids aligned along the loading axis, indicative of ductile
microvoid coalescence. At 1×10⁻⁵ s⁻¹, both surface cracks and internal
voids were oriented perpendicular to the loading axis, exhibiting oblate
ellipsoidal shapes characteristic of HEDE-driven embrittlement.

These observations highlight distinct hydrogen embrittlement mech-
anisms at each strain rate. At 5 × 10⁻⁴ s⁻¹, hydrogen-induced surface
cracks and ductile microvoid nucleation in the bulk occurred simul-
taneously, with internal shearing conducting to the ligament failure
between surface cracks and internal voids. At 1 × 10⁻⁵ s⁻¹, more ex-
tensive hydrogen diffusion triggered simultaneous hydrogen-induced
cracking in both the surface and bulk.

This work delivers the first experimental validation of the failure
mechanisms predicted by Pinto et al. [42], confirming the strain-rate-
dependent shift in damage initiation from the specimen surface to its
center under hydrogen exposure. By integrating 3D X-ray tomography
with SEM, it has been provided quantitative insights into void volume,
morphology, spatial distribution and orientation. These results not
only substantiate existing numerical models but also establish a robust
experimental foundation for future advancements in the modeling of
hydrogen embrittlement.

CRediT authorship contribution statement

**L.M. Santana:** Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **V. Okumko:** Software, Methodology, Investigation, Data curation. **A. King:** Writing – review & editing, Supervision, Resources, Methodology, Data curation. **T.F. Morgeneyer:** Writing – review & editing, Supervision, Methodology, Formal analysis, Conceptualization. **J. Besson:** Writing – review & editing, Supervision, Project administration, Funding acquisition. **Y. Madi:** Writing – review & editing, Visualization, Validation, Supervision, Software, Project administration, Methodology, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.

Acknowledgments

The authors would like to express sincere gratitude to Dr. Kamel
Madi (3dmagination.uk) for his invaluable support. This work is funded
by the ANR Chair program MESSIAH (ANR-20-CHIN-0003).

Appendix A

See Fig. A.1.

Appendix B

Introduction

This appendix provides a theoretical explanation of the methodolo-
gies used to analyze particle data in the context of void analysis. The
focus will be on how the data is processed to derive the center of mass,
moments of inertia, Euler angles, and adimensional moments of inertia.
<figure><img src="image_21.png" /><figcaption>(a) Generation of the internal seed and the external seed.</figcaption></figure>

<figure><img src="image_22.png" /><figcaption>(b) schematic illustrating the operational principles of the Watershed tool.</figcaption></figure>

<caption>(c) Result of the watershed operation.</caption>

**Fig. A.1.** The Initial Seed is first eroded to create a slightly smaller version of the specimen (Internal Seed) and then inverted and eroded to form an External Seed that represents the background (A.1a). The watershed segmentation tool is applied to grow these seeds until they match the specimen's surface (A.1b and c).

### Calculation of center of mass

The center of mass (COM) of a particle is calculated as the mean of the coordinates of all voxels that constitute the particle. Given a labeled binary mask of the particle, the coordinates of the particle's voxels are determined using the following steps:

1. Identify the voxels that belong to the particle using the labeled data.

2. Extract the coordinates of these voxels.

3. Compute the mean of the x, y, and z coordinates to obtain the center of mass:

$$x_{cm} = \frac{1}{V} \sum_{i} x_{i}, \quad y_{cm} = \frac{1}{V} \sum_{i} y_{i}, \quad z_{cm} = \frac{1}{V} \sum_{i} z_{i}$$

where V is the number of voxels in the particle.

### Calculation of moments of inertia

The moments of inertia are computed based on the coordinates of the voxels relative to the center of mass. For a given particle, the moments of inertia about the principal axes are calculated as follows:

1. Calculate the differences between each voxel's coordinates and the center of mass:

$$x' = x_i - x_{cm}, \quad y' = y_i - y_{cm}, \quad z' = z_i - z_{cm}$$

2. Compute the moments of inertia using the following formulas:

$$I_{xx} = \sum (y'^2 + z'^2), \quad I_{yy} = \sum (x'^2 + z'^2), \quad I_{zz} = \sum (x'^2 + y'^2)$$

$$I_{xy} = -\sum (x' \cdot y'), \quad I_{xz} = -\sum (x' \cdot z'), \quad I_{yz} = -\sum (y' \cdot z')$$

The resulting inertia tensor captures the distribution of mass in the particle and is used in subsequent analyses.

### Eigenvalue decomposition of the inertia tensor

To analyze the orientation and distribution of the mass in a particle, we utilize the inertia tensor, which is defined as:

$$I = \begin{pmatrix} I_{xx} & I_{xy} & I_{xz} \\ I_{xy} & I_{yy} & I_{yz} \\ I_{xz} & I_{yz} & I_{zz} \end{pmatrix} \quad (5)$$

The eigenvalue decomposition of this tensor is performed to extract the principal moments of inertia and their corresponding principal axes. The eigenvalue equation can be expressed as:

$$I v = \lambda v \quad (6)$$

where:

* I is the inertia tensor,

* λ are the eigenvalues (the principal moments of inertia),

* v are the eigenvectors (the principal axes).

This decomposition yields three eigenvalues corresponding to the principal moments of inertia, which are essential for understanding the dynamic properties of the particle.

### Calculation of Euler angles

The principal axes identified through eigenvalue decomposition allow us to calculate the orientation of the particle. The angles of rotation, known as Euler angles (α, β, and γ), are computed from the eigenvector corresponding to the smallest eigenvalue (indicating the principal axis with the lowest moment of inertia).

The normalized eigenvector **u**₁ associated with the smallest eigenvalue is given by:

$$\mathbf{u}_1 = \begin{pmatrix} u_{1x} \\ u_{1y} \\ u_{1z} \end{pmatrix} \quad (7)$$

The Euler angles can be determined using the following relationships:

$$\alpha = \arccos \left( \frac{u_{1x}}{\| \mathbf{u}_1 \|} \right) \quad (8)$$

$$\beta = \arccos \left( \frac{u_{1y}}{\| \mathbf{u}_1 \|} \right) \quad (9)$$

$$\gamma = \arccos \left( \frac{u_{1z}}{\| \mathbf{u}_1 \|} \right) \quad (10)$$

This provides a representation of the particle's orientation in space, facilitating further analysis of its mechanical behavior.

### Adimensional moments of inertia

In addition to the Euler angles, the adimensional moments of inertia, denoted as $l_1$ and $l_2$, are computed. These values are normalized ratios of the principal moments of inertia, allowing comparison across different particles regardless of their absolute sizes. They are defined as:

$$l_1 = \frac{I_{\max}}{I_{\text{total}}} \quad (11)$$

$$l_2 = \frac{I_{\text{second}}}{I_{\text{total}}} \quad (12)$$

where:

* $I_{\max}$ is the largest principal moment of inertia,

* $I_{\text{second}}$ is the second-largest principal moment of inertia,
<table><caption>Table B.1
Damage morphologies.</caption><thead><tr><th>Sphere</th><th>Prolate ellipsoid</th><th>Oblate ellipsoid</th><th>Flat ellipse</th></tr></thead><tbody><tr><td>a = b = c</td><td>a > b = c</td><td>a = b > c</td><td>a = b &gg; c</td></tr></tbody></table>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

* $I_{total} = I_{max} + I_{second} + I_{third}$ is the sum of all principal moments of inertia.

The adimensional moments of inertia provide insights into the mass distribution and rotational characteristics of the particles, allowing for effective classification and analysis.

Additionally, the adimensional moments of inertia provide a means to classify particle morphology by comparing their values to reference geometrical shapes such as spheres, prolate ellipsoids, oblate ellipsoids, and flat ellipses.

Table B.1 presents idealized morphological shapes along with their corresponding dimensional relationships. To facilitate straightforward comparison between different morphologies, the generic parameters *a*, *b*, *c* are employed instead of the specific notation used for the adimensional moments of inertia.

## Appendix C. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.ijhydene.2025.04.398.

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