Effect of Hydrogen in Mixed Gases on the Mechanical Properties of Steels—Theoretical Background and Review of Test Results

: This review summarizes the thermodynamics of hydrogen (H 2 ) in mixed gases of nitrogen (N 2 ), methane (CH 4 ) and natural gas, with a special focus on hydrogen fugacity. A compilation and interpretation of literature results for mechanical properties of steels as a function of hydrogen fugacity implies that test results obtained in gas mixtures and in pure hydrogen, both at the same fugacity, are equivalent. However, this needs to be veriﬁed experimentally. Among the test methods reviewed here, fatigue crack growth testing is the most sensitive method to measure hydrogen effects in pipeline steels followed by fracture toughness testing and tensile testing.


Introduction
Significant efforts are ongoing in the European Union and worldwide to defossilize private and industry sectors by reducing the emission of green house gases. In the energy sector, one important goal is to replace natural gas (NG) with hydrogen. This goal shall be reached stepwise by blending natural gas with increasing amounts of hydrogen (H 2 ). Worldwide, significant research activities are dedicated to investigate, whether the existing natural gas storage and transport infrastructure can be used for NG-H 2 blends with up to 30% of hydrogen or even for 100% hydrogen gas, see e.g., [1] for a German case study. The analysis of the material compatibility is one important aspect.
It is well established that the mechanical properties of most metallic alloys including steels deteriorate under the influence of hydrogen. This effect is often referred to as 'hydrogen embrittlement'. It is further known that the deterioration of mechanical properties of steels increases with increasing hydrogen concentration inside the steel, which increases with increasing hydrogen gas pressure, more precisely hydrogen fugacity [2]. The fugacity is often described as the activity of the real gas, i.e., the gas in states that are not well described by the ideal gas law. It has been found that the fugacity of pure hydrogen is different from the fugacity of hydrogen in gas mixtures [3] and that (small) additions of oxygen even mitigate hydrogen absorption into the steel [4,5].
Several publications report the effect of hydrogen in NG-H 2 gas blends upon the mechanical properties of steels, see e.g., [6,7]. In other publications, natural gas is replaced by methane (CH 4 ) [8] or nitrogen (N 2 ) [9] to exclude unwanted secondary effects originating from the complex chemical composition of natural gas. However, in most studies, the degradation of mechanical properties is plotted as a function of the volume fraction of H 2 added to NG at a given total gas pressure. To come to more general conclusions, such studies were reviewed, hydrogen fugacities were calculated, and results were compared to tests performed in pure hydrogen gas at comparable fugacities. It will be shown that the hydrogen fugacity can be used as a single parameter to describe hydrogen effects on steels independent of testing these in a gas blend or in pure hydrogen, and that testing in gas blends is not necessary to assess hydrogen effects on materials used in NG-H 2 infrastructures.

Fugacity of Hydrogen in Gas Mixtures
The state of a real gas is described by the van der Waals equation of state (EOS) which takes into account finite sizes of molecules (co-volume parameter (b) and attractive interactions between molecules (molecular-attraction parameter (a) as follows: The van der Waals EOS as well as other empirical relationships for non-ideal gases with two or more parameters, or virial expansions, are complicated to use for enginering applications because of non-linearities. For applications to hydrogen systems, the Abel-Noble EOS, which is a simplified one-parameter variant of the van der Waals EOS, setting the molecular-interaction parameter a to zero, provides a reasonably good description of hydrogen-gas data with a sufficient accuracy at relevant engineering conditions (T > 223 K and p < 200 MPa) [10].
The Estimation of the amount of hydrogen dissolved in the crystal lattice of a metal from a gas requires the knowledge of the fugacity. For hydrogen as a single-component gas, the Abel-Noble equation of state provides a sufficient prediction of it's real gas behaviour [10]. For a more general approach see e.g., [11].
The estimation of the hydrogen fugacity in gas mixtures of multiple components is presented in [3,12,13]. In the following the relevant equations are concisely summarized. For convenience, the same nomenclature as in [12] is used here. The hydrogen fugacity f HH in a gas mixture of H 2 and another gas can be calculated as [12].
x HH : molar fraction of H 2 , • P: total pressure of the gas mixture, • b: co-volume constant of the gas mixture.
The molar fraction of hydrogen as well as the compressibility factors of H 2 and another gas in a mixture of two gases, (Z HH and Z Gas ) can be calculated as [12]: The co-volume constant of the gas mixture is defined as [13]: Using this set of equations requires both b HH and b Gas for the calculation of f HH in a gas mixture according Equation (2). Within the given temperature and pressure range for most engineering applications, the co-volume constant of hydrogen can be assumed as constant (b HH = 15.84 cm 3 /mol [10]) whereas the co-volume constant of the other gas (b Gas ) can be derived from Equation (4) as a function of pressure using experimentally measured compressibility factors.
It shall be emphasized here that the application of the Abel-Noble EOS is restricted to such gases as helium, neon or hydrogen where the kinetic interaction of the molecules can be neglected [13,14]. This is typically not the case for nitrogen (N 2 ), methane (CH 4 ) or natural gas (NG) [13,14]. However, it will be shown in the following that the error is acceptable using the Abel-Noble EOS to assess the fugacity of hydrogen in N 2 -H 2 and CH 4 -H 2 gas mixtures at relevant engineering conditions, e.g., room temperature and pressures up to 20 MPa.
Experimentally measured compressibility factors of N 2 , CH 4 and NG are shown in Figure 1. The general trends of N 2 , CH 4 and NG are similar. For N 2 , Z drops slightly below unity with increasing pressure, reaches a minimum of about 0.994 at about 6 MPa and then strongly increases at pressures higher than 10 MPa to Z values significantly higher than unity. Since the decrease of Z below unity is very slight, it can fairly be assumed (at least for engineering purposes) that N 2 behaves like an ideal gas up to pressures of 10 MPa at room temperature. For CH 4 (and NG), Z drops significantly below unity with increasing pressure, reaches a minimum of about 0.8 at a pressure of about 16 MPa and then slightly increases with increasing pressure. Z < 1 means that the movement of the molecules in not hindered, i.e., the attractive forces dominate, which is captured by the molecular attraction parameter a in the Van der Waals equation (Equation (1)) and the co-volume parameter b can be neglected. On the other hand, Z > 1 means that repulsive forces between molecules dominate which is captured by the co-volume parameter b and the molecular attraction parameter a can be neglected. The results for N 2 and CH 4 from the different references appear very consistent (Figure 1a,b), while the results for NG (Figure 1c) scatter significantly presumably due to the different compositions of the natural gas qualities investigated in the individual studies. It can be seen that in terms of compressibility, natural gas is better represented by CH 4 than by N 2 because methane is the main constituent of natural gas, typically more than 80 vol%. However, both, the results for N 2 and CH 4 can be fitted by a polynomial function of the total pressure P as follows with the coefficients given in Table 1. Equation (6) and the fit coefficients from Table 1 can now be used to calculate Z Gas for N 2 or CH 4 , respectively. Now, the co-volume constant b Gas can be calculated according to Equation (4). The results are shown in Figure 2 together with the corresponding compressibility factors.
Using the data from Figure 2, the co-volume constant of the respective gas mixture b (N 2 -H 2 or CH 4 -H 2 ) can be calculated according to Equation (5), and finally the fugacity of hydrogen in a gas mixture f HH can be calculated according to Equation (2).
The error of this method can be assessed by comparing calculated compressibility factors of a gas mixture (Z mix ) using Equation (7) with experimentally measured compressibility factors. Figure 1. Experimental compressibility factors of (a) N 2 data from [15][16][17], (b) CH 4 data from [18][19][20][21] and (c) Natural Gas data from [20,[22][23][24][25]. Table 1. Fit coefficients for the calculation of the compressibility factor according to Equation (6) and coefficient of determination (R 2 ) for N 2 and CH 4 according to Figure 1a,b.  Examples for a 75%N 2 -25%H 2 and a 78%CH 4 -22%H 2 gas mixture are shown in Figure 3. It can be seen that the absolute error between calculated and measured compressibility factors is less than 0.03 for the N 2 -H 2 mixture and less than 0.08 for the CH 4 -H 2 mixture at room temperature and the given pressure range. Such errors appear tolerable for engineering applications assessing hydrogen fugacities in mixed gases.  [17] and (b) a 78% CH 4 -22% H 2 gas mixture data from [21] as a function of total pressure P.

Coefficient
As an example, the evolution of f HH as a function of p HH in N 2 -H 2 and CH 4 -H 2 gas mixtures at a total pressure of 20 MPa is shown in Figure 4a. For N 2 -H 2 gas mixtures, f HH ≈ p HH up to hydrogen partial pressures of about 10 MPa and f HH > p HH for higher hydrogen partial pressures with f HH up to about 22 MPa at p HH = 20 MPa. For CH 4 -H 2 gas mixtures, f HH < p HH up to p HH of about 15 MPa. The highest deviation is at p HH = 9 MPa, where f HH is calculated as low as about 7.2 MPa. In Figure 4b, the same data is plotted as a function of the hydrogen fugacity in pure hydrogen, f H2 . For N 2 -H 2 gas mixtures, f HH ≈ f H2 and the deviation appears negligible for engineering applications. For CH 4 -H 2 gas mixtures, f HH < f H2 . The highest deviation is at f H2 = 12 MPa, where f HH is calculated as low as about 9.4 MPa.

Compilation and Interpretation of Literature Results for Mechanical Properties as a Function of Hydrogen Fugacity
In the following, literature results from tests performed in pure hydrogen gas as well as in gas mixtures are plotted as a function of hydrogen fugacity f. The designation "fugacity f " is used for both, hydrogen fugacity in pure H 2 and hydrogen fugacity in gas mixtures. The fugacities were calculated as described in chapter 0.
It is well known that the degradation of mechanical properties of steels tested in a gaseous hydrogen atmosphere increases with increasing hydrogen fugacity following a power law HEI ∼ m f n (8) where HEI means any hydrogen embrittlement index, m is a factor and n is an exponent [2]. 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 reduction of area (RRA = RA H2 /RA air ) of tensile specimens (smooth and notched), the relative notched ultimate tensile strength (UTS H2 /UTS air ), the relative fracture toughness (K H2 /K air ), and the relative crack growth rate (da/dN H2 /da/dN air ) were calculated based on published experimental data. Using such indices, the degree of embrittlement increases as the index decreases except for the crack growth tests where the degree of embrittlement increases as the index increases because crack growth is accelerated in hydrogen compared to air.
In the context of this study, literature results on the effect of pure gaseous hydrogen as well as gas mixtures upon the mechanical properties of API 5L X42, X52, X60, X70 and X80 grades were reviewed. The data discussed in the following focuses on X52, X70 and X80 grades where a comparatively large set of data is available to allow justified conclusions. The compilation of data from various sources revealed a large scatter so that the power law dependency described above is not always obvious. However, clear trends were observed and will be discussed despite the large scatter.

Tensile Tests
Tensile RRA of smooth specimens as a function of hydrogen fugacity for X70 and X80 steels is displayed in Figure 5a. It can be seen as a clear trend that RRA decreases with increasing hydrogen fugacity. A significant amount of results show RRA values around 100% up to a fugacity of about 1.2 MPa (dashed square in Figure 5a) whereas a single result reports a RRA value as low as about 75% at a fugacity as low as about 0.2 MPa [6] (arrow in Figure 5a). Since a large amount of data suggests negligible hydrogen effects at a low fugacity below 1.2 MPa, this review implies that tensile RRA of smooth specimens is a comparably insensitive HEI compared to other indices, as will be shown in the following.

Fracture Toughness Tests
The relative fracture toughness (K) as a function of hydrogen fugacity for X52 and X80 steels is plotted in Figure 5d. To increase the data set, elastic-plastic fracture toughness data obtained from J-integral tests were converted to K [39][40][41]44,45] using K = (JE/(1-ν 2 )) 0.5 . Also here, the relative fracture toughness decreases with increasing fugacity from nearly 100% at 0.6 MPa down to 30% at 10 MPa. Relative fracture toughness values between 45% and 50% are reported for low fugacities between 0.7 MPa and 2.0 MPa (dashed square in Figure 5d). From this review it appears that the sensitivity of fracture toughness results to hydrogen effects in pipeline steels is comparable to notched RRA results (Figure 5b) and significantly higher compared to notched UTS results (Figure 5c). The latter is surprising because a correlation between notched UTS and fracture toughness was reported for stress concentration factors k t greater than 6 [55]. However, the stress concentration factors of the specimens tested in the referenced studies was less than 6, with one exception (kt ≈ 6.3 [38]), which might be one reason for the lack of correlation between the two material properties.

Fatigue Crack Growth Tests
The relative crack growth rate as a function of hydrogen fugacity for X52, X70 and X80 steels is displayed in Figure 5e,f. For grade X52 an increase in crack growth rate by a factor of about 2 at a fugacity of 1.6 MPa was reported [36] (arrow in Figure 5e) whereas for X70/X80 grades an increase in crack growth rate by a factor of about 10 to 15 at a fugacity less than 0.5 MPa (dashed square in Figure 5f) was measured [9,44,53]. The results from grades X70 and X80 clearly indicate that the growth of an initial crack or flaw is greatly accelerated under the influence of gaseous hydrogen even at a hydrogen fugacity well below 1 MPa and it is worth to mention that no result was found which reports no increase in crack growth rate at a fugacity below 1 MPa.

General Comments
It was shown in the previous sections that all reviewed HEI follow the known trends as a function of hydrogen fugacity, i.e., all the HEI decrease with increasing fugacity except the relative crack growth rate which increases with increasing fugacity. Although this study only includes results where the test conditions were similar enough to allow a direct comparison of the results, the scatter of the reviewed data is high. Plausible reasons are the different chemical compositions and microstructures allowed within the respective steel specifications, slightly different test parameters (e.g., strain rate, frequency, R ratio) or test conditions (e.g., purity of the test gas especially oxygen residues) as well as differences in sample preparation. This clearly emphasizes the urgent necessity for the development of international test standards.
Furthermore, the results in gas mixtures (N 2 -H 2 , CH 4 -H 2 , NG-H 2 ) and in pure H 2 overlap, which indicates that hydrogen fugacity is the governing parameter for both, tests in pure hydrogen and tests in gas mixtures. It appears that the influence of the other gas (N 2 , CH 4 or natural gas) upon hydrogen-surface interactions, i.e., transport of hydrogen to the crack tip, physical adsorption, dissociative chemical adsorption and absorption [2] is small and that their effect on the mechanical response is smaller than the scatter of the data. If this assumption is true, then test results obtained in gas mixtures and in pure hydrogen, both at the same fugacity, are equivalent. However, this conclusion must be verified since a study supporting this assumption by a direct comparison of results measured in gas mixtures and in pure hydrogen could not be found.

Conclusions
The aforementioned results allow the following conclusions:

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For materials testing purposes requiring a defined atmosphere, testing in CH 4 -H 2 mixtures is preferred compared to N 2 -H 2 mixtures to simulate the effect of H 2 additions to NG.

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The reviewed results imply no significant difference between tests in pure H 2 gas and tests in gas mixtures at the same hydrogen fugacity. This needs to be verified experimentally.

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Among the test methods reviewed here, fatigue crack growth testing is the most sensitive method to measure hydrogen effects in pipeline steels even at a very low fugacity (less than 0.5 MPa). Fracture toughness testing appears less sensitive followed by tensile testing, especially with smooth specimens. Funding: This research was financially supported by Fraunhofer through project "H 2 D-a hydrogen economy for Germany".
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