Investigation Of The Thermodynamics Of Hydrogen Interactions In Steel

Introduction

Steel often interacts with hydrogen in a variety of ways, especially because steel is used typically in structural components. Today these applications may vary from bridges to the transportation of natural gas, making the knowledge of this interaction useful [1]. Due to its high chemical reactivity, hydrogen can diffuse into the surface of steel and then appear ionically or molecularly in its lattice. Often, the effect of hydrogen on metals can be complex or varied, as it is affected by several thermodynamic phenomena. Generally, it results in degradation of steel’s structural integrity causing several problems such as embrittlement and hydrogen-assisted fracture.

This paper will investigate the thermodynamic principles and phenomena of hydrogen in steel, and the thermodynamic principles of solubility, fugacity, effects of stress, and trapping. Then these principles will be applied to the hydrogen-steel system. Next, historic cases of failure caused by hydrogen degradation will be discussed, with mentions of what has been learned from these situations. Then ways that engineers can solve these problems will be mentioned.

Theory and Background

To understand the thermodynamic phenomena that are experienced when hydrogen interacts with steel, knowledge of solubility of hydrogen into steel, fugacity of gaseous hydrogen, the effects of stress on the lattice of steel, and trapping of hydrogen in steel is necessary.

Solubility is a chemical property that describes the ability of a solute, an added minor component, to dissolve into a solvent, which can be a substance of varying phases, but typically a solid, gas, or supercritical fluid. There are two ways to define solubility, being kinetic and thermodynamic, but for the focus of this paper, we will focus on the latter. Thermodynamic solubility focuses on equilibria and phase stability. Equilibria vary with specific phases of materials, specifically with their thermodynamic stability. The goal of the equilibria is to obtain the lowest possible energy to gain stability. The more stable the material, the more likely that it will form when equilibrium is reached [1]. However, kinetic factors may alter this effect, allowing the unfavorable material to form, typically a metastable state, where Gibb’s free energy is at a local minimum, but not an ultimate minimum as it would be at stable. Gibb’s free energy is a measurement of the potential to calculate work that can be performed. Thermodynamic solubility, dependent on equilibria, can determine and predict which phases and amounts of materials will occur during a chemical reaction or mixture.

n most structural metals, such as steel, the equilibrium is reached and the energy is minimized when there is a low concentration of hydrogen in the metal lattice. The standard state of this equilibrium is where it is stated aH is equal to co. Co is the number of moles of hydrogen per mole of steel atoms and aH is the activity of the hydrogen. [1] Comment by Laura Dawson: Comment by Laura Dawson:

Fugacity is a quantity used to estimate the behavior of a real or nonideal gas regarding the relationship of the molar Gibbs free energy and the logarithm of the pressure of the gas. [3] It is necessary to use this because non-ideal gases do not follow the same linearity that occurs in ideal gases with the ideal gas law and proportionalities that follow. When fugacity is used, however, linearity in the relationship can be obtained. Typically it is used for Van der Waals gases or for more realistic predictions of gas behaviors since conditions of true ideality are rare.

When considering an ideal gas, we can use the ideal gas law to analyze the molar volume (Vm). The law is as follows in Equation 2. R is known as the universal gas constant (with a value of 8.314 J/(mol*K)) and T is the temperature of the reaction. P represents the pressure of the reaction. This equation is derived from the ideal gas law, PV=nRT, where n is the moles of the gas [1].

However, for hydrogen, the focus of our paper, at varying temperatures and pressures, the ideal case can fail. A more calculation can be done for non-ideality with the Abel-Noble equation, below in Equation 3. This equation adds b, the co-volume constant, which represents the volume of the molecules. This equation can be used when the volume tends to be larger than an ideal gas. In Somerday and San Marchi’s experimentation, they used 15.84 cm^3/mol as the value of b [1].

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Then, this equation can be used and altered to determine fugacity as a fraction over the total pressure, seen below in Equation 4. The equation creates a ratio referred to as the fugacity constant [1].

With this equation, we can predict the fugacity of the hydrogen to increase when it is in a mixture as opposed to when it is in a pure form.

Stress alters how much of a solute can be dissolved by affecting the spacing of the lattice sites. The more stress that is applied to the material, the more lattice strain, or change from its original spacing is created. Most materials tend to exhibit the same relationship between stress and lattice strain.

This relationship can also be expressed as shown in Equation 5 below, where cL represents the moles of gas atoms per moles of metal able to diffuse under stress and cO represents the same quantity under no stress. σ represents the stress experienced locally and VH used the same as expressed in earlier equations, is the partial molar volume. When tensile stress is applied (positive stress), the possible concentration of gas diffused is increased, while with compression (negative stress) the concentration decreases. [1] This then, with combination with thermodynamic equilibrium, can be assumed that positive stress in materials such as steel, shifts the equilibria away from the gaseous environment and towards the molecules diffused into the material.

Trapping is experienced due to a solute’s mobility. Trapping is the idea that a solute, hydrogen in this specific investigation, interacts with varying features of the solvent’s, in this case, steel’s, microstructure and thus can be trapped within this matrix [1]. The trapping can be defined by the energy binding the hydrogen to the trap site, with a thermodynamic equilibrium outlined by Orani, in his article “The diffusion and trapping of hydrogen in steel”, where he establishes an equilibrium. The equilibrium equation can be seen in Equation 6 [1] [5].

θT represents the fraction of how many total sites are filled and θL is the fraction of how many of the sites in the lattice are filled by hydrogen. WB is the energy that is used to bind the hydrogen molecules to the trap site. In the equilibrium, similar to previous ones discussed in solubility, the most stable state will be achieved. In our specific case, in structural metals, the amount of lattice sites that hydrogen occurs in is very small. [1]

Applications

Metallurgists must take note of hydrogen content in their materials because a marginal amount, down to parts per million, can create embrittlement, blistering, and loss of ductility, especially in steel in large parts, such as in slabs or beams. [8] However, materials scientists and engineers can take several steps to prevent these sources of material failure. First, they can control stress levels, particularly tension, to minimize the allowance of greater amounts of hydrogen diffusion. They can also design for the avoidance of hydrogen sources, which could be anything from the natural elements to utilized hydrogen in a processing plant. An additional procedure is to bake the material to remove hydrogen.

Noteworthy examples of problems caused by hydrogen in steel are primarily seen in cases of failure analysis of structural components. One application of hydrogen behavior in steel, specifically involving hydrogen embrittlement is the failure of the East Span of the San Francisco-Oakland Bay Bridge. [10] In 1989, a major earthquake caused the upper east section to collapse causing fatalities and a significant amount of damage. [11] In 2013, the east span was replaced with a self-anchored suspension bridge, increasing its flexibility during seismic activity. This design used ninety-six anchor rods. This came with one flaw, however, that these types of bridges can potentially amplify stresses exerted upon them. After construction was finished and load transfer was performed, the anchor rods installed with the new bridge design were pre-tensioned under their minimum tensile strength [11]. After two weeks, thirty-two of the ninety-six anchor rods had failed by fracture.

It was after this failure that engineers questioned the use of similar rods throughout the rest of the bridge’s design. They tested the failed rods and found that the steel alloy had failed to reach expected toughness requirements. The fracture surface of one of the failed rods. Under extensive investigation by the California Department of Transportation, they had found that aided by the large amounts of tension, hydrogen embrittlement was to blame. Hydrogen had corroded the ASTM A354 Grade BD steel because they were not protected from the saltwater from the ocean the bridge was located over, despite the use of Denso tape, a precaution to avoid corrosion. It was found that the rods of the other sections of the bridge, not exposed to the ocean, exhibited behavior as expected, proving them to be safe [11].

References

1. Chris San Marchi and B. P. Somerday, “Thermodynamics of Gaseous Hydrogen and Hydrogen Transport in Metals,” MRS Proc., vol. 1098, pp. 1098-HH08-01, 2008.
2. Luqman Saleem, “quantum mechanics - How presence of metastable state ensure that there is first order phase transition?,” Physics Stack Exchange. [Online]. Available: https://physics.stackexchange.com/questions/418982/how-presence-of-metastable-state-ensure-that-there-is-first-order-phase-transiti. [Accessed: 17-Dec-2019].
3. D. R. Gaskell, Introduction to the Thermodynamics of Materials, Fifth Edition, 5th ed. CRC Press, 2008.
4. J.-P. Liu et al., “Supplementary Information.” 08-Jul-2013.
5. R. A. Oriani, “The diffusion and trapping of hydrogen in steel,” Acta Metallurgica, vol. 18, no. 1, pp. 147–157, Jan. 1970.
6. “Hydrogen Embrittlement of Steel,” Industrial Metallurgists. [Online]. Available: https://www.imetllc.com/training-article/hydrogen-embrittlement-steel/. [Accessed: 17-Dec-2019].
7. Ali Tehranchi, “Scale bridging modelling of hydrogen embrittlement.” [Online]. Available: https://www.mpie.de/3040571/Scale-bridging-modelling-of-hydrogen-embrittlement. [Accessed: 17-Dec-2019].
8. “Hydrogen in Steels,” Total Materia, 01-Aug-2007. [Online]. Available: https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=kts&NM=206. [Accessed: 16-Dec-2019].
9. “Different Types of Corrosion: Hydrogen Embrittlement,” WebCorr Corrosion Consulting. [Online]. Available: https://www.corrosionclinic.com/types_of_corrosion/hydrogen_embrittlement_HE.htm. [Accessed: 17-Dec-2019].
10. Norm Moriber and Kathy Riggs Larsen, “Failed Anchor Rods on the San Francisco-Oakland Bay Bridge: A Corrosion Discussion,” Materials Performance, 02-Nov-2015. [Online]. Available: http://www.materialsperformance.com/articles/material-selection-design/2015/11/failed-anchor-rods-on-the-san-francisco-oakland-bay-bridge-a-corrosion-discussion. [Accessed: 16-Dec-2019].
11. Thomas Langill, “Lessons Learned from the Bay Bridge Bolt Failure,” Structure Mag, 01-Feb-2017. [Online]. Available: https://www.structuremag.org/?p=11041. [Accessed: 16-Dec-2019].