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[Akinobu Shibata](https://orcid.org/0000-0001-8577-6411), Yazid Madi, Jacques Besson, Akiko Nakamura, [Taku Moronaga](https://orcid.org/0000-0002-6915-0627), [Kazuho Okada](https://orcid.org/0000-0003-0183-4528), [Ivan Gutierrez-urrutia](https://orcid.org/0000-0003-1438-3703), [Toru Hara](https://orcid.org/0000-0002-9715-6444)

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[Relationship between Three-dimensional Crack Morphology and Macroscopic Mechanical Properties of Hydrogen-related Fracture in Martensitic Steel](https://mdr.nims.go.jp/datasets/19a2a55e-d903-4338-a7ec-6dd1d1e417c5)

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660* Corresponding author: E-mail: SHIBATA.Akinobu@nims.go.jp© 2024 The Iron and Steel Institute of Japan. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs license (https://creativecommons.org/licenses/by-nc-nd/4.0/).ISIJ International, Vol. 64 (2024), No. 4, pp. 660–667https://doi.org/10.2355/isijinternational.ISIJINT-2023-3161.  IntroductionHydrogen embrittlement is a phenomenon that materi-als exhibit premature brittle fracture due to the presence of hydrogen.1,2) Since hydrogen embrittlement is more pronounced in high-strength steels, material design to improve hydrogen embrittlement properties is necessary for the widespread application of advanced high-strength steels. To date, several models for hydrogen-related frac-ture have been proposed, such as high hydrogen pressure bubbles or voids,3) hydrogen-induced reduction in cohesive energy,4–6) hydrogen-enhanced localized plasticity (so-called HELP),7–10) and hydrogen-enhanced strain-induced vacancy.11,12) The dominant model in actual hydrogen-Relationship between Three-dimensional Crack Morphology and Macroscopic Mechanical Properties of Hydrogen-related Fracture in Martensitic SteelAkinobu SHIBATA,1)*  Yazid MADI,2) Jacques BESSON,2) Akiko NAKAMURA,3) Taku MORONAGA,3)  Kazuho OKADA,1)  Ivan GUTIERREZ-URRUTIA1) and Toru HARA1)1)  Research Center for Structural Materials, National Institute for Materials Science (NIMS), 1-2-1, Sengen, Tsukuba, 305-0047 Japan.2)  Centre des Matériaux, MINES Paris-PSL, CNRS UMR 7633, BP 87, Evry, 91003 France.3)  Research Network and Facility Services Division, National Institute for Materials Science (NIMS), 1-2-1, Sengen, Tsukuba, 305-0047 Japan.(Received August 6, 2023; Accepted November 2, 2023; Advance online published November 11, 2023; Published February 28, 2024)In the present study, several parameters related to crack morphology in the case of hydrogen embrittle-ment were estimated by X-ray computed tomography and correlated with the macroscopic mechanical responses (J-integral and tearing modulus) obtained from the fracture mechanics tests. Even when the hydrogen content was high up to 4.00 wt ppm, unstable premature fracture did not immediately occur, and a certain crack-growth resistance could be confirmed. The three-dimensional crack morphology was not continuous with the formation of un-cracked ligaments in the uncharged specimen. In contrast, the hydrogen-related intergranular crack propagated more continuously with a smaller crack opening-displace-ment. The J-integral value monotonically increased with increasing estimated values of the surface area divided by the projected surface area on the macroscopic crack plane, indicating that crack meandering and branching increased the fracture energy. We defined crack-propagated thickness (standard deviation of the crack surface area at each section (parallel to the macroscopic crack plane) divided by the crack surface area) as a parameter representing crack meandering. The tearing modulus increased as the crack-propagated thickness increased, suggesting that crack meandering also increased the crack-growth resis-tance.KEY WORDS:  hydrogen embrittlement; fracture toughness; crack morphology; three-dimensional analysis; martensitic steel.related fracture depends on several factors, i.e., the strength level of the materials, the constitutive microstructure, the deformation condition, the hydrogen content, and so on. The relationship between the macroscopic mechanical response (degree of hydrogen-induced degradation of mac-roscopic mechanical properties) and each fracture model remains to be understood.Typical modes of hydrogen-related fracture in steels are quasi-cleavage and intergranular. According to Hagihara et al.,13) with increasing hydrogen content, the fracture mode changes from quasi-cleavage to intergranular, resulting in more brittle behavior. Martensitic steels are one of the typical high-strength steels. The martensite structure is complicated and consists of several microstructural units with different size scales, such as lath, block, packet, and prior austenite grain.14–17) The quasi-cleavage fracture New Developments in Elucidation of Hydrogen Embrittlement  Phenomena from the Incubation Stage to Fracturehttps://creativecommons.org/licenses/by-nc-nd/4.0/https://orcid.org/0000-0001-8577-6411https://orcid.org/0000-0003-0183-4528https://www.jstage.jst.go.jp/article/isijinternational/64/4/64_Contents/_pdf/ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ661corresponds to a transgranular occurring on non-typical cleavage planes (specifically, {011} planes) within the lath, and local plastic deformation plays a crucial role in the hydrogen-related quasi-cleavage fracture.18–21) On the other hand, the hydrogen-related intergranular cracks propagate mainly on prior austenite grain boundaries.22–25) The primi-tive mechanism of hydrogen-related intergranular cracking is very simple. Segregation of hydrogen reduces the cohe-sive energy of the boundary, resulting in decohesion of the boundary. The reduction of cohesive energy by hydrogen has been estimated by first-principles calculations.26–29) Yamaguchi and Kameda30) performed a combined analysis using first-principles calculations and fracture mechanics tests for intergranular fracture in thermally aged Ni–Cr steels. They reported that the decrease in the boundary cohe-sive energy is accompanied by a decrease in the plastic work associated with cracking and insisted that the boundary cohesive energy is a very important parameter to account for intergranular cracking.Previously, we investigated the intergranular fracture behavior of a martensitic steel by multi-scale three-dimensional analysis and found that the intergranular crack propagation along prior austenite grain boundaries is basi-cally irregular and discontinuous with the formation of un-cracked ligaments.31,32) The un-cracked ligaments were likely to be formed at the prior austenite grain boundary segments with small misorientation. Because the ductile fracture of the un-cracked ligaments at the later fracture stage would contribute to the macroscopic mechanical responses,33–37) we believe that the crack morphology is also an important parameter affecting the macroscopic frac-ture toughness. In the present study, the fracture toughness test results previously reported for as-quenched martensitic steel31,38) were used to investigate the relationship between three-dimensional crack morphology and macroscopic mechanical properties of hydrogen-related fracture.2.  Experimental ProcedureThis study used an Fe-8Ni-0.1C alloy (C: 0.116, Si: 0.005, Mn: 0.01, P: 0.001, S: 0.0015, Al: 0.033, Ni: 7.94, and Fe: balance (mass%)), which is a model steel contain-ing a large amount of nickel to increase the hardenability. The steel plates were austenitized at 1 000°C for 30 min, and then ice-brine quenched and sub-zero cooled in liquid nitrogen to obtain a fully martensitic microstructure. The 0.2% proof strength and tensile strength of the heat-treated specimens evaluated by uniaxial tensile tests were 920 and 1 191 MPa, respectively.38) Pre-cracked compact ten-sion specimens were prepared from the heat-treated plates (width: 25 mm, thickness: 12.5 mm, and net thickness at the root of side grooves: 10 mm). In order to introduce hydrogen, the pre-cracked compact tension specimens were electrochemically charged in an aqueous solution contain-ing 3% NaCl and 3 g L −1 NH4SCN for 3 days at ambient temperature. The current densities employed for hydrogen charging were changed from 0.625 A m −2 to 3 A m −2, and the diffusible hydrogen contents (HD) measured by thermal desorption analysis were 0.28 wt ppm (0.625 A m −2), 0.42 wt ppm (1.25 A m −2), 1.01 wt ppm (2 A m −2), and 4.00 wt ppm (3 A m −2).The microstructure of the heat-treated specimen was observed by scanning electron microscopy (SEM, JEOL: JSM-7800F and Hitachi High-Tech: SMF-1000) and scan-ning transmission electron microscopy (STEM, JEOL: JEM-2800 (operated at 200 kV) and JEM-ARM300F (oper-ated at 300 kV)). Thin foils for STEM observation were fabricated using a focused ion beam (FIB) – SEM system (ThermoFisher Scientific: Scios2 and Hitachi High-Tech: SMF-1000). The crack-growth properties were evaluated by unloading compliance tests using the single specimen test method according to ASTM E1820-17.39) The unload/reload sequences were performed at a displacement interval of 0.025 mm. The J-integral was calculated from Jel +  Jpl, where Jel was computed from linear elastic fracture mechan-ics, and Jpl was incrementally computed using the plastic area under the load – load-line displacement curve. Accord-ing to ASTM E1820-17,39) the crack extension length (Δa) at each stage was evaluated from the elastic compliance obtained by the unload/reload sequences. In order to make the strain rate sufficiently slow, the load-line displacement was set to 2.5 ×  10 −5 mm s −1, whose initial rate of stress intensity factor for a0/W = 0.5 was 8.5 × 10−3 MPa m1/2 s−1. The details of the mechanical testing are described in the previous paper.38)The fracture surfaces and cracks in the mid-thickness section after the unloading compliance tests were observed by SEM. X-ray computed tomography (X-ray CT, ZEISS: Xradia 620 Versa) was used to reconstruct the three-dimen-sional crack morphology. A specimen with dimensions of approximately 2 mm ×  16 mm ×  1 mm was cut from the mid-thickness region of the tested specimen by spark wire cutting, and absorption contrast images were taken around a 360° rotation of the specimen in 0.1° steps using an optical magnifying lens (×  4 and ×  20 magnification) at an accel-eration voltage of 100 kV.3.  Results and Discussion3.1.  Microstructure and Mechanical PropertiesFigure 1 presents (a) SEM image, (b, c) STEM images, and (d) energy dispersive X-ray (EDX) analysis result (sulfur distribution map) of the heat-treated specimen. The observation areas of (c) and (d) are identical, and the position of prior austenite grain boundary is indicated by the broken line. The specimen exhibits a typical lath martensite structure as shown in Figs. 1(a), 1(b). The STEM-EDX result indicates that sulfur is segregated at the prior austenite grain boundary (~0.12%), though sul-fur was not intentionally added to the steel (the nominal composition of sulfur is 0.0015%). It has been reported that dissolution of sulfides during austenitization leads to segregation and re-precipitation of sulfur at austenite grain boundaries.40) The intergranular fracture that occurred even in the uncharged specimen shown below could be attributed to the segregated sulfur at the prior austenite grain boundaries.Figure 2(a) presents the J–Δa resistance curves of the uncharged specimen and hydrogen-charged specimens with HD =  0.42 wt ppm and 4.00 wt ppm (the resistance curves of the specimens exactly used for the X-ray CT measure-ments shown below are indicated by the arrows). All speci-ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ 662mens (including the hydrogen-charged specimens) satisfied the required specimen dimensional criteria for obtaining a valid plane-strain JIC according to ASTM E1820-17.39) The dimensionless tearing modulus (TR) obtained from the unloading compliance tests is plotted as a function of HD in Fig. 2(b) (the data from our previous paper38) were reused). The dimensionless tearing modulus is a parameter represent-ing crack-growth resistance and can be calculated from the following equation; TE dJd aR �� 02 �................................ (1)where E is a Young’s modulus (200 GPa), σ0 is a 0.2% offset yield strength (920 MPa), and dJ/dΔa is an average slope of the linear region in the J–Δa resistance curve (after the intersection of the 0.2 mm offset line). For the hydrogen-charged specimens, the J-integral values cor-responding to the onset of crack propagation were much lower compared to the uncharged specimen. As shown in Fig. 2(b), the tearing modulus decreases with increasing HD. The results indicate that hydrogen promoted crack initiation and decreased crack-growth resistance. However, even when the hydrogen content was high up to 4.00 wt ppm, unstable premature fracture did not immediately occur. We can confirm a certain crack-growth resistance (positive slope of J–Δa resistance curve and ~0.5 of tear-ing modulus). It should be noted here that, from a fracture mechanics standpoint, the strict criterion for the initiation of unstable fracture is when the differentiate of crack driving force curve exceeds that of crack-growth resis-tance curve. Because the present study did not evaluate crack driving force curves, the obtained tearing modulus may not exactly correspond to that assuming stable crack propagation.3.2.  Crack Propagation Behavior Analyzed by SEM and X-ray CTFigures 3(a)–3(c) shows the fracture surfaces after the unloading compliance tests in the (a) uncharged specimen, (b) hydrogen-charged specimen with HD = 0.42 wt ppm, and (c) hydrogen-charged specimen with HD = 4.00 wt ppm. The fatigue pre-cracked regions are located on the left side of the figures. All the surfaces mainly consist of intergranular surfaces, although dimples and quasi-cleav-age surfaces are partly observed. As described above, the intergranular fracture that occurred in the uncharged speci-men could be attributed to the segregated sulfur at the prior austenite grain boundaries (Fig. 1(d)). Because the present 8Ni-0.1C as-quenched martensitic steel always exhibits intergranular fracture, it is an appropriate material to study the effect of hydrogen on this failure mechanism. Two-dimensional crack propagation morphologies are shown in the SEM images of Figs. 3(d)–3(f); (d) uncharged speci-men, (e) hydrogen-charged specimen with HD = 0.42 wt ppm, and (f) hydrogen-charged specimen with HD = 4.00 Fig. 1.  (a) SEM image, (b, c) STEM images, and (d) STEM-EDX sulfur distribution map of the heat-treated specimen. The observation areas of (c) and (d) are identical.ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ663wt ppm. The intergranular cracks propagated from the fatigue pre-cracks to the right in the images. The inter-granular cracks in the uncharged specimen were notably meandering and branching (Fig. 3(d)). In contrast, the morphology of the intergranular cracks in the hydrogen-charged specimens tended to be more continuous (Figs. 3(e), 3(f)).Figure 4 presents the three-dimensional crack mor-phologies around the macroscopic crack tip reconstructed by X-ray CT using a ×  4 optical magnifying lens in the (a, b) uncharged specimen (voxel size: 0.863 μm3), (c, d) hydrogen-charged specimen with HD =  0.42 wt ppm (voxel size: 1.523 μm3), and (e, f) hydrogen-charged specimen with HD =  4.00 wt ppm (voxel size: 0.873 μm3). In Figs. 4(b), 4(d), 4(f), the thickness of each crack component is expressed by the change in color according to the color bar inserted in the figures (min: 5.0 μm, max: 25.0 μm). The specimen coordinate system in the present study is defined as ±  X: the macroscopic tensile axis (parallel to the load-line displacement), - Y: the macroscopic crack propagation direction, and ±  Z: the thickness direction of the compact tension specimen. The crack regions in the absorption images were segmented by machine learning with the U-net function using ORS Dragonfly Pro software. After meshing the segmented crack region, the thickness between the boundary points was calculated as the diameter of a hypothetical sphere fitting into each boundary point. In the uncharged specimen (Fig. 4(a)), the three-dimensional crack morphology is not continuous and there are a lot of macroscopically isolated non-cracked regions (so called un-cracked ligaments). This indicates that the crack propagated discontinuously and that the crack was locally arrested. As reported previously, the discontinuous crack propagation could be attributed to the high crack arrestability of low-angle boundary segments.31) In contrast, both the number and size of macroscopically un-cracked ligaments are Fig. 3.  SEM images of the (a–c) fracture surfaces and (d–f) two-dimensional crack morphologies of the (a, d) uncharged specimen, (b, e) hydrogen-charged specimen with HD =  0.42 wt ppm, and (c, f) hydrogen-charged specimen with HD =  4.00 wt ppm.Fig. 2.  (a) J–Δa resistance curves of the uncharged specimen and hydrogen-charged specimens (HD = 0.42 wt ppm and 4.00 wt ppm) and (b) change in tearing modulus with HD (the data from previous study was reused31,38) (repro-duced with permission from Elsevier)). The specimens used for the X-ray CT measurements are indicated by the arrows in (a).ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ 664small in the hydrogen-charged specimen (Figs. 4(c), 4(e)), indicating that the hydrogen-related intergranular cracks propagated more continuously.Figures 5(a)–5(c) presents the crack thickness profiles in the volume of 6003 μm3 around the macroscopic crack tip; (a) uncharged specimen, (b) hydrogen-charged specimen with HD =  0.42 wt ppm, and (c) hydrogen-charged speci-men with HD =  4.00 wt ppm. The average thickness of the hydrogen-charged specimens tends to be small (3.27 ±  0.48 μm (HD =  0.42 wt ppm) and 3.76 ±  0.69 μm (HD =  4.00 wt ppm)) compared to that of the uncharged specimen (4.45 ± 0.96 μm). The crack-tip opening angle (CTOA) estimated from the average crack thickness divided by the analyzed crack length (600 μm) is 0.00741 (uncharged specimen), 0.0055 (hydrogen-charged specimen with HD =  0.42 wt ppm), and 0.0062 (hydrogen-charged specimen with HD = 4.00 wt ppm). The results indicate that the hydrogen-related intergranular crack propagated while maintaining a small crack opening-displacement. However, increasing HD does not simply decrease the average crack thickness and CTOA. This could be due to the fact that the mechanical responses were scattered depending on the individual specimen as confirmed by the J–Δa curves shown in Fig. 2(a). Figure 5(d) presents the relationship between the crack thickness and exact J-integral value at the actual crack length of the specimens used for X-ray CT measurements. We can find a clear tendency for the J-integral value to increase monotoni-cally with increasing crack thickness.The energy criterion for fracture is that the strain energy release rate reaches the fracture energy (wf) which includes the cack surface energy (γs) and plastic work (γp).41–43) Although the contribution of plastic work to fracture in Fig. 4.  Three-dimensional crack morphologies reconstructed by X-ray CT of the (a, b) uncharged specimen, (c, d) hydrogen-charged specimen with HD =  0.42 wt ppm, and (e, f) hydrogen-charged specimen with HD =  4.00 wt ppm. The color in (b, d, f) expresses the thickness value of the crack components according to the color bar (Min: 5.0 μm, Max: 25.0 μm).ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ665Fig. 5.  Crack thickness profiles in the (a) uncharged specimen, (b) hydrogen-charged specimen with HD =  0.42 wt ppm, and (c) hydrogen-charged specimen with HD =  4.00 wt ppm. (d) The relationship between J-integral and crack thickness.metallic materials is considerably high even for brittle frac-ture,30) the results in the present study are insufficient to dis-cuss the effect of plastic work on macroscopic mechanical properties. A clear reason for the degradation of mechanical properties by hydrogen-related intergranular fracture is the hydrogen-induced reduction of cohesive energy of prior austenite grain boundaries. In addition to those factors, we focus on the effect of crack morphology on mechanical responses and consider three parameters representing crack morphology that are related to crack surface energy: crack surface area (S), projected crack surface area on the YZ plane (Sp), and crack surface area at each YZ section (Ss). The analyzed length (parallel to Y direction) is ~1 200 μm from the crack tip. Figure 6(a) schematically explains these three parameters. Because the load-line displacement in the compact tension specimen is parallel to the ±  X direction, the YZ plane corresponds to the macroscopic crack plane. For an ideal brittle material, the crack plane is uniform and only S needs to be estimated. On the other hand, when crack is meandering and branching as confirmed by the three-dimensional crack morphologies (Fig. 4), the degrees of meandering and branching could affect the macroscopic fracture energy. According to Anderson’s textbook,44) the fracture energy in materials with crack meandering and branching can be expressed as:  wSSf sp� � .................................. (2)The J-integral is defined as the potential energy per unit area released by crack propagation, and the J-integral increases as the estimated value of S/Sp increases, as shown in Fig. 6(b).As shown in Fig. 4, the intergranular crack propagated discontinuously with the remaining un-cracked ligaments in the uncharged specimen, while the morphology of the intergranular crack was more continuous, and the uncracked ligaments tended to be smaller in the hydrogen-charged specimens. Because crack propagation with more meandering would consume more fracture energy, we can assume that the degree of crack meandering could affect the crack-growth resistance. Figure 6(c) shows the relative surface areas at each YZ section (i.e., surface area on a YZ section (Ss) divided by surface area (S)), and the vertical axis expresses the distance from the center section along X direction. The relative surface areas in the hydrogen-charged specimens are large around the center section, indicating that the degree of crack meandering is smaller in the hydrogen-charged specimens. We can consider that the standard deviation of each curve in Fig. 6(c) (i.e., 259 μm (uncharged specimen), 145 μm (hydrogen-charged specimen with HD =  0.42 wt ppm), and 103 μm (hydrogen-charged specimen with HD =  4.00 wt ppm) represents the degree of crack meandering and define it as “crack-propagated thickness”. As shown in Fig. 6(d), the crack-propagated thickness and tearing modulus have a clear correlation, i.e., larger crack-propagated thickness resulted in larger tearing modulus (crack-growth resistance). Accordingly, we can say that crack meandering also increases the crack-growth ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ 666resistance.The small meandering of the hydrogen-related crack propagation could be attributed to the fact that, even when the intergranular crack is locally arrested at a specific seg-ment of prior austenite grain boundary (particularly, a low-angle boundary segment), the crack can continue to propa-gate into the grain interior as a quasi-cleavage manner in the hydrogen-charged specimens.32) That is, the crack does not necessarily propagate along the prior austenite grain bound-ary, which is largely inclined from the macroscopic crack plane (YZ plane) (i.e., the boundary where the resolved normal stress is low), but can propagate along {011} plane, which is nearly parallel to the YZ plane with larger resolved normal stress, in a quasi-cleavage manner.45,46)As shown in Figs. 4–6, the crack morphologies reflect the macroscopic mechanical responses (such as J-integral and tearing modulus). Obviously, the data obtained in the present study are limited. However, the results shown above suggest that systematic analyses in the future will allow the estimation of the mechanical response during operation from the resultant crack morphology.4.  SummaryThe present study investigated hydrogen-related inter-granular cracks in 8Ni-0.1C as-quenched martensitic steel. We proposed several parameters related to crack morphol-ogy: crack thickness, crack surface area, projected crack surface area on the YZ plane (macroscopic crack plane), and crack surface area at each YZ section, and investigated the relationship between macroscopic mechanical responses and crack morphology. The main results are as follows.(1)  The X-ray CT images showed that the three-dimensional crack morphology was not continuous, and there were a lot of un-cracked ligaments in the uncharged specimen. This indicates that the crack propagated discontinuously. In contrast, both the number and size of un-cracked ligaments were small in the hydrogen-charged specimen, indicating that the hydrogen-related intergranular cracks propagated more continuously. In addition, the hydrogen-related intergranular crack propagated while maintaining a smaller crack opening-displacement.(2)  We quantitatively evaluated the crack thickness and surface areas from the X-ray CT results and found the clear tendency that the J-integral monotonically increased with increasing crack thickness. The J-integral also increased with increasing estimated values of the surface area divided by the projected surface area (S/Sp), indicating that the crack meandering and branching increased the fracture energy.(3)  From the value of the crack surface area at each YZ section (Ss) divided by the crack surface area (S), we Fig. 6.  (a) Schematic illustration of crack surface area (S), projected crack surface area on the YZ plane (Sp), and crack surface area at each YZ section (Ss), (b) change in J-integral value as a function of S/Sp, (c) relative sur-face area on an each YZ section (Ss/S), (d) change in tearing modulus as a function of crack-propagated thick-ness.ISIJ International, Vol. 64 (2024), No. 4©  2024  ISIJ667defined crack-propagated thickness (standard deviation of (Ss/S)) as a parameter representing crack meandering. The tearing modulus increased as the crack-propagated thickness increased, suggesting that crack meandering also increased the crack-growth resistance.AcknowledgmentsThis work was financially supported by JST PRESTO (Grant Number JPMJPR2096), JSPS KAKENHI (Grant Numbers JP22K18910 and JP23H01717), and MEXT Program: Data Creation and Utilization Type Mate-rial Research and Development Project Grant Number JPMXP1122684766.REFERENCES1)  S. Lynch: Corros. 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