Hydrogen in metallic alloys ─ embrittlement and enhanced plasticity: a review

3.1 Pros and cons of HELP theory

Localization of plastic deformation constitutes the important part of HELP phenomenon. This was not really substantiated in the HELP theory.

Ulmer and Altstetter (1991) supposed that hydrogen affects the ability of dislocations to cross-slip, thereby assisting slip planarity. A reason for that was supposed to be the stronger binding of hydrogen atoms to an edge dislocation than in the case with a screw dislocation because the normal stresses component is absent in the latter. This idea was supported by Ferreira et al. (1999) in their TEM studies of the dislocation character in aluminum, where hydrogen atoms are shown to stabilize the edge segments of dislocations, thereby inhibiting cross-slip. The hydrogen-caused increase in the propensity toward the edge character of dislocations in hydrogen-charged 310s austenitic steel was also observed by Robertson (2001). The clear hydrogen-enhanced formation of pile-ups was observed in the refined experiment performed earlier on this steel by Ferreira et al. (1998) who demonstrated a decrease in the separation distance between neighboring dislocations given increasing hydrogen content at constant load.

A similar result was obtained by Lu et al. (2001) in their simulations of dislocation slip in aluminum. It was shown that the hydrogen-caused decrease of SFE by 40 % does not cause dislocations to be dissociated into partials, and only the core width of dislocations significantly increases. A strong binding between hydrogen atoms and the edge component of dislocations was believed to be responsible for slip planarity.

Less evident is the planar dislocation slip in pure metals with the high stacking fault energy, SFE, and, consequently, narrow dislocations, namely iron, nickel, and aluminum. It does not occur in pure iron whatever hydrogen is present or not. Its observation by Hwang and Bernstein (1986) in hydrogen-charged iron single crystals, as well as by Le and Bernstein (1991) in hydrogen-charged spheroidized steel, is associated with silicon-rich particles cut by dislocations in the former case and with strain localization in the form of dense dislocation structure emanating from carbide particles in the latter case. The cutting of precipitates by the first moving dislocations eases the passing of the subsequent ones on the same planes leading to planar slip. No real slip bands were found either by Wang et al. (2014) in hydrogen-charged pure iron subjected to stress relaxation tests.

Hydrogen was found to increase waviness of dislocation slip in deformed nickel by McInteer et al. (1980). The prevailing formation of dislocation cells occurs in pure nickel subjected to high-pressure torsion decreasing cell size compared to uncharged nickel, see Wang et al. (2017). According to Bertsch et al. (2019), hydrogen also intensifies the formation of cell dislocation structure in nickel during uniaxial tensile deformation. These authors observed nearly equisized cells sheared by “second-generation” microbands as consistent with Hughes and Hansen (1991). In contrast, quite a different dislocation structure was observed by Delafosse (2012) in a hydrogen-charged Ni single crystal, where the equiaxed dislocation cell structure formed by 0.75 plastic shear strain was replaced by planar dislocation ensembles in the presence of hydrogen.

There is also no clear evidence of the hydrogen-caused localization of plastic deformation in pure aluminum. It occurs in the hydrogen-free Al–Li alloys because of cutting the Al₃Li precipitates by dislocations, see, e.g., Tayon et al. (2019), and disappears if the size of precipitates is too large for their cutting (Furukawa et al. 1985). Hydrogen in these alloys causes the prevailing intergranular fracture (Zhao et al. 2022).

At the same time, a possibility of planar dislocation slip in hydrogen-charged aluminum could be suggested based on a significant hydrogen-caused increase in the concentration of vacancies. This phenomenon has a thermodynamic nature, see Smirnov (1991) and Bobyr et al. (1991). It is caused by any interstitial element in metals, e.g., by hydrogen (Fukai et al. 2000, 2001, 2003, Fukai and Okuma 1993, 1994), carbon in fcc iron (McLellan 1988), and nitrogen in austenitic steels (Gavriljuk et al. 1996a; Kikuchi et al. 1974).

A feature of hydrogen in aluminum is that a single vacancy can trap up to 12 hydrogen atoms (Lu and Kasiras 2005) in contrast to 2 hydrogen atoms in bcc iron (Takeyama and Ohno 2003) and 6 hydrogen atoms in fcc iron (Nazarov et al. 2010). As shown earlier by Birnbaum et al. (1997), H-vacancy complexes in aluminum form platelets of about 15 nm in radius and 7 nm in thickness, which lie on the planes (111). This seems to be natural because the gliding dislocations are encased in hydrogen atom atmospheres, which can be suggested as reason for prevailing concentration of vacancies at the slip planes. If so, the hydrogen-induced vacancies should act as microvoids in accordance with the “voids sheeting” model proposed by Teirlinck et al. (1988):

where A _b is the slip area, r _v is the void radius, and N _v is void density per unit volume.

The decrease in the load-bearing area d A b A b corresponds to the shear increment dγ; therefore, the slip localizes there.

A widely shared idea for the interpretation of hydrogen-caused localization of plastic deformation is associated with the hydrogen-decreased stacking fault energy, SFE, which is expected to inhibit the cross slip of dislocations assisting thereby its planarity.

The uncertainty in the concept of a remarkable role of stacking fault energy, SFE, in the slip localization can be clearly demonstrated by the comparison of strikingly different dislocation substructures in the cold worked carbon and nitrogen austenitic steels.

Carbon in the austenitic steels is known to increase SFE, see, e.g., Charnock and Nutting (1967) and Volosevich et al. (1972), whereas nitrogen increases it, e.g., Gavriljuk et al. (2006). Nevertheless, irrespective of the SFE and in the whole area of their content in steel, carbon always assists formation of tangled dislocations during the cold work and reveals no tendency to assist strain localization. In contrast, nitrogen facilitates the planar dislocation slip and localizes plastic deformation, see, e.g., Gavriljuk and Berns (1999) and Gavriljuk et al. (2008). This distinctive difference between the carbon and nitrogen effects on dislocation substructure occurs in the austenitic steels of different basic compositions. In any case, whatever retarded cross slip and prevailing planar movement of dislocations on the slip planes occurs, it remains unclear why hydrogen assists their accumulation in the separate slip bands.

Closer to physical reality is a mechanism proposed by Gerold and Karnthaler (1989) who presented evidence that short-range atomic order, SRO, is the main reason for planar slip in fcc alloys, whereas the low SFE or a high yield stress are of minor significance.

Generally, the term SRO simply designates any deviation from the random distribution of solute atoms in the solid solutions and nothing more. According to Cowley (1950), SRO is characterized by its parameter α introduced using the following formula:

where

P _lmn is the probability that an atom with coordinates l, m, and n with respect to a B atom in the co-ordinates origin should be an A atom,

c _A is the atomic fraction of A atoms in the binary solid solution with c _A + c _B = 1.

In other words, P _lmn /c _A is equal to the atomic ratio N _AB ^real/N _AB ^ideal between the number N of atomic pairs AB in a real binary solid solution and that in the case of random atomic distribution. A preference in the nearest neighborhood for different kinds of atoms, AB, or for the same kind, AA, is denoted as short-range atomic ordering or short-range atomic decomposition of solid solutions, respectively, with α < 0 in the first case and α > 0 in the second case.

If short-range atomic ordering occurs, the passage of the first dislocations emitted by their sources needs energy spent to locally destroy the atomic order. Therefore, subsequent dislocations can easily move on the planes close to that of the first ones resulting in the formation of slip bands. The short-range decomposition of solid solutions creates submicroscopic volumes of a different chemical composition, where hydrogen solubility should be also different, see first-principle calculations performed by Movchan et al. (2010) for iron–nickel alloys.

For example, this is the case of CrNi austenitic steels and Ni-based superalloys. As shown by Garner and McCarthy (1990), alternating regions enriched in Ni and those rich with Fe and Cr atoms, with their spatial extent of ∼600 nm, exist in the Fe–Cr–Ni solid solutions after their irradiation with neutrons within the temperature range of 450–700 °C. Rotman et al. (1990) observed a similar short-range decomposition of the Fe–45Ni–16.0Cr alloy after its 1 MeV electron irradiation at 500 °C.

The role of irradiation amounts merely to an increase in the concentration of vacancies, which accelerates the diffusion of metallic atoms. The inherent thermodynamic nature of this process has been proven by Wiedenmann et al. (1989) who detected the oscillating fluctuations of Ni concentration between 28.5 and 36.5 at.% within the temperature range of 625–725 °C in their measurements of small-angle neutron scattering in the Fe-34 at.% Ni alloy. The spatial extent of these fluctuations exceeded 200 nm.

Consequently, the nickel-based superalloys in their solution-treated state reveal the excellent resistance to hydrogen embrittlement, see, e.g., Michler et al. (2014) and loose it after heat treatment, see Louthan and Caskey (1976), Lecoester et al. (1999), Rezende et al. (2015), and Zhang et al. (2016). Their heat treatment occurs just within the temperature range of the short-range atomic decomposition of which the role in their hydrogen embrittlement should be taken into account, but has never been discussed.

Thus, the character of dislocation slip in the hydrogen-charged metallic materials is hardly affected by hydrogen itself because, at least at ambient temperatures, it cannot change the distribution of metal atoms in the crystal lattice. Only at elevated temperatures, e.g., in the course of technological processing, hydrogen accelerates their diffusion, see, e.g., Hayashi et al. (1998), and causes short-range decomposition of substitutional metal solutions, e.g., Noh et al. (1991, 1996, assisting thereby the localization of plastic deformation.

Therefore, arising from the short-range atomic ordering or short-range atomic decomposition, shear localization is the inherent phenomenon in many metallic alloys, while hydrogen only intensifies this phenomenon because of its different solubility in the submicrovolumes of disintegrated solid solutions accelerating thereby dislocation velocity in those with higher hydrogen content, which in turn results in the locally enhanced plastic deformation and the quasi-brittle fracture.

Temperatures and strain rates: The HELP theory allows to understand an important feature of hydrogen embrittlement, namely its display within a certain range of temperatures and strain rates. One of the earliest observations of this feature was made by Boniszewski and Smith (1963), see Figure 3, who demonstrated that the tensile tests in liquid nitrogen of nickel moderately charged with hydrogen do not reveal its any remarkable effect on plasticity. As temperature of tests increased, the relative elongation started to decrease at about −120 °C. This effect was enhanced by a further increase of testing temperature up to −50 °C, and, at higher temperatures, plasticity increased again. The hydrogen-caused loss of relative elongation also decreased with increasing strain rate and disappeared at that of ∼1 s⁻¹.

Figure 3:

Relative elongation of hydrogen-free nickel and nickel containing 40 ml_NTP H₂/l00 g Ni (∼0.2 at.% H₂) at various temperatures and strain rates. Boniszewski and Smith (1963), reproduced with permission from Elsevier.

The authors supposed that “hydrogen embrittlement in nickel occurs at temperatures and strain rates at which hydrogen atoms can segregate to moving dislocations.” Later on, the shift of the HE phenomenon to higher temperatures with increasing strain rate and the absence of brittleness at some threshold rate was observed by Popov (1969) in a plain carbon steel.

These experimental results suggest that dislocation slip is accompanied by hydrogen atmospheres as a necessary condition for hydrogen embrittlement. Popov has also obtained that the greatest decrease of plasticity occurs at an appropriate combination of temperature and strain rate, where hydrogen atom diffusivity is consistent with dislocation velocity. Brittleness diminishes with increasing temperature or strain rate as a result of hydrogen atmospheres being diluted or breaking away from dislocations, respectively.

Similar data were obtained by Gabidullin et al. (1971) in titanium alloys and Fournier et al. (1999) in Inconel 718.

Critical comments on the HELP theory have being made in relation to experimental data on the high velocities of crack propagation in hydrogen-charged metals and alloys. For example, it was claimed that crack velocities can exceed the diffusion rate of solute hydrogen atoms and even the velocity of their transport by dislocations, see, e.g., Lynch (1987), where a collection of experimental data on the crack growth rate is compared with the calculations of hydrogen transport by dislocations performed by Tien et al. (1976). A correct discussion of this objection to the HELP theory requires a careful estimation of the energy of binding between hydrogen atoms and dislocations and the real velocity of dislocations which in principle is limited only by that of sound in metals.

Another point of criticism in relation to HELP concerns the temperature range of hydrogen embrittlement display in steels. Based on the temperature of ∼70 °C determined by Livne et al. (1986) as the upper limit for the temperature range of hydrogen-assisted crack growth in steel AISI 4340 steel and the correlation between the crack propagation rate and concentration of hydrogen adsorbed at the iron surface but not dissolved in the crystal lattice, see Ransom and Ficalora (1980), Lynch (2008) suggested that solute hydrogen is innocuous for embrittlement compared with adsorbed hydrogen because the hydrogen-dislocation interaction in iron alloys should occur up to about 200 °C.

However, the point is that the temperature of ∼200 °C reported by Lynch refers only to the interaction between carbon or nitrogen atoms with dislocations in bcc iron resulting, e.g., in the Snoek–Köster relaxation. In the case of hydrogen, this interaction occurs at about −25 °C, see Takita and Sakamoto (1976). Therefore, it is natural that the hydrogen-caused degradation of mechanical properties in the iron alloys weakens if temperature increases above RT.

Similar arguments are also true concerning the discussed role of solute or adsorbed hydrogen atoms and hydrogen-dislocation interaction in the embrittlement of bcc β-titanium alloys. Referring to the ductile behavior of the hydrogen-charged β-titanium alloy Timetal 21S despite the extremely high hydrogen/metal ratio of up to ∼0.21, see Teter et al. (2001), Lynch (2008) claimed that “solute hydrogen is not a potent embrittler in this material.”

It is expedient in this relation to compare the enthalpy of hydrogen binding to dislocations, 0.035 eV, and that of hydrogen migration, 0.27 eV, in β-titanium, see Teus et al. (2017), with those in austenitic steels, ∼0.1 eV and ∼0.5 eV, respectively, see Gavriljuk et al. (2010). It follows from this comparison that, the extremely weak hydrogen binding to dislocations, as well as the high diffusivity of hydrogen atoms in β-Ti alloys, suggest formation of hydrogen atmospheres around dislocations at rather low temperatures and their quick dilution with increasing temperature. Therefore, in accordance with the criteria for dislocation slip accompanied by hydrogen atmospheres, hydrogen embrittlement of β-titanium alloys should proceed within the temperature range far lower than RT. Along with the absence of localized plasticity, just this feature is responsible for the ductile behavior of β-titanium alloys at RT despite the rather high hydrogen content.

Some questions appear in relation to the aforementioned shielding of elastic stresses within the distance between neighboring dislocations, see Figure 2. These calculations were carried out only for edge dislocations in niobium, where dislocation properties are significantly controlled by the Peierls relief of the bcc crystal lattice. However, hydrogen embrittlement also occurs in the fcc metals having a shallow Peierls relief, e.g., in the iron- and nickel-based alloys.

A role of Peierls barrier was analyzed by Taketomi et al. (2008) who performed the atomistic studies of hydrogen’s effect on the mobility of edge dislocations in the bcc iron using the embedded atom method developed by Wen et al. (2001). According to the obtained hydrogen-caused decrease in the energy barrier for dislocation motion, hydrogen diminishes the Peierls relief in the iron bcc lattice. At the same time, no significant change in the stress distribution around the edge dislocations and, consequently, in the interaction between dislocations was detected, which is in contradiction with the HELP theory.

Additionally, the atomistic simulation of hydrogen’s effect on the mobility of edge and screw dislocations in bcc iron was carried out by Wang et al. (2013) who reported that the core energy and Peierls potential are reduced by hydrogen for both types of dislocations. This result suggests that decisive for hydrogen embrittlement is the hydrogen effect on the properties of single dislocations, not on the interactions between the neighboring dislocations, as it is stated in the HELP theory.

Finally, a feature of this theory is that hydrogen atom is presented as merely a point defect, which induces elastic distortions in the crystal lattice. If so, any interstitial elements in the solid solution are expected to affect dislocation velocity like hydrogen, provided their atoms accompany dislocations during the plastic flow.

It is particularly interesting in this relation to compare the carbon and nitrogen effects on dislocation properties because their atoms have nearly the same effective size in the bcc α-iron, see Chen and Tang (1990), and quite a comparable size in the fcc γ-iron, see Gavriljuk and Berns (1999). Therefore, the shielding effect for dislocations in their iron-based solid solutions is expected to be nearly the same and, consequently, mobility of dislocations should be comparable.

Mechanical spectroscopy is an appropriate tool for testing dislocation dynamics. The so-called α relaxation in the bcc iron is caused by the vibrations of 71° dislocations under applied alternating mechanical loading, while the hydrogen-caused Snoek–Köster relaxation arises from the same dislocations, the vibrations of which are accompanied by hydrogen atmospheres. The intensity of both relaxation peaks is proportional to the area crossed by dislocations during their vibrations.

As follows from the comparison of intensity of the α- and Snoek–Köster peaks, see Figure 4a, hydrogen in bcc iron increases dislocation velocity in consistency with HELP theory. At the same time, as follows from Figure 4b, dislocation velocities in the carbon and nitrogen solid solutions in the bcc iron are quite different despite the equal crystal lattice distortions, which is at variance with HELP theory.

Figure 4:

(a) Snoek–Köster relaxation caused by hydrogen in the bcc iron in comparison with α-relaxation arising from the formation of paired kinks on the 71°-dislocations (modified from Figure 1 in Takita and Sakamoto 1976, reproduced with permission from Elsevier); (b) Snoek–Köster relaxation caused by carbon and nitrogen in martensitic steels Cr15Mo1C0.6 and Cr15Mo1N0.62 (Gavriljuk Valentin et al. 2013), respectively.

The same difference was observed in the austenitic steels using the strain-dependent internal friction, which makes it possible to study dislocation dynamics at increasing strain amplitudes, i.e., to observe the emission of dislocations and change in their velocity, see Figure 5.

Figure 5:

(a) Hydrogen effect on the strain-dependent internal friction, Q⁻¹, in steel Cr25Ni20: (1) hydrogen-free state, (2) after hydrogen charging at 50 mA/cm² for 48 h, (3) after subsequent hydrogen degassing at 100 °C (Shyvanyuk et al. 2001); (b) the same for the logarithmic decrement δ = πQ ⁻¹ caused by carbon and nitrogen in steel Cr18Ni16Mn10 (Gavriljuk et al. 2010).

As follows from Figure 5a, hydrogen decreases the stress for the start of dislocation sources and increases the velocity of emitted dislocations. The consequent hydrogen degassing returns these properties to their initial state except for a small increment of internal friction due to the increased density of dislocations resulting from plastic deformation during the electrochemical hydrogen charging.

Because of the slower carbon and nitrogen atom diffusivity in austenitic steels in the comparison with hydrogen, these measurements were performed at elevated temperatures to allow the carbon or nitrogen atmospheres follow the vibrating dislocations. Despite the nearly equal crystal lattice distortions, nitrogen assists to the start of dislocation emission at the earlier applied stresses than carbon and enhances dislocation velocity, see Figure 5b.

Both results give the evidence that viewing the HELP phenomenon within the frames of continuum mechanics is not sufficient. In fact, hydrogen in the HELP theory is not determined as a chemical element, which ignores a change in the interatomic bonds due to the overlapping between the valence electrons brought in by hydrogen and those of metallic atoms. Some additional mechanism should exist according to which hydrogen changes the properties of dislocations.

3.2 Electron approach to HELP phenomenon

Focused on the electron exchange between atoms in solid solutions, studies of the hydrogen effect on the electron structure of metals and their alloys make it possible to take into account the chemical nature of hydrogen atoms. Such analysis differentiates between free and localized electrons and includes the spatial distribution of valence electrons, as well as the spatial symmetry of electrons contributing to hydrogen–metal interactions. Three metals, namely iron, nickel, and titanium, constituting the basis for three main classes of engineering metallic materials were the important objects of these studies.

The density of electron states, DOS, controls distribution of valence electrons on their energy levels in these metals free of hydrogen and those hydrogen-charged ones. It has been calculated taking into account the magnetism of iron and nickel atoms, i.e., the electron spin orientations along and against the internal magnetic field, up and down, respectively. As example, the DOS is shown in Figure 6 for the d-electron band in the fcc iron, see Gavriljuk et al. (2017) for details. The same measurements have been carried out in bcc iron, fcc nickel, and bcc titanium. The DOS at the Fermi level proportional to the concentration of free electrons is of a particular interest and the obtained data are presented in Table 1.

Figure 6:

Density of electron states in fcc iron without (solid line) and with (dashed line) hydrogen at the atomic ratio H/Fe of 1/32. The insets on the left show the density of states at the Fermi level for spin up and spin down electrons.

As follows from Figure 6 and Table 1, hydrogen increases the DOS at the Fermi level in the all studied metals. This effect occurs in the fcc iron at any hydrogen concentration, see Gavriljuk et al. (2010). In contrast, DOS at the Fermi level in nickel and titanium changes nonmonotonously with increasing H/Ni and H/Ti ratios, which is caused by miscibility gap in the Ni–H system and formation of hydrides in titanium.

With Ni content increased up to the H/Ni ratio of 6/32, the DOS at the Fermi level rises and then drops at higher Ni contents. At the same time, as shown by Teus and Gavriljuk (2018), the enthalpy of hydrogen solution in the Ni–H thermodynamic system rises with an increase in the H/Ni ratio up to 0.2 and drops above it, whereas the cohesion energy depends on the Ni content monotonously, demonstrating thereby the absence of any energy barrier for the hydrogen-induced phase transformation.

Moreover, the second derivative of H solution enthalpy as a function of hydrogen content acquires the negative sign between the H/Ni values of 0.03 and 0.75, which is a sign of miscibility gap in the Ni–H solid solutions and, consequently, of two coexisting solid solutions within the crown on the Ni–H phase diagram. This result is in a clear contradiction with formation of a Ni hydride claimed by Baranowski (1959).

The hydrogen-caused increase in the density of electron states at the Fermi level suggests an increase in the concentration of free electrons enhancing thereby the metallic character of interatomic bonds, which has been confirmed for hydrogen in iron using measurements of conduction electron spin resonance, CESR, see Figure 7.

Figure 7:

Conduction electron spin resonance, CESR, in hydrogen-free (dashed line) and hydrogen-charged (solid line) steel Cr18Mn20N0.88 and corresponding concentrations of free electrons n ₀ ^e and n _H ^e, Shanina et al. (1999). Measurements were performed at 77 K. Signal A₀ belongs to the reference sample (borate glass) containing 10¹⁵ electron spins and is seen on the left side of the main signal.

The austenitic steel Cr19Mn20N0.88 chosen for this experiment remains paramagnetic at temperatures below −196 °C, which was a precondition for such measurements. The CESR signal is a derivative of the energy spent on the transfer of free electrons between their ground and excited energy states under the applied magnetic field. The area A under the CESR signal is proportional to the concentration of free electrons in the measured sample.

It is seen that hydrogen significantly increases the concentration of free electrons in the austenitic steel.

The spatial distribution of valence electrons throughout the crystal lattice in the 2D format is presented as an example in Figure 8 for hydrogen in the three aforementioned metals.

Figure 8:

Spatial distribution of valence electrons in 2D format on the atomic plane (002) throughout (a) fcc iron, (b) fcc nickel, and (c) bcc titanium lattices at the hydrogen/metal ratio of 1/32.

Encased in the clouds of valence electrons, hydrogen atoms occupy the octahedral interstitial sites in fcc iron and nickel and tetrahedral sites in bcc titanium. The latter is also true for hydrogen in bcc niobium, which is a stronger hydride former in comparison with titanium, see Figure 9.

Figure 9:

Spatial distribution of valence electrons in 2D format in the bcc Nb at H/Nb = 1/54.

A deeper insight into the topology of electron density distribution can be obtained while performing the electron charge integration inside the spheres surrounding selected atoms, see Gavriljuk et al. (2022). Using the calculation technique proposed by Bader (1995, 1998, this analysis was carried out for bcc Fe–H and bcc Nb–H solid solutions, where hydrogen atoms occupy the tetrahedral sites. In both cases, the electron charge around a hydrogen atom exceeds one electron: 1.39 e⁻ and 1.65 e⁻, respectively.

Two conclusions can be derived from the obtained result: (i) the electron density around a hydrogen atom dissolved in both metals is increased in comparison with a neutral H atom, i.e., hydrogen atoms in these metals are the electron acceptors; (ii) as the value of the integrated charge around a hydrogen atom dissolved in the hydride-forming niobium is higher than in the case of H in Fe, the interatomic bonding between hydrogen and hydride-forming elements is stronger.

Moreover, as shown in Figure 10, hydrogen decreases the density of electron states at the Fermi level in Nb, in contrast to that in Fe, Ni, and Ti.

Figure 10:

Density of electron states in the niobium hydrogen-free (solid line) and hydrogen-doped (dash-dot line) at the atomic ratio H/M = 1/54. DOS in the vicinity of Fermi level is presented in the inset.

Along with decreasing DOS in titanium at high H concentrations, this suggests the enhancement of covalent interatomic bonds by hydrogen in hydride-forming elements. Consequently, a remarkable difference should occur in the hydrogen effect on the elasticity moduli, which control the properties of dislocations in these metals.

Let us compare, for example, the ab initio calculated shear moduli in iron and niobium. Due to the cubic symmetry of the crystal lattice in both metals, only three independent elastic constants, namely c ₁₁, c ₁₂, and c ₄₄, need to be calculated as components of the full elastic tensor. Thus, only three types of strain are required for that in the crystal lattice, namely bulk tension-compression, tetragonal, and rhombohedral distortions. By fitting the Murnaghan solid state equation to the dE(V)/dV curve with the total energy E and volume V, respectively, see Murnaghan (1944), the (c ₁₁ + c ₁₂ + c ₄₄) combination is obtained. The values of (c ₁₁ − c ₁₂) and (c ₁₁ + 2c ₁₂ + 2c ₄₄) were calculated from two other total energy functions of the strain in the rhombohedral and tetrahedral distortions, respectively. As a result, the system of three equations containing three elastic moduli was obtained.

The earlier obtained by Teus (2007) shear modulus c ₄₄ for hydrogen in fcc iron and those calculated in this study for hydrogen in bcc niobium are presented in Table 2 along with the densities of electron states at the Fermi level. Significantly higher values of total DOS for niobium are due to the increased number of metallic atoms included in the calculated cell.

While increasing the DOS at the Fermi level, hydrogen decreases modulus c ₄₄ in fcc iron. Having been calculated for 0 K, these data cannot be correctly compared with the experiment because the γ-iron phase is thermodynamically stable only at temperatures above 910 °C.

Nevertheless, the obtained results demonstrate a clear trend: hydrogen in iron decreases the shear modulus, whereas in niobium elastic constants, c ₄₄, c ₁₁, and c ₁₂ are increased. Moreover, the constant c′ = (c ₁₁ − c ₁₂)/2 controlling the shear stress along the slip planes {110} in niobium is significantly increased by hydrogen from 60.5 to 64 GPa.

The calculated data for H in Nb are consistent with the experiments performed using the ultrasonic technique. The shear constants c ₄₄, c ₁₁, and c ₁₂ for niobium doped with hydrogen were measured by Magerl et al. (1976). In the H-free niobium, these authors obtained 28, 246, and 133 GPa for c ₄₄, c ₁₁, and c ₁₂, respectively. Alloying with hydrogen increased c ₄₄ by 18.4 × 10⁻³ per 1 % of H and, unexpectedly, decreased c′ as −4.7 × 10⁻³ per 1 % of H. A reason for that is clearly caused by a small plastic deformation identified as Snoek relaxation, which accompanies ultrasonic measurements and causes a modulus defect due to diffusion hops of hydrogen atoms. Similar experimental results were also reported earlier by Fisher et al. (1975).

Thus, in contrast to strong hydride forming metals, the hydrogen-enhanced metallic character of interatomic bonds in fcc iron, fcc nickel, and in bcc titanium, for the latter at H concentrations far below those for hydride formation, results in the decrease of the shear moduli, which is expected to change properties of dislocations in the following way:

1. A decrease in the critical stress for the start of dislocation sources, e.g., σ ≈ 2 μb/L for the Frank-Reed dislocation source, where L is the distance between the pinning points, which decreases the yield stress under mechanical loading;

2. A decrease in the specific energy of dislocations termed their line tension Γ ≈ (μb ²/4π)/log(ℜ/5b), where ℜ is the dislocation curvature radius, which enhances dislocation mobility;

3. A decrease in the distance d ≈ (πμb)/16(1 − ν)nσ between dislocations in the pile-ups under applied stress σ, which increases the number of dislocations n in the pile-up resulting in the increased shear stress at the leading dislocation, τ _L = nτ, and causing the earlier opening of a microcrack due to the coalescence of dislocations in the pile-ups.

All these predicted effects were observed in the above analyzed experimental studies of hydrogen embrittlement in iron, nickel, and titanium alloys.

The hydrogen-induced softening of interatomic bonds should be particularly manifested in the vicinity of dislocations encased in hydrogen atmospheres if the latter accompany dislocations during plastic deformation. Along with localization of plastic deformation, the nature of which is discussed above, this joint movement of dislocations and hydrogen atoms appears to be a precondition for hydrogen embrittlement and is its distinctive feature compared to other numerous dramatic examples of hydrogen damages in metals.

As mentioned in the Introduction, another feature of hydrogen embrittlement is its display in the definite range of temperatures and strain rates. This phenomenon can be easily understood taking into account the enthalpy of hydrogen migration in the crystal lattice and the enthalpy of binding between hydrogen atoms and dislocations. The probability of diffusion hops of a hydrogen atom depends on the value of the energy barrier between the neighboring interstitial sites. Increasing the concentration of free electrons, hydrogen decreases this barrier, which explains the extremely small hydrogen migration enthalpies in metals, e.g., ∼0.04 eV in bcc iron, see Nagano et al. (1982), or ∼0.27 eV in a bcc Ti alloy, see Teus et al. (2017). However, with decreasing temperature, this barrier increases diminishing the hydrogen diffusivity. Thus, a temperature should exist below which hydrogen atoms cannot follow dislocations. Along with the hydrogen migration enthalpy, that of hydrogen binding to dislocations, ∼0.28 eV for hydrogen in bcc iron, see Gibala (1967), and ∼0.035 eV in a bcc Ti alloy, Teus et al. (2017), controls the highest temperature of HE manifestation, above which the hydrogen atoms are not bound with dislocations and easily migrate in the crystal lattice.

It can be also noted that, in contrast to aforementioned models of hydrogen embrittlement, where the initial crack exists a priori and only its propagation is analyzed, the electron concept of the HELP phenomenon inherently contains the hydrogen-assisted crack nucleation following from the earlier start of dislocation sources and dislocation emission under smaller applied stresses. The opening of cracks can occur via any operating mechanism, e.g., the crack nucleation in front of a pile-up due to the coalescence of edge dislocations, as suggested by Stroh (1954, 1957, or due to the coalescence of screw dislocations along the intersecting (111) planes in the fcc metals forming the saw-tooth relief of the fracture surface as it was demonstrated in Figure 1 for austenitic steels.

It follows also from the electron approach to HELP phenomenon that, in the absence of clearly developed short-range atomic order in the metallic solid solutions, hydrogen is expected to enhance their plasticity.

3.3 HELP + HEDE and HELP-mediated HEDE models

In the last decade of the current century, the attempts to take into account plastic deformation and find a connection between the HELP and HEDE theories have been renewed. The key ideas of the HELP + HEDE concept were formulated by Djukic et al. (2014, 2015, 2019 and amount to the following statements.

1. Based on relating studies performed by Lee and Unger (1988) and Komarigi et al. (2008), the fundamental statement of the original HEDE model about the decisive role of a normal stress in front of the crack tip remains unchanged. Due to this stress, hydrogen’s concentration increases in the fracture process zone and the crack tip opens atom per atom when the stress becomes higher than a cohesive strength.

   However, the abovementioned studies of hydrogen embrittlement in Fe- and Ni-based amorphous ribbons performed by Nagumo and Takahashi (1976), Ashok et al. (1981), and Slavin and Stoloff (1984) demonstrated that this also occurs in the absence of normal stresses. Moreover, whatever the occurrence or the absence of hydrostatic stress components, a shear instability of the crystal lattice appears under applied mechanical loading resulting in the nucleation or the emission of dislocations preceding development of fracture, see the molecular dynamics simulations along with ab initio electronic calculations for single Fe and Mo nanocrystals performed by Kotrechko et al. (2006, 2015 and their tensile nanotests inside a field-ion microscope by Shpak Anatoliy et al. (2009).

1. Hydrogen-enhanced dislocation mobility combined with localized plasticity is considered only as a possible previous phenomenon preparing necessary conditions for HEDE to be activated. It is substituted by the hydrogen-caused impeded mobility of dislocations, which facilitates HEDE, see, e.g., Djukic et al. (2016).

   The idea of two-fold hydrogen-enhanced/impeded dislocation mobility aroused from the studies performed by Deng and Barnoush (2018) who claimed that hydrogen-caused facilitation of dislocation emission from the crack tip in a single crystalline FeAl intermetallic alloy under applied stresses is replaced by subsequent suppression of their mobility. The same statement was declared by Rogne et al. (2018) based on the studies of the Fe–26Al–0.5Cr alloy. As a confirmation of the hydrogen-impeded dislocation mobility, Djukic et al. (2019) referred also to Delafosse and Magnin (2001) who described a mechanism of stress corrosion cracking as formation of the cracks ahead of a planar dislocation ensemble interacting with dislocations moving on the alternative slip planes.

   In fact, the impeded slip of dislocations occurs because of their blocking by some particles and grain boundaries or by dislocations moving on the intersecting slip planes in fcc alloys forming thereby a sessile dislocation denoted as the Lomer–Cottrell barrier. This phenomenon bears no relation to the inherent hydrogen effect on dislocation mobility. It is observed in any hydrogen-free metallic alloys having a low stacking fault energy or characterized by the short-range atomic ordering and cannot be interpreted as a hydrogen-caused suppression of dislocation mobility.

   Hydrogen decreases stacking fault energy, see, e.g., Pontini and Hermida (1997) for H in austenitic steels, Lu et al. (2001) for H in aluminum. Therefore, it is expected to accelerate formation of Lomer–Cottrell barriers. An indirect confirmation was obtained by Hänninen and Hakkarainen (1979), see Figure 3, and by Ulmer and Altstetter (1991). Both authors observed a saw-tooth relief on the fracture surface of hydrogen-charged austenitic steels, which presumably was formed by dislocation slip on the intersecting slip planes, formation of cracks, and their subsequent integration.

   The analysis of the available experimental data about the hydrogen-dislocation interactions in terms of softening–hardening has been performed by Gavriljuk et al. (2022). Presented below is a part of this analysis.

   Matsui et al. (1979) observed the hydrogen-caused hardening of pure iron at temperatures below 190 K and ascribed this effect to hydrogen pinning of kinks on the screw dislocations. Generally, this effect is expected if the interstitial atoms become immobile at low temperatures and cannot accompany dislocations serving as point obstacles for their slip. It is also intriguing that, performing the synchronized cathodic charging and mechanical testing, the authors observed a sharp decrease in the flow stress down to about 50 % of its original level if the charging current has been switched on. On its subsequent switching off, the flow stress began to gradually increase and recover to roughly the same stress level as before charging. In fact, the authors did not take into account the electroplasticity, i.e., an effect of the electron wind on mobility of dislocations that occurs in pure metals.

   Noteworthy in this relation are two features of conducted experiments: (i) the H-induced softening did not occur if the iron samples contained some impurities even in spite of their preliminary refining in the wet or dry hydrogen and (ii) softening was completely absent in the substitutional iron-based solid solutions even if the latter were extremely diluted.

   Using molecular dynamics, Song and Curtin (2011, 2012 obtained that accumulation of hydrogen atoms around a crack tip suppresses crack-tip dislocation emission and thus eliminates the ability of the material to blunt cracks. At the same time, as shown in the ab initio calculations performed by Jiang and Carter (2004), as well as in the studies of Gerberich et al. (1991) and Song et al. (2010), even at full saturation of hydrogen atoms on the cleavage plane ahead of a crack in α-iron, dislocation emission remains easier.

   According to Kirchheim (2012), the softening–hardening is generally related with solute atoms controlling time τ _g for double kink generation and time τ _m necessary to move the kinks to the ends of a dislocation segment. Segregating to the kinks, solute atoms reduce the energy for kinks formation and, therefore, decrease τ _g. On the condition of τ _m < τ _g, it leads to softening. With increasing contents of solutes, they increase the dragging force on the moving kinks, which increases τ _m and can reverse the above written condition to τ _m > τ _g. For this reason, the hydrogen drag on the kinks dominates over hydrogen enhancement of kink formation and results in the pinning of dislocations and consequent hardening.

   Unfortunately, this approach ignores the nature of solutes as chemical elements, interpreting solute atoms just as the point centers of elastic dilatation in the crystal lattice. Beside this, the Peierls barrier in fcc metals is shallow, kinks are lengthy and play no remarkable role in the plastic deformation. Consequently, mobility of dislocations under applied stress is controlled by their intersections, not by kink formation.

   Xie et al. (2016) prepared a thin single-crystal Al pillar with the diameter of ∼620 nm transparent for TEM observations, used preliminary “cyclic healing” to reduce the number of dislocations to five, subjected this sample to the electron beam irradiation, and analyzed the effects of subsequent mechanical cycling on the position of each dislocation after hydrogen charging and aging. As a result, they found that all five dislocations stood firm despite 85 loading cycles and attributed this phenomenon to a “hydrogen locking of dislocations.”

   An essential objection against this conclusion is related with the use of electron irradiation. Along with vacancies, electron irradiation produces self-interstitial atoms, which migrate to dislocations, grain boundaries, and free surfaces. On reaching dislocations, these atoms block their mobility, which was first detected by Professor Karl Lücke and for many years now demonstrated for visitors at the Max Planck Institute in Aachen, Germany.

1. Above a certain critical hydrogen concentration at the crack tip, the HELP mechanism is replaced by HEDE, which becomes an independent mechanism of hydrogen embrittlement, see Djukic et al. (2016, 2019 with references herein to experimental studies performed by Wang (2009) and Dmytrakh et al. (2015, 2018, as well as the molecular dynamics simulations of hydrogen effect on the lattice defect energies carried out by Matsumoto et al. (2014) and the molecular statics simulations of the effect of hydrogen content on the mobility of edge dislocations in the alpha iron, see Taketomi et al. (2008, 2017.

It is relevant to note that all the quoted experimental data about the critical hydrogen content were obtained using electrochemical hydrogen charging, which is accompanied by severe plastic deformation and consequent cold work hardening, see, e.g., Mogilny et al. (2015, 2020. Plastic deformation is found to be absent in the case of gaseous hydrogenation, see Mogilny et al. (2020). Therefore, it is not surprising that tensile tests of electrochemically charged specimens revealed their plasticity to decrease with an increase in hydrogen content. The plasticity resource of these specimens is already depleted during the electrochemical charging before mechanical tests, which is a reason of the erroneous estimation of critical hydrogen content.

Within the electron approach to HELP phenomenon, the role of the hydrogen-increased concentration of free electrons amounts to the experimentally confirmed softening of the crystal lattice, which compensates for the inherent embrittling effect of hydrogen atoms as interstitial point defects. Of course, sooner or later, this compensation is expected to cease with increasing hydrogen concentration. In these terms, a critical hydrogen content should exist, as it is the case of nitrogen in austenitic steels, where it similar way increases the concentration of free electrons and enhances plasticity and impact toughness up to its critical content, see Gavriljuk and Berns (1999).

Also indicative in this connection is the analysis of hardness and fracture toughness as a function of the distance from the edge of fracture zone in the boiler evaporator tube subjected to electrochemical charging, as performed by Djukic et al. (2014). The authors attributed a zone of the increased hardness and decreased fracture toughness to the realization of the HEDE mechanism, whereas that of low hardness and high fracture toughness was credited to the HELP mechanism. Unfortunately, they did not take into account the uneven hydrogen concentration profile at the electrochemical charging resulting in a different local plastic deformation and corresponding difference in the work hardening.

The same scientific group carried out a similar analysis for the hydrogen-caused embrittlement of a low carbon steel subjected to electrochemical charging, see Wasim et al. (2021). Again, the applied electrochemical hydrogen charging resulting in the local plastic deformation and the accompanying cold work hardening were not taken into account.

The decisive role of the hydrogenation technique causing electrochemical hydrogen hardening and gaseous hydrogen softening was convincingly demonstrated by Zhao et al. (2015) and interpreted by Mogilny et al. (2015, 2020.

It would also not go amiss to mention a model that appeared recently claiming the unification of hydrogen enhanced plasticity and decohesion, see Lin et al. (2022). It was developed within the framework of fracture mechanics describing a metal containing a definite volume fraction of the pores. Empirical equations characterizing their evolution and coalescence as the hydrogen concentration increases were analyzed based on some parameters taken from different experiments. The following features of this analysis are noteworthy:

1. Any part played by dislocations is overlooked, which seems to be strange for a model pretending to modify the HELP theory the essence of which is the effect of hydrogen atoms on dislocation properties;

2. The hydrogen-assisted nucleation of microcracks or their propagation is excluded a priori;

3. Also overlooked are the available experimental data about the dependence of hydrogen embrittlement on the strain rate, temperature effects, etc.;

4. Only the interaction of hydrogen atoms as dilatation centers with the elastic fields of micropores is analyzed, whereas their strong binding to dislocations and grain boundaries, which plays a much greater part, is not taken into account.

Summing up, despite initiating a number of useful experimental studies, the above comments do not allow to estimate the HELP + HEDE model as properly substantiated.

The HELP-mediated HEDE model, recently proposed for intergranular fracture, also includes the HELP phenomenon as a stage in preparation for hydrogen-caused decohesion, see, e.g., Nagao et al. (2012, 2014, 2018, Bertsch et al. (2019), and Nygren et al. (2021).

In its initial version, it is related to the intergranular hydrogen embrittlement of lath martensitic steels and is based on the statistical micro-mechanical model proposed earlier by Novak et al. (2010). These authors studied high-strength martensitic steel AISI 4340 after its quenching and tempering at 200 °C followed by gaseous hydrogen saturation under increasing hydrogen pressure. In their experiments, fracture strength dramatically decreased with increasing hydrogen concentration and the ductile transgranular fracture of hydrogen-free steel was replaced by the brittle intergranular one of hydrogen-doped steel.

As shown by the authors, having accumulated at the carbide/matrix interface, hydrogen atoms themselves did not control cracking because, regardless of its pressure, hydrogen fully, more than 99 %, saturated both the grain boundaries and the carbide interface. Instead, they ascribed the brittle fracture to a stress created by dislocation pile-ups blocked at the carbides located near the grain boundaries, see Figure 11.

Figure 11:

Hydrogen-saturated dislocation pile-up locked at the grain-boundary carbide and responsible for microcrack nucleation and consequent brittle intergranular fracture. Red circles denote hydrogen atoms in the solid solution, green circles – H atoms at the carbide/matrix interface, and blue circles – H atoms at dislocations. Redrawn from Novak et al. (2010), reproduced with permission from Elsevier.

In accordance with the HELP theory, the repulsive stress between dislocations is reduced by the hydrogen atmospheres around dislocations, which increases the number of dislocations in the pile-up, thereby enhancing impingement on the carbide/matrix interface and ultimately resulting in the opening of a crack in the ferrite at its interface with the carbide particle and, consequently, brittle fracture.

It is worth noting that the scheme presented in Figure 11 can be also convincingly interpreted as an illustration of the widespread mechanism for microcrack opening by pile-up dislocations in metals at any obstacle, as it was first proposed by Stroh (1954, 1957.

Under applied stress τ, the stress τ _L at the leading dislocation increases as τ _L = nτ until it reaches the threshold value needed for the opening of a crack due to the coalescence of dislocations under shear stress. Further propagation of the initially nucleated crack can proceed in an autocatalytic way, i.e., breaking the interatomic bonds atom after atom, only if, at the moment of its nucleation, this crack satisfies the Griffith conditions:

where σ _f is the ultimate strength (fracture stress),

E _Y is the Young modulus, γ _s is the surface free energy per unit area, and L _c is the length of an initial surface crack.

In other case, as with the nucleation of a hydrogen-induced crack, its propagation is assisted by dislocations. It was confirmed by TEM studies of the microstructure beneath the fracture surface of a middle-carbon ultra-high strength martensitic steel performed by Nagao et al. (2012). They detected intense slip bands and partial destruction of lath boundaries for both intergranular and “quasi-cleavage” fracture and proposed that, along with normal interstitial lattice sites, hydrogen is redistributed due to the hydrogen-enhanced mobility of dislocations segregating on prior austenite grains and lath boundaries. As a result, along with the work hardening of matrix due to plastic deformation, the cohesive strength of boundaries is reduced leading to the intergranular and quasi-cleavage failure along the prior austenite grains or the lath boundaries.

In subsequent studies, Nagao et al. (2014) found that fracture paths are determined by the orientations of the slip bands. In the case of intergranular fracture, the intersection between the slip bands is inclined toward the prior austenite grain boundaries, whereas in the case of quasi-cleavage fracture, this inclination occurs with respect to the lath boundaries.

It was concluded that hydrogen-enhanced localized plasticity disrupts intersected boundaries, leading to the initiation of a crack and its propagation by interface decohesion under the combined action of macroscopic and local stresses. The intergranular failure occurs when slip systems intersect the prior austenite grain boundaries, whereas “quasi-cleavage” is realized when they intersect the lath boundaries.

The final substantiation of this model was developed by Nagao et al. (2018). Irrespective of the carbide particles occurrence at grain boundaries, the hydrogen-induced intergranular fracture of lath martensitic steel was claimed to be related to the movement of dislocations with their hydrogen atmospheres within the blocks surrounded by the high-angle grain boundaries and their piling up against prior austenitic grains. Quasi-cleavage transgranular failure occurs when these dislocations move within the blocks and are piled up against the lath/block boundaries. The occurrence of nanosized (Ti,Mo)C precipitates acting as hydrogen traps improves resistance to hydrogen embrittlement because they decrease hydrogen segregation at the grain boundaries.

The HELP-mediated HEDE model was supported in studies of the intergranular fracture performed by Robertson group, e.g., in pure nickel (Bertsch et al. 2019; Martin et al. 2012) and α-titanium (Kacher and Robertson 2014). Investigating the hydrogen effect on the dislocation substructure in polycrystalline nickel subjected to tensile tests, Bertsch et al. (2019) found the hydrogen-reduced crystallographic texture along the loading axis resulting in the corresponding decrease of grain elongation. Additionally, it was shown that hydrogen decreases the size of dislocation cells in the grain interior making cell walls thicker and increasing the difference between orientation deviations in neighboring grains adjacent to the grain boundary.

The same features of dislocation substructure were also observed by Nygren et al. (2021) in AISI 316 austenitic stainless steel hydrogen-charged under hydrogen gas pressure and subjected to tensile or fatigue tests.

Analyzing the crystallographic orientation gradient in the neighboring grains as a function of distance from the grain boundary, Bertsch et al. (2019) detected that hydrogen restricts strain communication across the grain boundary and reduces cooperative grain deformation affecting the structure of grain boundaries. With increasing strain, the cell dislocation structure is being intersected by second-generated microbands disrupting the structure of grain boundaries. Finally, hydrogen-caused intergranular fracture was attributed to the combined effect of the following factors: compatibility constraint across grain boundaries, the locking of dislocations in their specific configurations by hydrogen, and the hydrogen weakening of grain boundaries.

These studies are somewhat contradicted by the results obtained by Harris et al. (2018), who compared the intergranular failure of hydrogen-charged nickel subjected to tensile tests at room temperature and at 77 K. They found significantly larger engineering and true strains and a smaller hydrogen-caused decrease in relative elongation and reduction in area at 77 K than at RT. Moreover, along with the facets, the surface of intergranular fracture in H-charged samples tested at 77 K exhibited traсes of ductile fracture as evidence of higher plastic deformation occurring prior to fracture. The authors interpreted these results in terms of a predominant role in the fracture of hydrogen segregated at grain boundaries prior to straining.

To some extent, this conclusion is consistent with the remarkable early experiment reported by Lassila and Birnbaum (1988) who performed the charging of nickel by hydrogen at 1423 K with subsequent quenching in the liquid nitrogen to retain the obtained homogeneous distribution of hydrogen followed by the subsequent tensile tests with the fast and slow strain rates at 208 K, where hydrogen atoms are diffusively mobile. The observed percent of intergranular fracture was negligible if the tests with a high strain rate of 3 × 10⁻² s⁻¹ were initiated after short holding at 208 K, which was insufficient for redistribution of hydrogen between the interior and the grain boundaries. Moreover, the intragranular fracture started only at the hydrogen content of more than 400 at. ppm. With the small strain rate of 3 × 10⁻⁵ s⁻¹, the intergranular fracture started at the hydrogen content smaller than 200 at. ppm and quickly reached 100 %. The even earlier initiation of the intergranular fracture with increasing hydrogen content and the fast increase of its part in the combination with the shear ductile rupture occurred in the case of holding of samples at 208 K prior to straining, which allowed hydrogen atoms to segregate at grain boundaries.

These thoroughly performed experimental studies of intergranular fracture support the HELP-mediated HEDE model. At the same time, two remarks are worth noting.

First, taken from its original theory, the term HEDE is not correct because it suggests crack propagation by breaking interatomic bonds atom-per-atom under existing normal stresses without any involvement of dislocations. In fact, the opening of any crack is preceded by plastic deformation due to the nucleation and sliding of dislocations. Dislocations also take part in crack propagation. Convincing results in this regard were obtained in the studies performed by Kotrechko et al. (2006, 2015, where atomic mechanisms governing the strength of defect-free bcc Fe and Mo single crystals were simulated using molecular dynamics and first-principle calculations. It was shown that both uniaxial and hydrostatic tensions cause local lattice instability. This shear instability results in local lattice reorientation and the formation of dislocations, which leads to a ten-fold decrease in tensile stress. Cracks are nucleated within the shear bands or in their boundaries, not in the homogeneous elastically deformed lattice. Therefore, plastic deformation is necessary for cracking, even in a crystal with predominantly covalent bonds.

Moreover, using the uniaxial tension inside a field-ion microscope, Shpak Anatoliy et al. (2009) performed tensile nanotests of Mo single-crystalline nanorods free of dislocations and observed the plastic mode of failure due to multiple gliding in the ( 11 2 ‾ ) [ 111 ] and ( 112 ) [ 11 1 ‾ ] systems forming thereby a chisel-edge tip, so that the strength constituted only 7.5 % of Young’s modulus.

Second, the HELP-mediated HEDE model of intergranular fracture does not take into account the role of vacancies themselves produced by hydrogen segregated at the grain boundaries prior to straining causing hydrogen transport to grain boundaries by dislocations. As shown using the positron annihilation and thermal desorption spectroscopies by Lawrence et al. (2017) for nickel and by Nagumo and Takai (2019) for steels, free volume within the grain boundaries is generated by hydrogen charging, and this effect is only enhanced by subsequent straining.

The accumulation of hydrogen and vacancies near grain boundaries in α-iron was also demonstrated in the atomistic calculations performed by Momida et al. (2013). The authors performed first-principle studies of tensile tests showing hydrogen-vacancy complexes lowering the strength at grain boundaries. The uniaxial straining of bi-crystalline nickel in presence of hydrogen was also simulated by Ding et al. (2021). The hydrogen-facilitated nucleation and growth of nanovoids at the grain boundaries was shown to cause intergranular fracture in contrast to transgranular one in the absence of hydrogen.

Let us finally characterize merits and shortcomings of the discussed HEDE and HELP theories using the following Table 3.

Summing up, one can state that hydrogen embrittlement is a complicated phenomenon resulting from a number of competing and, at the same time, mutually complementary processes. Processes inherent in the metallic alloys, e.g., short-range atomic ordering or the short-range decomposition of metal solid solutions, both aroused from the interaction between the atoms of constituting elements, interfere with the effects induced by hydrogen, which complicates the correlation between atomic interactions and mechanical properties of hydrogen-charged materials. Among these, the hydrogen effect on the atomic interactions, namely the softening of the crystal lattice and the hydrogen-caused change in the properties of individual dislocations, seems to be dominant.

One can also state that hydrogen in metals is expected to increase their plasticity and toughness due to the increase in the concentration of free electrons provided the plastic deformation is not localized.

4.1 Hydrogen-enhanced plasticity in Ti alloys

4.1.2 Ambient temperatures

Kolachev et al. (1974) were also the first to discover that a favorable hydrogen effect on the plasticity of β-alloy VT15 (Ti–11Cr–7Mo) and transition alloy VT30 (Ti–11Mo–6Zr-4.5Sn) occurs even at ambient temperatures despite increased yield strength.

Charged by higher than 1 mass% of hydrogen, cylindric samples of 10 mm in diameter and 15 mm in length were deformed close to 100 % during upsetting tests, see Figure 12.

Figure 12:

Hydrogen effect on yield strength σ _0.2 and critical upsetting deformation degree ε _cr of quenched alloy VT30 at RT before the appearance of the first crack. Redrawn from Kolachev (1993), reproduced with permission from Springer Nature.

Later, Nosov et al. (1995, 2008 demonstrated the high deformability of β-alloys VT22 (Ti–5Al–5Mo–1Cr–1Fe), VT22I (Ti–3Al–5Mo–1Cr–1Fe), and alloy Ti–10V–2Fe–3Al at the ambient temperature, see Figure 13. The increased allowable deformation degree was attributed by the authors to the hydrogen-caused mechanical stability of the β phase with respect to β→α″ transformation.

Figure 13:

Hydrogen effect on the ultimate plasticity of alloys VT 22I (1) and Ti–10V–2Fe–3Al (2) during cold deformation. Redrawn from Nosov et al. (2008), reproduced with permission from Springer Nature.

These results demonstrated a difference between the high-temperature and low-temperature hydrogen-enhanced plasticity. The former occurs at temperatures of 500–1100 °C depending on the phase composition. It is manifested by the decreased flow stress of metals and the increased maximum allowable degree of deformation.

The latter occurs at ambient temperature or close to that and is characterized by an increased degree of deformation, whereas the flow stress may increase because of the cold work hardening. At the same time, hydrogen increases its intensity, see Figure 14.

Figure 14:

Specific force q of deformation by upsetting as function of strain φ = ln(H ₀/H _i) for alloys (a) Ti–10V–2Fe–3Al and (b) VT22I. Hydrogen content in wt% is presented at the curves. Redrawn from Nosov et al. (2008), Springer.

The strengthening of β-Ti phase by hydrogen was claimed by Froes et al. (2004) based on the data of hydrogen-increased shear modulus obtained in the measurements performed at 960 °C. The authors supposed the hydrogen-caused transformation-induced plasticity, TRIP, to be responsible for such a huge plastic deformation of β-Ti alloys at ambient temperatures.

However, this interpretation is at variance with the available experimental data. For example, Ilyin et al. (1995) observed hydrogen-facilitated β→α″ transformation accompanied by the shape memory effect in commercial alloy VT23 (Ti–6Al–4.6V–1.7Mo–1.2Cr–0.7Fe), whereas Li et al. (2019) studied stress-induced martensitic transformation in the Ti–50.8Ni shape memory alloy. The recovered strain in alloy VT23 did not exceed 3 %, and the total strain of the Ti–Ni alloy including the TRIP effect amounted only to ∼3 %.

Therefore, it is extremely doubtful that the huge hydrogen-induced plasticity at RT, as observed by Ilyin et al. (1995a), could be related with the TRIP effect.

The hydrogen-assisted slip of dislocations, their more intensive multiplication, and the activation of additional slip systems were mentioned as reasons for the low-temperature hydrogen-enhanced plasticity already at the early stage of its studies, see, e.g., Kolachev et al. (1974). It is remarkable that all the above phenomena are exactly what is expected from hydrogen’s effect on the electron structure, which seems to be a more reliable interpretation of hydrogen-enhanced plasticity in titanium alloys.

4.2 Murakami effect in CrNi austenitic steels

Studying the hydrogen effect on fatigue of the gaseous hydrogen charged AISI type 304 and 316L austenitic steels, Murakami et al. (2010) observed the unexpected phenomenon of hydrogen-increased fatigue life. As shown in Figure 15, the hydrogen-caused accelerated growth of the fatigue crack in steel 304 containing 23.9 wt. ppm of hydrogen was replaced by its slowing down with the further increase in hydrogen concentration.

Figure 15:

Effect of hydrogen content on fatigue crack growth. Redrawn from Murakami et al. (2010), reproduced with permission from Springer Nature.

The authors interpreted this result in terms of supposed hydrogen-caused softening/hardening claiming that dislocations are pinned by hydrogen atoms located at the dislocation core within the dilatation stress field. The higher the hydrogen concentration, the stronger is the pinning effect. Once a dislocation is released from pinning by hydrogen at its core, its mobility is increased. At the same time, if the hydrogen content increases, the extension of the plastic zone at a crack tip is blocked by the surrounding material, which has a higher flow stress. This phenomenon retards the fatigue crack growth rate despite the slip enhancement at a crack tip.

It is worth noting in connection with this interpretation that, as analyzed in Section 3, the most part of available data on the hydrogen-induced hardening in iron and austenitic steels were obtained using the electrochemical hydrogen charging, see, e.g., Ulmer and Altstetter (1991), Asano and Otsuka (1976), etc. However, as shown by Mogilny et al. (2015, 2020, electrochemical charging is accompanied by plastic deformation, which causes hardening, whereas the hydrogen-induced softening occurs in the case of gaseous hydrogenation, see Zhao et al. (2015), Mogilny et al. (2020).

A rather different interpretation was proposed by Kirchheim (2007, 2012 based on his defactant theory for the formation and motion of kinks under the effect of mobile solute interstitial atoms. According to Kirchheim (2012), time τ _g for double kink generation and time τ _m needed to move the kinks to the ends of a dislocation segment control dislocation slip. Solute atoms segregated at dislocations decrease τ _g. If τ _m < τ _g, the strain rate increase, i.e., softening occurs. With increasing contents of solutes, they enhance the dragging force on the moving kinks and τ _m increases, which results in τ _m > τ _g. In the case of austenitic steels supersaturated by hydrogen atoms, their drag on the kinks dominates over hydrogen-caused enhancement of kink formation leading to the decreased strain rate, i.e., to the hardening.

However, as mentioned above, see Section 3, the Peierls relief is rather shallow in the fcc crystal lattice of austenitic steels. Moreover, even in the bcc iron, hydrogen softens the Peierls relief, see Wang et al. (2013), so that formation of kinks on dislocations and their movement along the secondary Peierls relief become insubstantial. For example, just for this reason, the Snoek–Köster relaxation interpreted by Seeger (1979) as the formation and motion of paired kinks does not occur in fcc metallic solid solutions including austenitic steels. An exceptional case, see Zielinski et al. (1996), is the hydrogen Snoek–Köster relaxation in nickel having a high stacking fault energy, SFE, of ∼120–130 mJ/m², see Carter and Holms (1977) and, consequently, a high Peierls barrier and narrow dislocations on which the kinks are easily formed.

Because of the shallow Peierls relief, which is a rule for the fcc crystals, mobility of dislocations under applied stress is controlled by their intersections, not by kink formation and motion, see, e.g., Seeger’s (1954, 1955 theory for yield stress in fcc crystals and its experimental verification by Obst and Nyilas (1991), Nyilas et al. (1993), and Gavriljuk et al. (1998) for austenitic steels and by Obst (1998) for Cu as well as for the CuNiMn and AlMgMn alloys.

A more appropriate interpretation of the hydrogen-prolonged fatigue life of austenitic steels can be proposed taking into account a particular nature of plastic deformation during fatigue tests. Margolin et al. (1976) were possibly the first to analyze fatigue crack initiation in compression-tension tests depending on the character of dislocation slip. In their observations, reversed cycling during fatigue tests led to the formation of folds accompanying the wavy slip in Cu and Al, whereas these folds disappeared in the case of Cu–7.5Al alloy characterized by the planar slip mode. The authors supposed that the gliding of dislocations hither and thither on the same slip planes is accompanied by the annihilation of dislocations with opposite signs, which leads to softening.

In fact, localization of plastic deformation with the planar slip of dislocations and formation of parallel slip bands in the Cu–Al alloys is a consequence of the significant deviation in their atomic distribution from the ideal solid solution. For example, Epperson et al. (1978) studied atomic distribution in the bcc phase of Cu–Al alloys with the Al content of 4–15 at.% using three-dimensional X-ray diffuse scattering. The observed absence of the Al–Al nearest neighbor pairs and the prevailing Cu–Al neighborhood were a convincing proof of short-range atomic ordering in these alloys.

As mentioned in Section 3, the dislocation slip band substructure is formed during the plastic deformation of hydrogen-charged austenitic steels where the short-range atomic order, mainly the short-range atomic decomposition, inherently exists and, in the areas of its higher solubility, hydrogen enhances the localization of plastic deformation due to the locally increased mobility of dislocations.

Indicative in this relation is comparison of the fatigue properties of hydrogen-charged and nitrogen-alloyed austenitic steels. Like hydrogen, nitrogen in austenitic steels causes planar slip and localizes plastic deformation, see, e.g., Gavriljuk and Berns (1999) and Gavriljuk et al. (2008). The localization of plastic flow is caused by nitrogen-induced short range atomic ordering, see Gavriljuk (1996, 2000. This similarity in the interatomic bonds and the resulting dislocation substructures makes it reasonable to compare hydrogen and nitrogen effects on fatigue crack rate in austenitic steels.

Like the observations made by Murakami et al. (2010) for hydrogen, Tobler and Reed (1984) have found that nitrogen decreased the fatigue crack propagation rate in the AISI 304 type steel Cr18Ni10 if the nitrogen content was increased from 0.039 to 0.240 wt%. The residual carbon content in several studied heats statistically varied between 0.028 and 0.094 wt% and did not change the effect of nitrogen substantively.

This result was confirmed by Taillard and Foct (1989) and Degallaix et al. (1989) carrying out a thorough analysis of the dislocation substructure in steel AISI 316 alloyed with 0.08 or 0.25 % of nitrogen. Presented in Figure 16 are their fatigue stress data at two levels of strain amplitudes.

Figure 16:

Fatigue stress versus number of cycles for two austenitic steels with nitrogen contents 0.08 (dashed lines) and 0.25 mass% (solid lines) tested at ambient temperature with the strain amplitudes 0.6 and 2(2.5) %. Dislocation substructures formed at different stages of fatigue tests are characterized in rectangles. Modified from Taillard and Foct (1989) and Degallaix et al. (1989).

Nitrogen increases the fatigue life of the austenitic steel and is distinguished by its enhanced softening as the number of cycles increases. At the strain amplitude of 0.6 %, softening is observed in the entire range of cycling, while weak hardening is noticeable at the start during tests on low nitrogen steel. An increase in the strain amplitude leads to the hardening of low nitrogen steel up to its fracture, whereas this occurs only during ∼10 cycles in the high nitrogen steel. A nitrogen-caused decrease in the rate of fatigue crack propagation was also observed at cryogenic temperatures by Vogt et al. (1991) in nitrogen-containing steel 316LN and by Nyilas et al. (1993) in steel Cr25Ni15Mn4 N0.35.

It is relevant to note in this connection that, like hydrogen, see Shanina et al. (1999), nitrogen increases the concentration of free electrons in austenitic steel, see Gavriljuk et al. (1993) and Shanina et al. (1995), which in both cases enhances metallic character of interatomic bonds and thereby decreases the line tension of dislocations.

The observed softening is accompanied by dense planar dislocation arrays, which is just a case of reversible cyclic slip, whereas the hardening of a low nitrogen steel is typical of dislocation cell structures.

The data presented make it possible to conclude that the hydrogen effect against hydrogen embrittlement, as found by Murakami et al., is identical to that caused by nitrogen in austenitic steels. Based on the similarity of hydrogen and nitrogen effects on their electron structure and dislocation properties and taking into account the occurrence of a short range atomic order in both cases, one can conclude that the Murakami effect represents a unique case when a combination of specific tension-compression plastic deformation localized within the dislocation bands because of the short-range atomic order and softening of the crystal lattice by the increased concentration of free electrons assists reversible dislocation slip resulting in the prolonged fatigue life.

It would not go amiss that above analysis did not take into account a local martensitic transformation occurred in the 304 stainless steel ahead of the crack tip, which involves dislocations and also can affect plasticity. This effect should be smaller in the case of steel AISI 316. As also mentioned above, the increased fatigue life occurs in the nitrogen austenitic steels and in the Cu–Al alloys, where strain-induced phase transformations are absent, but the SRO effect exists.

4.3 Hydrogen-induced grain refinement

Density of electron states at the Fermi level is known as a factor controlling thermodynamic stability of phases in metals and their alloys, see, e.g., Pettifor (1970, 1996. At the same time, as discussed in Section 3.2, the increase of the DOS in the Fe-, Ni-, and Ti-based alloys results in the increased concentration of free electrons, which softens the crystal lattice. As shown by Teus and Gavriljuk (2020a), hydrogen increases mobility of grain boundaries in iron like it occurs with dislocations. Therefore, it seems reasonable to analyze a role of the hydrogen-changed thermodynamic stability of phases and mechanical stability of crystal lattice in the successful usage of hydrogen for the grain refinement leading to improvement of mechanical properties.

Particularly important in this case is that hydrogen embrittlement is absent at temperatures of recrystallization because hydrogen atmospheres around the dislocations become diluted and disappear with increasing temperature.

4.3.1 Titanium alloys

Kerr et al. (1980) were the first to propose the temporary introducing of hydrogen in the Ti–Al alloys aiming at the grain refinement, which they denoted as “hydrovac.” The hydrogen-charging of alloy Ti–6Al–4V at temperatures above 800 °C resulted in a single β phase followed by its decomposition at lower temperatures through the eutectoid reaction. Subsequent quenching in water and final annealing for hydrogen degassing made it possible to obtain a fine and nearly equiaxed microstructure.

Related phase transformations were studied by Kerr (1985). For example, the orthorhombic α″ martensite plus the β(H) phase saturated with hydrogen were observed in the Ti–6Al–4V alloy after its hydrogen charging with 0.73 wt%H at 870 °C and subsequent cooling down to 590 °C for the eutectoid transformation. Thereafter, the dehydrogenating annealing was performed accompanied by partial reverse eutectoid transformation. In addition, the partitioning of vanadium and aluminum between the β and α phases occurred during hydrogen degassing stabilizing the former by vanadium and the latter by aluminum.

Such a change in the microstructure points to a combination of phase transformation and recrystallization at lower temperatures in comparison with the hydrogen-free titanium alloys. A significant increase in yield strength from 900 to 1200 MPA in combination with improved relative elongation from 5 to 15 % results from the small size of β particles and the essentially equiaxed α phase.

This favorable hydrogen effect was obtained due to a decrease in the temperature of thermodynamic equilibrium between β and α phases, which occurs at 1155 K in hydrogen-free titanium. As follows from the Ti–H phase diagram, the temperature of β→β+α transformation decreases with an increase in hydrogen concentration. The analysis of hydrogen effect on the thermodynamic stability of the titanium α and β phases in terms of Helmholtz free energy was performed by Teus at hydrogen content of ∼1.8 at.% using harmonic approximation and the small displacement method, see Figure 17.

Figure 17:

Temperature dependence of the Helmholtz free energy for bcc β and hcp α phases in Ti–H system.

The performed simulation demonstrates that hydrogen dissolved in the crystal lattice increases the thermodynamic stability of the bcc titanium lattice and decreases the temperature of α–β phase equilibrium down to 1080 K.

A number of other treatments proposed for the grain refinement of Ti alloys were based on the change in hydrogenation temperature, different hydrogen contents, and varied phase transformation reactions, e.g. Guitar et al. 2009; Ilyin et al. 1995a; Ivasishin et al. 2000; Ivasishin and Moxson 2015; Kolachev et al. 1991a; Schmidt et al. 2014; Senkov et al. 1994; Smickley and Dardi 1985, etc.

4.3.2 Austenitic steels

A combination of cold work and hydrogen charging of unstable austenitic steels was used by Shyvaniuk et al. (2012) for a significant decrease in temperature of the reverse α→γ transformation resulting in an ultrafine-grain structure. A reason for that is the different hydrogen effect on the Helmholtz free energy of the α and γ phases, see Figure 18.

Figure 18:

Temperature dependence of the Helmholtz free energy for a Fe–H system with fcc and bcc crystal lattices.

In comparison with 1183 K in hydrogen-free iron and ∼1000 K in CrNi austenitic steels, hydrogen significantly stabilizes the γ phase relating to α decreasing the phase equilibrium temperature down to nearly 430 K. The obtained result characterizes a general trend in the γ-α thermodynamic equilibrium that is consistent with hydrogen’s effect on the density of electron states at the Fermi level of γ iron. The effect of cold work on the balance between the γ and the α phases in 304 type steel is presented in Figure 19.

Figure 19:

X-ray diffraction patterns of 304 type steel containing, in mass%, 18.06 Cr, 9.09 Ni, 1.05 Mn, and 0.02 C: (a) deformed by 15 % of tension at RT: noncharged and charged with gaseous hydrogen at 543 K for 200 h after tension; (b) deformed by 45 % of tension at RT: noncharged, aged at 573 K in vacuum after tension, charged with gaseous hydrogen at 543 K after tension.

Plastic deformation by 15 % induces the α-phase, whereas subsequent hydrogenation at 543 K for 200 h under the hydrogen gas pressure of 100 MPa substantially removes it, Figure 19a.

The increase of the deformation degree up to 45 % intensified the γ→α transformation so that subsequent annealing in vacuum at 573 K for 12 h is not sufficient to restore the austenitic state. However, the full austenitic structure was obtained by hydrogen charging at 543 K for 200 h under the hydrogen pressure of 100 MPa, Figure 19b.

Along with the remarkably decreased temperature of recrystallization, hydrogenation at these conditions produced uniform grain distribution in the wire of 1 mm in diameter, see Figure 20.

Figure 20:

Grain size distribution in 304 type steel after plastic deformation and subsequent gaseous hydrogenation at 543 K under pressure of 100 MPa.

Therefore, saturation with hydrogen allows a striking decrease in the recrystallization temperature of metastable austenitic steel and a consequent ultrafine grain microstructure. For comparison, as obtained by Herrera et al. (2007), the recrystallization temperature in the prestrained type 304 austenitic steel is by 150 K higher than that of α′-martensite reversion and constitutes about 950 K. Thus, hydrogen treatment decreased the recrystallization temperature by more than 400 K.

This favorable hydrogen effect has its origin in the changed electron structure, namely in the hydrogen-increased density of electron states at the Fermi level causing two remarkable effects: (i) softening of the crystal lattice resulting in the enhanced mobility of grain boundaries and (ii) decrease of thermodynamic stability of the low temperature phase. The latter has been confirmed by the ab initio calculations of free energy presented in this section.