Review and Assessment of the Effect of Hydrogen Gas Pressure on the Embrittlement of Steels in Gaseous Hydrogen Environment

: Hydrogen gas pressure is an important test parameter when considering materials for high-pressure hydrogen applications. A large set of data on the effect of hydrogen gas pressure on mechanical properties in gaseous hydrogen experiments was reviewed. The data were analyzed by converting pressures into fugacities ( f ) and by ﬁtting the data using an f | n | power law. For 95% of the data sets, | n | was smaller than 0.37, which was discussed in the context of (i) rate-limiting steps in the hydrogen reaction chain and (ii) statistical aspects. This analysis might contribute to deﬁning the appropriate test fugacities (pressures) to qualify materials for gaseous hydrogen applications. as the coefﬁcient of determination ( R 2 ), are summarized in Table 1. All experimental data were ﬁtted using Equation (2) with a reasonably high R 2 value greater than approximately 0.6. For most of the data, the R 2 value was greater than 0.8. The analysis of the absolute value of the ﬁt exponent reveals a range of | n | between approximately 0.05 and 0.3. of HY-100 and the relative da/dN for fugacities higher than 100 MPa might be explained by approaching the transition to unstable crack growth at such high fugacities. For the cyclic data sets, the analysis of the absolute value of the ﬁt exponent revealed a range of | n | between approximately 0.08 and 0.4. (Table Based on this analysis, the | n | values for cyclic tests and quasi-static tests are in the same range (Table


Introduction
Mobility based on hydrogen-powered vehicles such as fuel cell vehicles is a promising way to reduce greenhouse emissions. For high market penetration, the prognosis is that the costs of a hydrogen infrastructure are significantly lower compared to a battery-charging infrastructure [1]. However, there are special issues associated with the realization of a hydrogen infrastructure. One issue is the susceptibility of most structural materials, especially steels, to hydrogen embrittlement. Despite this issue, the overall goal is to realize safe and affordable infrastructure and mobility.
For automotives as well as for many infrastructure applications, the design must be safe, affordable and lightweight. The qualification of materials for use in hydrogen applications is specified in relevant standards. It is generally accepted that a material's qualification for gaseous hydrogen applications should be performed under conditions reflecting the final use of the material, i.e., in gaseous hydrogen atmospheres. Material testing in gaseous hydrogen atmospheres requires very specialized equipment [2,3] as well as strong safety protocols. Altogether, this results in high technological efforts, reflected by the costs being 15 to 150 times more expensive compared to tests in ambient air, depending on the test method (tensile test, crack growth test, etc.) [4]. Generating and maintaining a high hydrogen gas pressure throughout the test duration remains a technical challenge, especially at sub-ambient temperatures. The primary motivation of this study was to review the experimental data investigating the influence of external gas pressure on the degree of hydrogen effects in materials. The data were analyzed to quantify the effect of high hydrogen gas pressures of up to 100 MPa on the mechanical properties of steels and to propose a rationale for the definition of test pressures for high-pressure hydrogen applications.

Experimental and Analytical Details
This study reviews the experimental results of the influence of external high-pressure hydrogen on the various mechanical properties of steels. This study only reviews the 1.
Transport of hydrogen to the crack tip, proportional to p; 2.
Transport of hydrogen to regions of tensile stress, not dependent on p; 6.
Hydrogen-material interactions, not dependent on p.
At high pressures (and low temperatures), the behavior of a gas deviates from that of an ideal gas. The appropriate thermodynamic parameter is fugacity (f ), which is correlated to the pressure according to f = pe pb RT (1) where b = the constant, R = the universal gas constant and T = the temperature [9]. The correlation between pressure and fugacity is shown in Figure 1a. At room temperature, f ≈ p for pressures lower than 1 MPa. For higher pressures, the non-ideal gas behavior must be considered, especially in the power laws of rate-limiting Steps 3 and 4. Using Sievert s law as an example, Figure 1b shows the hydrogen concentration as a function of hydrogen gas pressure, as well as a function of hydrogen fugacity calculated using Equation (1). For a pressure range up to 100 MPa, the fugacity can also be fitted by a power law, and p 0.5 translates to f 0.46 with a very high accuracy of R 2 = 0.9965.

Experimental and Analytical Details
This study reviews the experimental results of the influence of external high-pressure hydrogen on the various mechanical properties of steels. This study only reviews the results obtained in gaseous hydrogen environments at room temperature, with a focus on hydrogen gas pressures of up to at least 70 MPa (Table 1). Such experiments were typically performed with apparatuses similar to those described in [2,3]. Studies investigating the influence of hydrogen gas pressure at temperatures other than room temperature were not found in the existing literature. Only results obtained by the hydrogen pre-charging of steels (gaseous or electrochemical) simulating external high hydrogen gas pressures were used to interpret the results.
Since the effect of hydrogen on the mechanical properties of steels typically increases with increasing hydrogen gas pressure (p), resulting in increased hydrogen concentration (c) [5][6][7], the experimental data must be fitted using an equation reflecting the rate-limiting steps in environmental hydrogen experiments. Such rate-limiting steps are [8]: 1. Transport of hydrogen to the crack tip, proportional to p; 2. Physical adsorption, proportional to p; 3. Dissociative chemical adsorption, proportional to p 0.5 ; 4. Hydrogen absorption, Sievert's law, proportional to p 0.5 ; 5. Transport of hydrogen to regions of tensile stress, not dependent on p; 6. Hydrogen-material interactions, not dependent on p.
At high pressures (and low temperatures), the behavior of a gas deviates from that of an ideal gas. The appropriate thermodynamic parameter is fugacity (f), which is correlated to the pressure according to = (1) where b = the constant, R = the universal gas constant and T = the temperature [9]. The correlation between pressure and fugacity is shown in Figure 1a. At room temperature, f ≈ p for pressures lower than 1 MPa. For higher pressures, the non-ideal gas behavior must be considered, especially in the power laws of rate-limiting Steps 3 and 4. Using Sievert´s law as an example, Figure 1b shows the hydrogen concentration as a function of hydrogen gas pressure, as well as a function of hydrogen fugacity calculated using Equation (1). For a pressure range up to 100 MPa, the fugacity can also be fitted by a power law, and p 0.5 translates to f 0.46 with a very high accuracy of R 2 = 0.9965.  In the following, the data were analyzed in terms of fugacity instead of pressure. Based on this analysis, the experimental data were fitted using the following equation: HEI ∼ m f n (2) where HEI = any hydrogen embrittlement index, m = the factor and n = the exponent. Typical hydrogen embrittlement indices use the ratio of the mechanical property measured in H 2 and in air, in percent. In this review, the relative fracture toughness (K H2 /K air ), relative crack growth rate (da/dN H2 /da/dN air ), relative reduction of area (RRA = RA H2 /RA air ) of the tensile specimens and the relative number of cycles to the failure (N f_H2 /N f_air ) of fatigue life tests were calculated based on the published experimental data. In most references, the mechanical property in the control atmosphere (in most cases, air) was not measured as a function of pressure. In other words, the value measured in ambient air was used to calculate the embrittlement index for all hydrogen fugacities. Using such indices, the degree of embrittlement increases as the index decreases, except for the crack growth tests, because crack growth is accelerated in hydrogen compared to air. The experimental data were fitted using the method of least squares. The most important experimental details of the results reviewed here are summarized in Table 1, including the fit exponent (n) from Equation (2), as well as the coefficient of determination (R 2 ). Further details can be found in the respective references. Figure 2 shows the quasi-static properties, i.e., the relative reduction of area (RRA) of the tensile specimens for heat-treatable steels (Figure 2a,b), carbon steels ( Figure 2c) and austenitic stainless steels (Figure 2d,e), as well as the relative fracture toughness (relative K) of heat-treatable and low alloyed steels (Figure 2f,g) as a function of hydrogen fugacity. Microstructures, tensile properties in air, fit parameters according to Equation (2), as well as the coefficient of determination (R 2 ), are summarized in Table 1. All experimental data were fitted using Equation (2) with a reasonably high R 2 value greater than approximately 0.6. For most of the data, the R 2 value was greater than 0.8. The analysis of the absolute value of the fit exponent reveals a range of |n| between approximately 0.05 and 0.3.

Results
In the following, the data were analyzed in terms of fugacity instead of pressure Based on this analysis, the experimental data were fitted using the following equation: where HEI = any hydrogen embrittlement index, m = the factor and n = the exponen Typical hydrogen embrittlement indices use the ratio of the mechanical propert measured in H2 and in air, in percent. In this review, the relative fracture toughnes (KH2/Kair), relative crack growth rate (da/dNH2/da/dNair), relative reduction of area (RRA RAH2/RAair) of the tensile specimens and the relative number of cycles to the failur (Nf_H2/Nf_air) of fatigue life tests were calculated based on the published experimental data In most references, the mechanical property in the control atmosphere (in most cases, air was not measured as a function of pressure. In other words, the value measured i ambient air was used to calculate the embrittlement index for all hydrogen fugacities Using such indices, the degree of embrittlement increases as the index decreases, excep for the crack growth tests, because crack growth is accelerated in hydrogen compared t air. The experimental data were fitted using the method of least squares. The mos important experimental details of the results reviewed here are summarized in Error Reference source not found., including the fit exponent (n) from Error! Reference sourc not found.), as well as the coefficient of determination (R 2 ). Further details can be found in the respective references. Figure 2 shows the quasi-static properties, i.e., the relative reduction of area (RRA) o the tensile specimens for heat-treatable steels (Figure 2a,b), carbon steels ( Figure 2c) and austenitic stainless steels (Figure 2d,e), as well as the relative fracture toughness (relativ K) of heat-treatable and low alloyed steels (Figure 2f,g) as a function of hydrogen fugacity Microstructures, tensile properties in air, fit parameters according to Equation (2), as we as the coefficient of determination (R 2 ), are summarized in Table 1. All experimental dat were fitted using Equation (2) with a reasonably high R 2 value greater than approximatel 0.6. For most of the data, the R 2 value was greater than 0.8. The analysis of the absolut value of the fit exponent reveals a range of | | between approximately 0.05 and 0.3.   Figure 2. Results of the quasi-static tensile and fracture toughness tests as a function of hydrogen fugacity. Relative reduction of area (RRA) in the tensile tests for (a,b) heat-treatable steels, (c) carbon steels, (d,e) austenitic stainless steels. Relative fracture toughness of (f) heat-treatable steels, (g) low alloyed pipeline steels. References, test details and fit parameters are given in Table 1. Figure 3 summarizes the cyclic properties as a function of hydrogen fugacity, i.e., the relative crack growth rates (relative da/dN) for carbon steels (Figure 3a), heat-treatable steels ( Figure 3b) and pure iron (Figure 3c), as well as the relative number of cycles to the failure of heat-treatable steels (Figure 3d). It should be noted here that the trend for the Hydrogen fugacity [MPa] Low alloyed steels X60HIC X70/X80 Figure 2. Results of the quasi-static tensile and fracture toughness tests as a function of hydrogen fugacity. Relative reduction of area (RRA) in the tensile tests for (a,b) heat-treatable steels, (c) carbon steels, (d,e) austenitic stainless steels. Relative fracture toughness of (f) heat-treatable steels, (g) low alloyed pipeline steels. References, test details and fit parameters are given in Table 1. Figure 3 summarizes the cyclic properties as a function of hydrogen fugacity, i.e., the relative crack growth rates (relative da/dN) for carbon steels (Figure 3a), heat-treatable steels ( Figure 3b) and pure iron (Figure 3c), as well as the relative number of cycles to the failure of heat-treatable steels ( Figure 3d). It should be noted here that the trend for the X80 pipeline steel was extrapolated (Figure 3d). Extrapolation of trends is generally associated with a high risk. However, the relative N f at a fugacity of 8 MPa was already at a very low value of 0.1 and a significant further reduction in N f with increasing fugacity was not expected. This allowed a meaningful extrapolation of the trend for this specific data set. Cyclic data systematically studying the influence of pressure for austenitic stainless steels were not found in the existing literature, but results in [10] suggest a negligible influence between 10 and 103 MPa. All data in Figure 3 were fitted using Equation (2) with a reasonably high R 2 value greater than 0.55. For most of the data, the R 2 value was greater than 0.9. The two different results for carbon steel SM490B were remarkable and even surprising (Figure 3a). Although the reported mechanical properties of the steels were very similar and the test conditions were identical (Table 1), significantly different crack growth rates were reported. A reason for this discrepancy could not be identified based on the available information in the respective references. Most relative da/dN values were calculated at ∆K ≈ 25 MPa m 0.5 . For steel HY-100, the data were acquired at ∆K = 55 MPa m 0.5 (Figure 3b). Quasi-static fracture toughness values between 30 and 80 MPa m 0.5 measured in high-pressure hydrogen were reported in [11] for steels with similar tensile properties. In other words, the cyclic stress intensity range of ∆K = 55 MPa m 0.5 might be close to the fracture toughness of HY-100 and the increasing relative da/dN values for fugacities higher than 100 MPa might be explained by approaching the transition region to unstable crack growth at such high fugacities. For the cyclic data sets, the analysis of the absolute value of the fit exponent revealed a range of |n| between approximately 0.08 and 0.4. (Table 1). Based on this analysis, the |n| values for cyclic tests and quasi-static tests are in the same range (Table 1).

Results
was not expected. This allowed a meaningful extrapolation of the trend fo data set. Cyclic data systematically studying the influence of pressure stainless steels were not found in the existing literature, but results in [ negligible influence between 10 and 103 MPa. All data in Figure 3 wer Equation (2) with a reasonably high R 2 value greater than 0.55. For most o R 2 value was greater than 0.9. The two different results for carbon steel remarkable and even surprising (Figure 3a). Although the reported mechan of the steels were very similar and the test conditions were identical (Table 1 different crack growth rates were reported. A reason for this discrepancy identified based on the available information in the respective references. da/dN values were calculated at ΔK ≈ 25 MPa m 0.5 . For steel HY-100, t acquired at ΔK = 55 MPa m 0.5 (Figure 3b). Quasi-static fracture toughness va 30 and 80 MPa m 0.5 measured in high-pressure hydrogen were reported in with similar tensile properties. In other words, the cyclic stress intensity ran MPa m 0.5 might be close to the fracture toughness of HY-100 and the incre da/dN values for fugacities higher than 100 MPa might be explained by ap transition region to unstable crack growth at such high fugacities. For the cy the analysis of the absolute value of the fit exponent revealed a range o approximately 0.08 and 0.4. (Table 1). Based on this analysis, the | | values and quasi-static tests are in the same range (Table 1).    Table 1. Table 1. Steel designations, similar grades for other regions and mechanical properties of the steels reviewed in this study. Normal letters refer to data explicitly given in the respective reference. (*) refers to data which were estimated from graphs or heat treatment conditions given in the respective references. F = ferrite, P = pearlite, TM = tempered martensite, B = bainite, AF = acicular ferrite. N f = number of cycles to failure in Wöhler-type fatigue life tests, K = fracture toughness, da/dN = crack growth rate, na = not annotated.

Ref.
Steel

Discussion
As mentioned previously, the experimental data were fitted using Equation (2). For |n| = 0.46, all rate-limiting steps ( Figure 4) were undistorted. However, the analysis performed in this study shows that for a wide variety of microstructures, strength levels and test methods (Table 1), the influence of hydrogen fugacity upon the mechanical properties of steels does not follow an f |0.46| law.

Discussion
As mentioned previously, the experimental data were fitted using Eq | | = 0.46, all rate-limiting steps ( Figure 4) were undistorted. However performed in this study shows that for a wide variety of microstructures, and test methods (Table 1), the influence of hydrogen fugacity upon th properties of steels does not follow an | . | law. The first part of the discussion focuses on the possible rate-limitin hydrogen reaction chain (Figure 4). It is known that for metals loaded in a environment, hydrogen-assisted crack initiation typically starts at the gas-m Upon further loading, this crack propagates into the material until a fina fails by overload fracture. In other words, special attention must be paid rate-limiting steps at the gas-metal interface.
As outlined in [8], the collision rate of gas molecules with a metal sur proportional to the gas pressure, and a sticking coefficient of approxim assumed for pure metal surfaces. Under such conditions, around one mo adsorbs within one second at a pressure of 10 −10 MPa hydrogen partial pres estimation, it appears very unlikely that Steps 1 and 2 (the transport of hy crack tip and physical adsorption) are rate-controlling under the test condit in this study with fugacities up to approximately 250 MPa.
The role of dissociative chemical adsorption was discussed in detail shown that on Fe and Ni single-crystal surfaces, the coverage of dissociativ at hydrogen gas pressures in the order of 10 −1 MPa. Whether this is also t distorted poly-crystals along a crack surface has not been investigated so far when considering fugacities up to approximately 250 MPa, it appears dissociative chemical adsorption is rate-limiting under the test condition this study.
The role of hydrogen absorption can be assessed by comparing test re in gaseous hydrogen atmospheres with those of hydrogen pre-charge Hydrogen pre-charging of materials is typically performed under charging ensure a homogeneously saturated microstructure, and it appears that modified Sievert's law accurately predicts the hydrogen concentration stainless steels pre-charged at high fugacities (Figure 5a). This method elim to 4 from the reaction chain ( Figure 4). However, the analysis of data The first part of the discussion focuses on the possible rate-limiting steps in the hydrogen reaction chain (Figure 4). It is known that for metals loaded in a hydrogen gas environment, hydrogen-assisted crack initiation typically starts at the gas-metal interface. Upon further loading, this crack propagates into the material until a final cross-section fails by overload fracture. In other words, special attention must be paid to the possible rate-limiting steps at the gas-metal interface.
As outlined in [8], the collision rate of gas molecules with a metal surface is linearly proportional to the gas pressure, and a sticking coefficient of approximately 1 can be assumed for pure metal surfaces. Under such conditions, around one monolayer of H 2 adsorbs within one second at a pressure of 10 −10 MPa hydrogen partial pressure. With this estimation, it appears very unlikely that Steps 1 and 2 (the transport of hydrogen to the crack tip and physical adsorption) are rate-controlling under the test conditions discussed in this study with fugacities up to approximately 250 MPa.
The role of dissociative chemical adsorption was discussed in detail in [49]. It was shown that on Fe and Ni single-crystal surfaces, the coverage of dissociative sites is 100% at hydrogen gas pressures in the order of 10 −1 MPa. Whether this is also true for highly distorted poly-crystals along a crack surface has not been investigated so far [8]. However, when considering fugacities up to approximately 250 MPa, it appears unlikely that dissociative chemical adsorption is rate-limiting under the test conditions discussed in this study.
The role of hydrogen absorption can be assessed by comparing test results obtained in gaseous hydrogen atmospheres with those of hydrogen pre-charged specimens. Hydrogen pre-charging of materials is typically performed under charging conditions to ensure a homogeneously saturated microstructure, and it appears that the fugacity-modified Sievert's law accurately predicts the hydrogen concentration in austenitic stainless steels pre-charged at high fugacities (Figure 5a). This method eliminates Steps 1 to 4 from the reaction chain ( Figure 4). However, the analysis of data obtained with hydrogen precharged materials (Figure 5b) reveals |n| values in the same range as obtained with tests in gaseous hydrogen atmospheres, being significantly lower than 0.46. Since this trend does not change after eliminating Step 4 from the reaction chain, it is unlikely that hydrogen absorption is a primary rate-limiting step when testing in gaseous hydrogen atmospheres.  [50,51], (b) the RRA of 304L austenitic stainless steel [5] and the relative fracture stress (RFS) of AISI 4135 martensitic high-strength steel [7] pre-charged with hydrogen as a function of hydrogen concentration.
Although not fugacity-dependent rather than microstructure-dependent, the transport of hydrogen to regions of tensile stress, i.e., the crack tip, can also be rate limiting. Hydrogen transport over distances larger than a few grain diameters is controlled by bulk Fickian diffusion, characterized by the diffusivity D. The diffusivities at room temperature are in the order of 10 −15 to 10 −16 m 2 /s for face cubic centered (fcc austenitic stainless steels [9] and 10 −8 m 2 /s to 10 −11 m 2 /s for body cubic centered (bcc) steels depending on the microstructure [52,53]. Although the diffusivities of bcc steels and austenitic steels differ by several orders of magnitude, a significant difference in thei mechanical response as a function of fugacity could not be identified (Figure 2). In othe words, if D were a primary rate-controlling parameter (at temperatures around room temperature), the fucacity dependence of the HEI data of bcc and fcc austenitic steels should be clearly different, which is not the case. Therefore, it appears unlikely tha hydrogen bulk diffusivity is a primary rate-limiting parameter when testing in a gaseous hydrogen atmosphere.
If Steps 1 to 5 of the hydrogen reaction chain are not rate-limiting, then the mechanisms involved in the hydrogen-material interactions (Step 6) must control the hydrogen embrittlement effects. The length scale is in the order of the plastic zone in fron of a flaw or crack tip, typically around a few 10 to a few 100 µm. Although the size of this zone comprises several grain diameters, the mechanisms are dominated by the so-called strain rate factor of the hydrogen transport equation, which is not a function of D [54][55][56] There is experimental evidence that hydrogen influences dislocation motion and it can fairly be assumed that this effect increases with increasing local hydrogen concentration around the dislocation core. In this case, the interaction of hydrogen with dislocations plays a predominant role [8,57,58]. Unfortunately, currently, such mechanisms are no understood at the level of detail to quantify such effects. However, modern simulation tools may provide a framework to study such effects, since a model based on hydrogen accumulation and transport around a micro-crack using embedded atom methods and density functional theory calculations showed promising results [59].
The second part of the discussion focuses on the selection of material test fugacities (pressures) for high-pressure hydrogen applications. Figure 6a shows a histogram of the fit exponents (| |) from Table 1, which suggests an asymmetric distribution. A statistica analysis revealed that these experimental data were well represented by a Weibul  [50,51], (b) the RRA of 304L austenitic stainless steel [5] and the relative fracture stress (RFS) of AISI 4135 martensitic high-strength steel [7] pre-charged with hydrogen as a function of hydrogen concentration.
Although not fugacity-dependent rather than microstructure-dependent, the transport of hydrogen to regions of tensile stress, i.e., the crack tip, can also be rate-limiting. Hydrogen transport over distances larger than a few grain diameters is controlled by bulk Fickian diffusion, characterized by the diffusivity D. The diffusivities at room temperature are in the order of 10 −15 to 10 −16 m 2 /s for face cubic centered (fcc) austenitic stainless steels [9] and 10 −8 m 2 /s to 10 −11 m 2 /s for body cubic centered (bcc) steels depending on the microstructure [52,53]. Although the diffusivities of bcc steels and austenitic steels differ by several orders of magnitude, a significant difference in their mechanical response as a function of fugacity could not be identified ( Figure 2). In other words, if D were a primary rate-controlling parameter (at temperatures around room temperature), the fucacity dependence of the HEI data of bcc and fcc austenitic steels should be clearly different, which is not the case. Therefore, it appears unlikely that hydrogen bulk diffusivity is a primary rate-limiting parameter when testing in a gaseous hydrogen atmosphere.
If Steps 1 to 5 of the hydrogen reaction chain are not rate-limiting, then the mechanisms involved in the hydrogen-material interactions (Step 6) must control the hydrogen embrittlement effects. The length scale is in the order of the plastic zone in front of a flaw or crack tip, typically around a few 10 to a few 100 µm. Although the size of this zone comprises several grain diameters, the mechanisms are dominated by the so-called strain rate factor of the hydrogen transport equation, which is not a function of D [54][55][56]. There is experimental evidence that hydrogen influences dislocation motion and it can fairly be assumed that this effect increases with increasing local hydrogen concentration around the dislocation core. In this case, the interaction of hydrogen with dislocations plays a predominant role [8,57,58]. Unfortunately, currently, such mechanisms are not understood at the level of detail to quantify such effects. However, modern simulation tools may provide a framework to study such effects, since a model based on hydrogen accumulation and transport around a micro-crack using embedded atom methods and density functional theory calculations showed promising results [59].
The second part of the discussion focuses on the selection of material test fugacities (pressures) for high-pressure hydrogen applications. Figure 6a shows a histogram of the fit exponents (|n|) from Table 1, which suggests an asymmetric distribution. A statistical analysis revealed that these experimental data were well represented by a Weibull distribution. This appears reasonable because Weibull distributions are often found in statistics where values are bound to natural limits-here, 0 ≤ |n| ≤ 0.5. The corresponding Weibull curves are shown in Figure 6b with an expected |n| value of approximately 0.12 and 95% of the |n| values are lower than 0.37.  The following discussion focuses on the two characteristic | | values, i.e., | | = 0.12 and | | = 0.37. To discuss the effect of these results on the definition of hydrogen test fugacities (pressures), two engineering applications were selected as use cases. The typical test pressure for automotive hydrogen tanks is 87.5 MPa (f 1 = 155 MPa) and the typical operating pressure of gas pipelines is 10 MPa (f2 = 11 MPa). These nominal fugacities were used to calculate severity factors as using | | = 0.12 and | | = 0.37 ( Figure 7). SF indicates how much less severe a test at f is compared to the reference fugacities f1 and f2, respectively. For example, for f1 = 155 MPa and | | = 0.12, the severity factor of SF = 0.94 indicates that a fugacity of approximately 93 MPa is less severe by a factor of 0.94 compared to a fugacity of 155 MPa (Figure 7).   The following discussion focuses on the two characteristic |n| values, i.e., |n| = 0.12 and |n| = 0.37. To discuss the effect of these results on the definition of hydrogen test fugacities (pressures), two engineering applications were selected as use cases. The typical test pressure for automotive hydrogen tanks is 87.5 MPa (f 1 = 155 MPa) and the typical operating pressure of gas pipelines is 10 MPa (f 2 = 11 MPa). These nominal fugacities were used to calculate severity factors as using |n| = 0.12 and |n| = 0.37 ( Figure 7). SF indicates how much less severe a test at f is compared to the reference fugacities f 1 and f 2 , respectively. For example, for f 1 = 155 MPa and |n| = 0.12, the severity factor of SF = 0.94 indicates that a fugacity of approximately 93 MPa is less severe by a factor of 0.94 compared to a fugacity of 155 MPa (Figure 7). The severity factor of the fugacity can then be compared with the inherent variation in the measured mechanical property. Repeatability and reproducibility studies on high-pressure gaseous hydrogen's effects on the tensile properties of various structural materials [60,61] revealed that when only considering the scatter of quasi-static tensile test results in a control atmosphere, the RRA value must be lower than 0.89 to 0.99 (89% to 99%), depending on the material, in order to account for this reduction in hydrogen effects with a 95% confidence level ( Table 2). The average value of 0.94 is represented by the solid horizontal line in Figure 7. Using again f 1 = 155 MPa and |n| = 0.12 as an example, the severity factor of SF = 0.94 indicates that a fugacity of approximately 93 MPa is less severe by a factor of 0.94 compared to a fugacity of 155 MPa. However, the measured hydrogen effects lie within the scatter of the results in the control atmosphere and, thus, are not statistically relevant with a 95% confidence level. In other words, for materials following an f 0.12 law, any hydrogen effects measured between 93 and 155 MPa are not statistically relevant with a 95% confidence level. The lower bound fugacities for f 2 = 11 MPa and |n| = 0.37 are given in Table 3. This analysis may provide a data-based rationale for defining appropriate test fugacities (pressures) for high-pressure hydrogen applications. using | | = 0.12 and | | = 0.37 (Figure 7). SF indicates how much less severe a test at compared to the reference fugacities f1 and f2, respectively. For example, for f1 = 155 M and | | = 0.12, the severity factor of SF = 0.94 indicates that a fugacity of approximatel MPa is less severe by a factor of 0.94 compared to a fugacity of 155 MPa (Figure 7).

Summary
The findings of this review can be summarized as follows: • The relative reduction in mechanical properties in gaseous hydrogen experiments follows an f |n| power law (f = fugacity).

•
The exponent |n| was found to be smaller than 0.4. Since theoretical assumptions predict n = 0.46 for a fully undistorted hydrogen reaction chain, the reviewed data are interpreted in a way that hydrogen-dislocation interactions are the rate-limiting step controlling hydrogen's effects in steels.

•
A statistical analysis of the reviewed data revealed that 95% of the |n| values are lower than 0.37.

•
This analysis might be used to define appropriate test fugacities (pressures) to qualify materials for high-pressure gaseous hydrogen applications.