Simulation study on mechanical properties of nanocrystalline Fe with hydrogen atom segregated on grain boundaries

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The primary focus is to discern the influence of varied hydrogen concentrations on the failure behaviors exhibited during plastic deformation. The investigation aims to straighten out the mechanical characteristics and failure mechanisms at the microscale in polycrystalline iron. Moreover, the study monitors and analyzes alterations in the crystal structure of the polycrystalline iron model under tensile loading, employing the common neighbor analysis technique. Findings indicate that tensile strength, Young's modulus, and strain when reaching the tensile strength diminish as hydrogen concentration increases, thereby heightening the propensity for failure in polycrystalline iron. In stress conditions, the congregation of hydrogen atoms tends to facilitate dislocation, void formation, and precipitate brittle fractures. The insights garnered from this investigation not only enhance our comprehension of micro-failure mechanisms in hydrogen-affected infrastructures but also furnish essential theoretical support for ensuring the reliability and safety of hydrogen transmission pipelines. Polycrystalline Fe Hydrogen embrittlement Grain boundary segregation Mechanical performance Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Globally, with the transformation of the energy structure and the growing demand for renewable energy, hydrogen energy, as a clean and efficient energy carrier, is becoming a hot spot for research and application. In the utilization of hydrogen energy, hydrogen transmission pipelines serve as critical infrastructures connecting the hydrogen source and the point of use, being of high priority in the overall performance of the hydrogen energy system in terms of its safe and efficient delivery capacity. However, compared to traditional natural gas or oil transmission pipelines, the diminutive size and elevated diffusivity of hydrogen atoms pose new challenges to the material selection, structural design, and maintenance of hydrogen pipelines. Hydrogen atoms ubiquitously permeate diverse environments[1, 2], including hydrocarbons, aqueous solutions, and other corrosive chemical environments, rendering their infiltration a common problem. This phenomenon significantly heightens the vulnerability of metallic materials to hydrogen, particularly in the case of Fe-based materials. The large diffusion coefficient of active hydrogen atoms enables them not only to occupy tetrahedral or octahedral interstices within the metallic lattice but also to infiltrate dislocation cores, grain boundaries as well as micropores. Hydrogen manifests in various forms within these structures, rendering the material highly susceptible to brittle fracture under external stresses, precipitously impairing its mechanical properties[3-5]. Several mainstream theories of hydrogen embrittlement have been proposed based on different physical processes and characteristics of metal-hydrogen interactions[6-8]. In research on fatigue crack extension in metals, Irwin[9] et al. observed that the hydrogen-containing environment accelerated the crack extension, and then investigated the phenomenon of hydrogen accumulation in microcracks and cavities in the metal. It was found that hydrogen accumulates in microcracks and cavities inside the material, creating high pressure, and this internal air pressure can drive crack initiation. Based on these observations, the hydrogen pressure theory was postulated. Katz[10] conceived the concept of hydrogen-enhanced deconstructive embrittlement (HEDE), stemming from the observation that certain metals can undergo a transition from ductile to deconstructive fracture when exposed to hydrogen. Concurrently, Beachem[11] devised the hypothesis of hydrogen-enhanced local plasticity (HELP) and assessed how hydrogen diffusion affected fracture motion. This hypothesis posits that hydrogen atom accumulation lowers the resistance to dislocation movement, thereby augmenting local plastic deformation. Such changes in material behavior are precursors to the origination and extension of cracks. Further elaborating on the directional dependency of these phenomena, Sun[12] et al provided initial evidence of orientation-dependent behaviors. Lynch[13, 14] et al. proposed the hydrogen enhanced strain induced vacancy theory, in which they argued that the existence of hydrogen atoms enhances the stress field and induces the formation of more vacancies. These vacancies then prompt the hydrogen atoms to accumulate in the vacancies and form microcracks, which further lead to brittle fractures. Additionally, Muhammad[15] et al. examined the composite impact of HEDE and HELP on the fracture resistance of steel, and proposed a model to articulate the synergistic effects of these mechanisms. Tools such as atom probes[16, 17] and transmission electron microscopy[18, 19] can provide insights into the microstructural changes in materials, but the movement of hydrogen atoms at the atomic level is challenging to depict graphically. Given these constraints, molecular dynamics simulation, as a formidable computational tool in materials science, offers the ability to observe and analyze the intricate interactions between hydrogen atoms and metallic substrates at an atomic scale[20-22]. This technique has proven its unique advantages in the study of hydrogen embrittlement mechanisms. Jiao[21] et al. demonstrated through molecular dynamics simulations that in Fe-C single crystals, hydrogen atoms markedly promote dislocation slip while simultaneously inhibiting martensitic transformation. As hydrogen atoms increase, dislocation slip emerges as the predominant mechanism of plastic deformation. This observation sheds light on the microscopic mechanisms underlying hydrogen embrittlement, illustrating how hydrogen influences material behavior at the atomic level. Grain size in nanocrystalline Fe has been reviewed by Zhou[22] concerning the hydrogen diffusion coefficient. The findings highlighted that as the grain size gets smaller, the trapping effect at triple junctions which is typically overlooked in materials with coarse grains becomes more significant. Zhu[23] investigated the deformation mechanisms in hydrogen-containing α-Fe twisted biocrystals under various twisting angles and loading directions and found that solute hydrogen notably influences dislocation behaviors and vacancy concentrations, elucidating the complex interactions that govern material behavior when hydrogen is available. Although these works have significantly expanded our comprehension of the role of hydrogen in influencing the mechanical characteristics of Fe-based materials. However, there is still a knowledge gap about how hydrogen concentration specifically modulates the hydrogen embrittlement phenomenon. Specifically, the intricate mechanisms by which hydrogen atoms affect the microstructure of Fe-based materials with hydrogen atoms distributed in the grain boundary influence zone and their macroscopic mechanical properties under various hydrogen concentrations are not fully elucidated. Therefore, this research aims to systematically consider the culmination of hydrogen concentration on the hydrogen embrittlement vulnerability of Fe-based metallic materials by theoretical simulations, to deepen the understanding of the process of hydrogen embrittlement and contribute a scientific foundation for the development of new, high-strength materials resistant to hydrogen embrittlement. 2. Microscopic model and simulation process for hydrogen pipelines Since iron usually does not react chemically during hydrogen transportation and has good mechanical properties, the pipeline for transporting hydrogen is regarded as a pure iron pipeline in this paper. The construction of the polycrystalline Fe model employs a two-dimensional Voronoi tessellation method. The Fe atoms in the model are arranged in a body-centered cubic (BCC) lattice and overlapping atoms with interatomic distances less than 0.14 Å will be deleted. The resulting model spans dimensions of 300 Å × 300 Å × 46 Å, oriented along the [1 0 0], [0 1 0], and [0 0 1] for X, Y and Z. The initial model, featuring approximately 348,000 atoms, is shown in Fig.1. It should be emphasized that the grain boundary typically exhibits an exceedingly narrow thickness at room temperatures. However, in our computational model, the grain boundary manifests as an expansive disordered region, as depicted in Fig.1(b). This representation is predicated on the concept of the grain boundary affected zone proposed by Zhang[24], reflecting the structural distributions and stress change induced by the segregation of hydrogen atoms at the grain boundary. Employing this model proves quintessential for the precise clarification of how hydrogen atom dispersion affects the mechanical attributes of substances. Especially, this is significant within the scope of examining the minuscule mechanisms that form the basis of hydrogen-induced fragility in materials. To seek out the impact of hydrogen atom segregation on the microstructural failure mechanisms, the grain boundaries of the model are randomized to incorporate hydrogen atoms to emulate the morphology of hydrogen segregation commonly observed in gas pipelines. The choice of hydrogen concentration was guided by the experimental approach outlined by Kuopanportti[25]. Given the inherently sluggish diffusion kinetics of hydrogen atoms, the selected concentration values were set slightly higher than those typically encountered in field experiments. Considering the above factors, the atomic concentrations of hydrogen were determined to be 1.6%, 7.1%, and 9.2%, respectively. In molecular dynamics simulation, it is highly crucial to select and verify the appropriate potential function. The main function of the potential function is to precisely depict how atoms or molecules interact inside the system, which directly affects the accuracy of atomic trajectories obtained by simulation, thereby impacting the overall fidelity and reliability of the computational results. The embedded atom method, as proposed by Meyer[26], has been selected to characterize the interactions between Fe atoms in the model. This potential function is extensively utilized to depict the interactions between Fe-H systems, enabling simulations that assess the structure, diffusion behavior, and stability under diverse conditions. This approach facilitates a deepened understanding of the micro-mechanisms governing Fe-H interactions and the properties of related materials. Prior to the commencement of the simulation, the model undergoes a relaxation process to coordinate the interaction between atoms in the system, thereby enhancing the geometric configuration and internal stress distribution of the sample. This procedure ensures the simulation system attains dynamic equilibrium devoid of external forces. During the relaxation process, periodic boundary conditions have been placed on the model along the X and Z axis to mitigate boundary effects arising from the finite size of samples, thereby enhancing the simulation's fidelity to an infinite system. Unconstrained boundary conditions are employed in the Y axis to facilitate loading. The Nose-Hoover thermostat method is employed to keep the temperature of the system stable at 300K, thereby regulating the thermodynamic conditions of the sample and mitigating the energy instability caused by temperature fluctuations. The model undergoes energy minimization employing the Conjugate Gradient method. Following this, a relaxation period of 30 picoseconds transpires within the NPT constant temperature and pressure ensemble, with a pressure of 0, thereby ensuring the simulation sample achieves a stable energy state. The Conjugate Gradient method is utilized to minimize the energy of the model. Following this, a relaxation period of 30 ps is conducted within the constant pressure and constant (NPT) ensemble, maintaining a pressure of 0 MPa. This procedure aims to ascertain the stable energy state of the simulation sample. The alterations in temperature, pressure, and potential energy of the model after relaxation are depicted in Fig.2. This visualization illustrates that both the temperature and pressure of the model have attained the predetermined values, while the average potential energy of atoms has stabilized. The tensile load is applied to the model sample along the Y-axis direction through displacement loading. The procedure is detailed as follows: along the Y-axis direction, four layers of atoms situated above and below the grain boundaries are designated as boundaries. Under loading, the lower four layers of atoms remain fixed, while the upper four layers of atoms undergo gradual displacement to induce stretching. The time step ∆t is set to 0.005ps, the engineering strain rate of tensile loading is 1×10 5 s -1 , and the timestep in the calculation process is set to 1×10 9 . The strain produced in the system can be expressed as: Wherein, ε represents the strain of the system; N denotes the number of timesteps for system simulation; ∆ t signifies the timestep of system simulation; and ε e represents the engineering strain rate. It can be calculated that the strain produced by the system is 20%, that is, the simulated system stops stretching when the strain is 20%. 3. Simulation results and discussion 3.1 Effect of hydrogen atom concentrations on mechanical performance of polycrystalline Fe model Fig.3 presents the stress-strain curves of polycrystalline Fe with varying hydrogen atom concentrations subjected to tensile loading at a room temperature of 300 K. Observations reveal that the strain-stress curves exhibit analogous changing trends. Notably, as the concentration of hydrogen increases, there is a discernible reduction in peak stress across various extents, accompanied by a decrease in the strain required to reach this maximum peak stress. As the tensile strain escalates, the stress increases continuously; Upon the strain reaches a threshold, the stress attains the peak; When the stress exceeds the peak value, the system enters the fracture stage, during which defects emerge, and the stress precipitously declines to a stable level. Subsequently, as the strain continues to increase, the stress fluctuates around this equilibrium value. The stress-strain curves obtained from the simulation system during tension closely mirror those reported by Xu[27], thus further verifying the accuracy of the model. Calculate the slope of each curve during the elastic stage to determine Young's modulus for each model. The peak stress (tensile strength) and the corresponding strain for each stress-strain curve are also counted. These parameters serve to assess the strength and ductility of the polycrystalline Fe model respectively, with higher values indicating superior material properties. In the macroscopic experiments, the presence of numerous dislocations in the material typically results in lower stress levels compared to those of an ideal crystal. Consequently, variations in stress levels are primarily attributed to dislocations and slips. Therefore, the peak stress observed in this paper is notably higher than that observed in the macroscopic experiment. Tab.1 Essential parameters of mechanical properties for polycrystalline Fe models with different hydrogen atom concentrations at 300 K Hydrogen atom concentration (%) Young's modulus (GPa) Tensile strength (GPa) Strain at maximum stress (%) 0 198.59 15.29 5.8 1.6 195.76 14.79 1.05 7.1 185.48 13.07 1.33 9.2 183.32 9.98 2.14 The curves of tensile strength and Young's modulus for these models under tensile loading have been plotted, as depicted in Fig. 4. At a hydrogen concentration of 0%, the polycrystalline Fe model exhibits an ultimate tensile strength of 15.29 GPa and Young's modulus of 198.59 GPa. Conversely, when the hydrogen concentration increases to 9.2%, the tensile strength drops to a minimum of 9.98 GPa and Young's modulus decreases to 183.32 GPa, reflecting reductions of 34.7% and 7.69% in tensile strength and Young's modulus. These findings decisively demonstrate that the mechanical properties of polycrystalline Fe decrease significantly with the climb of the volume fraction of hydrogen atoms, which further verifies the destructive effect of hydrogen on the structure and mechanism of materials. Concurrently, both the tensile strength and Young's modulus exhibit a decline with the rising hydrogen concentration. This shows that under the same conditions, a higher hydrogen concentration results in diminished tensile strength of the polycrystalline iron model, reducing its capacity to withstand deformation and increasing its susceptibility to failure. Their presence alters the interatomic forces among iron atoms, causing some to deviate from their original lattice positions and leading to lattice distortion. Such distortion impacts not only the microstructure of the material but also compromises its overall mechanical properties. 3.2 Influence of hydrogen atom concentration on microscopic phase transformation of polycrystalline Fe model Fig.5 illustrates the structural transformation process of the polycrystalline Fe model under tensile loading at varying hydrogen atom concentrations. Initially, within a small deformation range, the model largely retains the original atomic arrangement. However, as deformation progresses, distortion at the grain boundaries intensifies, vacancies proliferate, and grain boundary energy escalates. This sequence of changes results in the rupture of several metal bonds near the grain boundaries, initiating crack formation at these sites. The model then transitions into the plastic deformation stage, continuing until through-holes develop in the crystal, ultimately leading to its failure. Furthermore, atomic dislocations, hole nucleation, and crack propagation all originate from the grain boundary. This phenomenon occurs because the grain boundary acts as a transitional zone between different grains within the crystal, and the discontinuity and irregularity in its atomic arrangement result in notable differences in mechanical properties. Primarily, due to its structural discontinuity, the grain boundary frequently serves as the origin or accumulation point for dislocations. Additionally, stress concentration at these boundaries facilitates the formation and movement of dislocations. Secondly, the structural discontinuity of the grain boundary, coupled with the relative weakening of atomic bonding forces, predisposes these areas to hole nucleation. This tendency is particularly pronounced under tensile stress, where the formation and expansion of holes become more evident. Lastly, the inherent non-uniformity and weakened characteristics of grain boundaries facilitate the initial formation of cracks in these regions, which then propagate swiftly along the grain boundaries. According to the classical dislocation transport theory, hydrogen atoms can migrate in the crystal with dislocation, which significantly accelerates its diffusion speed in the crystal and leads to the significant enrichment of hydrogen at the grain boundary. In addition, the existence of hydrogen atoms promotes the occurrence of coplanar slip, which further accelerates the spread and migration of hydrogen. Hydrogen atoms can also reduce the binding energy between atoms, thus weakening the mechanical strength of grain boundaries or phase boundaries. Grain boundary fractures arise as a result of the significant stress concentration at the grain boundary brought on by the acceleration of hydrogen atoms' collecting speed at the grain boundary caused by an increase in material deformation. The existence of these cracks significantly accelerates the brittle fracture process along the grain boundary. Fig. 6 depicts how hydrogen atoms promote the formation of holes and the evolution of the internal surface of the model during grain boundary. In addition, Fig. 6 provides statistical data on the total surface area of voids and fracture surfaces throughout the deformation process. It is evident from the depiction that as strain increases, the voids in the polycrystalline Fe model progressively enlarge due to the influence of hydrogen atoms, and cracking even occurs along the grain boundaries. The data show that in the polycrystalline Fe model with hydrogen atom segregation concentrations of 0.1 and 0.2, compared with the sample with higher hydrogen concentration, there are fewer voids and a smaller surface area of defects. Especially, in the polycrystalline Fe model with a hydrogen atom concentration of 0.3, there is a marked increase in surface area during the deformation, whereas models with the other two concentrations exhibit only minor changes in surface area. Although the polycrystalline Fe alloy with the highest concentration of hydrogen atom segregation displays the smallest defect surface area during the tensile process, which indicates that the existence of excessive hydrogen atoms may directly lead to the fracture of the polycrystalline Fe model, overall, the higher the concentration of hydrogen atoms, the more defect surface area is produced in the polycrystalline Fe model, which further proves the destructive effect of hydrogen atoms in the material. Fig.7 employs von Mises shear stress to delineate and analyze deformation, illustrating local deformation in areas undergoing phase transformation. Notably, substantial stress concentration was observed around voids, predominantly located in high-energy grain boundary regions. Although the presence of a modest quantity of hydrogen atoms does not suffice to alter the BCC phase transformation as the primary mechanism of plastic deformation, it does facilitate the early generation of dislocations. The slippage of these dislocations causes local plastic deformation around nano-holes, markedly altering their shape, enhancing the likelihood of void growth and coalescence, and potentially precipitating macroscopic hydrogen embrittlement. From a mechanical response perspective, dislocation slip necessitates increased shear stress. Consequently, the polycrystalline Fe model containing more hydrogen atoms exhibits a lower threshold for the initiation of plastic deformation. This indicates that hydrogen presence diminishes the material’s resistance to external loads, enabling plastic deformation under reduced stress, thereby hastening the material's failure process. 4. Conclusion Utilizing molecular dynamics simulation, the failure behavior of polycrystalline Fe models with varying hydrogen concentrations has been investigated from a microscopic perspective, revealing the interactions between hydrogen and pure iron pipelines as well as the underlying failure mechanisms. The changes in crystal structure under tensile stress loading were observed and analyzed. The following is a summary of the main findings: (1) The stress-strain curves of the polycrystalline Fe model with varying hydrogen concentrations exhibit similar trends, with tensile strength, Young's modulus, and strain at maximum stress all decreasing as hydrogen atom concentration increases. Specifically, the maximum tensile strength and Young's modulus are 15.29 GPa and 198.59 GPa, at 0% hydrogen concentration, while the minimum values are 9.98 GPa and 183.32 GPa at 9.2% hydrogen concentration, reflecting reductions of 34.7% and 7.69%. (2) The infiltration and accumulation of hydrogen atoms at grain boundaries induce significant structural distortions and stress concentrations, leading to increased grain boundary energy, the rupture of metal bonds, and the initiation and propagation of cracks. These phenomena collectively facilitate plastic deformation under tensile load, the formation of through-holes, and expedite the brittle fracture process along grain boundaries. (3) The presence of hydrogen atoms markedly lowers the trigger stress for plastic deformation in materials, indicating that hydrogen accumulation diminishes the material's resistance to external loads and accelerates the failure process. This finding holds substantial scientific and engineering significance for understanding and preventing hydrogen embrittlement. Declarations Author contribution Feng Zhang designed the experiments. Youran Zhi, Qiaoyun Tang, and Deyong Wang investigated the traits. Youran Zhi and Qiaoyun Tang analyzed the data and wrote the manuscript; Feng Zhang and Liu Yang revised and edited the manuscript. All the authors have read and approved the fnal manuscript. Funding This project was supported by National Natural Science Foundation of China (51505212，52005248), Scientific research fund project of Nanjing Institute of Technology (CKJA202101), Natural Science Foundation of Jiangsu Province (BK20201031). Data availability All data generated or analyzed in this study are included in this published article. Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 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American Physical Society 9:57. https://doi.org/10.1103/PHYSREVB.57.5140 Xu T. H., Zhu Z. Q., Geng S. F.,Song H. Y. (2017) Molecular dynamics study of effect of hydrogen atoms on mechanical properties of α -Fe nanowires. Physics Letters A 381:3222-3227. https://doi.org/https://doi.org/10.1016/j.physleta.2017.08.012 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4303209","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":295572700,"identity":"5cea4dff-b6d9-4b8e-8c4e-d78d7fbfd6d5","order_by":0,"name":"Youran Zhi","email":"","orcid":"","institution":"Nanjing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Youran","middleName":"","lastName":"Zhi","suffix":""},{"id":295572701,"identity":"a8efa263-5fe6-4a18-a083-9e7a7ce7c912","order_by":1,"name":"Qiaoyun Tang","email":"","orcid":"","institution":"Nanjing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Qiaoyun","middleName":"","lastName":"Tang","suffix":""},{"id":295572702,"identity":"267a99b2-4519-4af4-ad04-f8d4c232a6e1","order_by":2,"name":"Feng Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIie3RvQrCMBDA8ZRCsoTOKUL7BEKkUOzSZ0kRnPoA3Sx0jbtDwWcQofNJoZPuWV2cOugufm069dwE899/3B1HiM32g1GXAfg3ulizCnDEYzqDKfWcje4UjgQcIiho4JQml8jFhFJgeOw6en8xPUmDcTlIMtitxJwyttwmNZlFMSCmtEJ23NGHZsQJZA2CyPaq7oKY/IQkHCQIoPJJKJIwrcAvqZroLkpqibglrFh7fpGQVUfTF2kwSD4SHPmad/KtsNlstr/oAToxQ6pv1KwYAAAAAElFTkSuQmCC","orcid":"","institution":"Nanjing Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Feng","middleName":"","lastName":"Zhang","suffix":""},{"id":295572703,"identity":"4656acb4-6a25-4a62-a64b-e8dd4c24d1bd","order_by":3,"name":"Deyong Wang","email":"","orcid":"","institution":"Xinjiang Lianhai Chuangzhi Information Technology Co., Ltd","correspondingAuthor":false,"prefix":"","firstName":"Deyong","middleName":"","lastName":"Wang","suffix":""},{"id":295572704,"identity":"3e54375d-3502-4bce-99c0-49af6f0653b6","order_by":4,"name":"Liu Yang","email":"","orcid":"","institution":"Nanjing Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Liu","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-04-22 05:18:55","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4303209/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4303209/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55366649,"identity":"02f386c3-2d94-4bd3-91ed-250e003b40c6","added_by":"auto","created_at":"2024-04-26 09:59:23","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":452679,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Polycrystalline Fe model with hydrogen atom segregation at the grain boundaries; (b) Structural characteristics in polycrystalline Fe model.\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/a4eaa963c242a489a38581c0.jpg"},{"id":55366653,"identity":"961b6a04-48f8-4267-a76e-b10b7f154f91","added_by":"auto","created_at":"2024-04-26 09:59:23","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":202760,"visible":true,"origin":"","legend":"\u003cp\u003eVariation curves of temperature, pressure, and potential energy with relaxation time\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/f2f4a29184d529490c31dfcf.jpg"},{"id":55367078,"identity":"161bf285-3331-42fb-bd91-7a3f91869d0d","added_by":"auto","created_at":"2024-04-26 10:07:23","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":253549,"visible":true,"origin":"","legend":"\u003cp\u003eThe stress-strain curves depicting tensile deformation of polycrystalline Fe model with different hydrogen atom concentrations, alongside the atomic structure diagrams during the deformation.\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/2e3ca55f41a0735bd5c816a5.jpg"},{"id":55367346,"identity":"3819d1d6-fcdf-4476-89f6-118a1d4d830d","added_by":"auto","created_at":"2024-04-26 10:15:23","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":195847,"visible":true,"origin":"","legend":"\u003cp\u003eCone diagram of tensile strength and Young's modulus of polycrystalline Fe model with different hydrogen atom concentrations.\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/8d4576fd295efc0197a207d5.jpg"},{"id":55367850,"identity":"3910c12f-51f9-4064-b193-ff84d6521db5","added_by":"auto","created_at":"2024-04-26 10:23:23","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1268758,"visible":true,"origin":"","legend":"\u003cp\u003eSequential screenshot of plastic deformation in nanocrystalline Fe with different hydrogen atom concentrations when it is stretched along the Y axis.\u003c/p\u003e","description":"","filename":"Picture5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/1ae4e5b3b03f773078f1916c.jpg"},{"id":55366650,"identity":"9daf871f-2c2c-40bd-8d6d-c7ceef7be037","added_by":"auto","created_at":"2024-04-26 09:59:23","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":445419,"visible":true,"origin":"","legend":"\u003cp\u003eThe growth and distribution of internal holes in the polycrystalline Fe model with different hydrogen atom concentrations during plastic deformation under different strains.\u003c/p\u003e","description":"","filename":"Picture6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/05a7bb1424ae751512d40f95.jpg"},{"id":55366656,"identity":"62bbcc9a-9972-47d4-bf37-92221086dc4a","added_by":"auto","created_at":"2024-04-26 09:59:23","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":1224806,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of internal atomic shear strain during plastic deformation of nanocrystalline Fe with different H atomic concentrations.\u003c/p\u003e","description":"","filename":"Picture7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/b98a1d3bfb004d4a01e02d16.jpg"},{"id":56972745,"identity":"22688bbf-9c8b-4c35-bbed-0375f75afd56","added_by":"auto","created_at":"2024-05-23 01:14:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4341592,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4303209/v1/9d2fc3ef-c067-4a2d-a464-db2d7438d3b9.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Simulation study on mechanical properties of nanocrystalline Fe with hydrogen atom segregated on grain boundaries","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eGlobally, with the transformation of the energy structure and the growing demand for renewable energy, hydrogen energy, as a clean and efficient energy carrier, is becoming a hot spot for research and application. In the utilization of hydrogen energy, hydrogen transmission pipelines serve as critical infrastructures connecting the hydrogen source and the point of use, being of high priority in the overall performance of the hydrogen energy system in terms of its safe and efficient delivery capacity. However, compared to traditional natural gas or oil transmission pipelines, the diminutive size and elevated diffusivity of hydrogen atoms pose new challenges to the\u0026nbsp;material selection, structural design, and maintenance of hydrogen pipelines.\u003c/p\u003e\n\u003cp\u003eHydrogen atoms ubiquitously permeate diverse environments[1, 2], including hydrocarbons, aqueous solutions, and other corrosive chemical environments, rendering their infiltration a common problem. This phenomenon significantly heightens the vulnerability of metallic materials to hydrogen, particularly in the case of Fe-based materials. The large diffusion coefficient of active hydrogen atoms enables them not only to occupy tetrahedral or octahedral interstices within the metallic lattice but also to infiltrate dislocation cores, grain boundaries as well as micropores. Hydrogen manifests in various forms within these structures, rendering the material highly susceptible to brittle fracture under external stresses, precipitously impairing its mechanical properties[3-5].\u003c/p\u003e\n\u003cp\u003eSeveral mainstream theories of hydrogen embrittlement have been proposed based on different physical processes and characteristics of metal-hydrogen interactions[6-8]. In research on fatigue crack extension in metals, Irwin[9]\u0026nbsp;et al. observed that the hydrogen-containing environment accelerated the crack extension, and then investigated the phenomenon of hydrogen accumulation in microcracks and cavities in the metal. It was found that hydrogen accumulates in microcracks and cavities inside the material, creating high pressure, and this internal air pressure can drive crack initiation. Based on these observations, the hydrogen pressure theory was postulated. Katz[10]\u0026nbsp;conceived the concept of hydrogen-enhanced deconstructive embrittlement (HEDE), stemming from the observation that certain metals can undergo a transition from ductile to deconstructive fracture when exposed to hydrogen.\u0026nbsp;Concurrently, Beachem[11]\u0026nbsp;devised the hypothesis of hydrogen-enhanced local plasticity (HELP)\u0026nbsp;and assessed how hydrogen diffusion affected fracture motion. This hypothesis posits that hydrogen atom accumulation lowers the resistance to dislocation movement, thereby augmenting local plastic deformation. Such changes in material behavior are precursors to the origination and extension of cracks. Further elaborating on the directional dependency of these phenomena, Sun[12]\u0026nbsp;et al provided initial evidence of orientation-dependent behaviors. Lynch[13, 14]\u0026nbsp;et al. proposed the hydrogen enhanced strain induced vacancy theory, in which they argued that the existence of hydrogen atoms enhances the stress field and induces the formation of more vacancies. These vacancies then prompt the hydrogen atoms to accumulate in the vacancies and form microcracks, which further lead to brittle fractures. Additionally, Muhammad[15]\u0026nbsp;et al. examined the composite impact of HEDE and HELP on the fracture resistance of steel, and proposed a model to articulate the synergistic effects of these mechanisms.\u003c/p\u003e\n\u003cp\u003eTools such as atom probes[16, 17]\u0026nbsp;and transmission electron microscopy[18, 19]\u0026nbsp;can provide insights into the microstructural changes in materials, but the movement of hydrogen atoms at the atomic level is challenging to depict graphically. Given these constraints, molecular dynamics simulation, as a formidable computational tool in materials science, offers the ability to observe and analyze the intricate interactions between hydrogen atoms and metallic substrates at an atomic scale[20-22].\u0026nbsp;This technique has proven its unique advantages in the study of hydrogen embrittlement mechanisms. Jiao[21]\u0026nbsp;et al. demonstrated through molecular dynamics simulations that in Fe-C single crystals, hydrogen atoms markedly promote dislocation slip while simultaneously inhibiting martensitic transformation. As hydrogen atoms increase, dislocation slip emerges as the predominant mechanism of plastic deformation. This observation sheds light on the microscopic mechanisms underlying hydrogen embrittlement, illustrating how hydrogen influences material behavior at the atomic level. Grain size in nanocrystalline Fe has been reviewed by Zhou[22]\u0026nbsp;concerning the hydrogen diffusion coefficient. The findings highlighted that as the grain size gets smaller, the trapping effect at triple junctions which is typically overlooked in materials with coarse grains becomes more significant. Zhu[23]\u0026nbsp;investigated the deformation mechanisms in hydrogen-containing \u0026alpha;-Fe twisted biocrystals under various twisting angles and loading directions and found that solute hydrogen notably influences dislocation behaviors and vacancy concentrations, elucidating the complex interactions that govern material behavior when hydrogen is available.\u003c/p\u003e\n\u003cp\u003eAlthough these works have significantly expanded our comprehension of the role of hydrogen in influencing the mechanical characteristics of Fe-based materials. However, there is still a knowledge gap about how hydrogen concentration specifically modulates the hydrogen embrittlement phenomenon. Specifically, the intricate mechanisms by which hydrogen atoms affect the microstructure of Fe-based materials with hydrogen atoms distributed in the grain boundary influence zone and their macroscopic mechanical properties under various hydrogen concentrations are not fully elucidated. Therefore, this research aims to systematically consider the culmination of hydrogen concentration on the hydrogen embrittlement vulnerability of Fe-based metallic materials by theoretical simulations, to deepen the understanding of the process of hydrogen embrittlement and contribute a scientific foundation for the development of new, high-strength materials resistant to hydrogen embrittlement.\u003c/p\u003e"},{"header":"2. Microscopic model and simulation process for hydrogen pipelines","content":"\u003cp\u003eSince iron usually does not react chemically during hydrogen transportation and has good mechanical properties, the pipeline for transporting hydrogen is regarded as a pure iron pipeline in this paper. The construction of the polycrystalline Fe model employs a two-dimensional Voronoi tessellation method. The Fe atoms in the model are arranged in a body-centered cubic (BCC) lattice and overlapping atoms with interatomic distances less than 0.14 \u0026Aring; will be deleted. The resulting model spans dimensions of 300 \u0026Aring; \u0026times; 300 \u0026Aring; \u0026times; 46 \u0026Aring;, oriented along the [1 0 0], [0 1 0], and [0 0 1] for X, Y and Z. The initial model, featuring approximately 348,000 atoms, is shown in Fig.1. It should be emphasized that the grain boundary typically exhibits an exceedingly narrow thickness at room temperatures. However, in our computational model, the grain boundary manifests as an expansive disordered region, as depicted in Fig.1(b). This representation is predicated on the concept of the grain boundary affected zone proposed by Zhang[24], reflecting the structural distributions and stress change induced by the segregation of hydrogen atoms at the grain boundary. Employing this model proves quintessential for the precise clarification of how hydrogen atom dispersion affects the mechanical attributes of substances. Especially, this is significant within the scope of examining the minuscule mechanisms that form the basis of hydrogen-induced fragility in materials.\u003c/p\u003e\n\u003cp\u003eTo seek out the impact of hydrogen atom segregation on the microstructural failure mechanisms,\u0026nbsp;the grain\u0026nbsp;boundaries of the model are randomized to incorporate hydrogen atoms to emulate the morphology of hydrogen segregation commonly observed in gas pipelines.\u0026nbsp;The choice of hydrogen concentration was guided by the experimental approach outlined by Kuopanportti[25].\u0026nbsp;Given the inherently sluggish diffusion kinetics of hydrogen atoms, the selected concentration values were set slightly higher than those typically encountered in field experiments. Considering the above factors, the atomic concentrations of hydrogen were determined to be 1.6%, 7.1%, and 9.2%, respectively.\u003c/p\u003e\n\u003cp\u003eIn molecular dynamics simulation, it is highly crucial to select and verify the appropriate potential function. The main function of the potential function is to precisely depict how atoms or molecules interact inside the system, which directly affects the accuracy of atomic trajectories obtained by simulation,\u0026nbsp;thereby impacting the overall fidelity and reliability of the computational results.\u0026nbsp;The embedded atom method, as proposed by Meyer[26],\u0026nbsp;has been selected to characterize the interactions between Fe atoms in the model. This potential function is extensively utilized to depict the interactions between Fe-H systems, enabling simulations that assess the structure, diffusion behavior, and stability under diverse conditions. This approach facilitates a deepened understanding of the micro-mechanisms governing Fe-H interactions and the properties of related materials.\u003c/p\u003e\n\u003cp\u003ePrior to the commencement of the simulation, the model undergoes a relaxation process to coordinate the interaction between atoms in the system, thereby enhancing the geometric configuration and internal stress distribution of the sample. This procedure ensures the simulation system attains dynamic equilibrium devoid of external forces. During the relaxation process, periodic boundary conditions have been placed on the model along the X and Z axis to mitigate boundary effects arising from the finite size of samples, thereby enhancing the simulation\u0026apos;s fidelity to an infinite system. Unconstrained boundary conditions are employed in the Y axis to facilitate loading. The Nose-Hoover thermostat method is employed to keep the temperature of the system stable at 300K, thereby regulating the thermodynamic conditions of the sample and mitigating the energy instability caused by temperature fluctuations.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe model undergoes energy minimization employing the Conjugate Gradient method. Following this, a relaxation period of 30 picoseconds transpires within the NPT constant temperature and pressure ensemble, with a pressure of 0, thereby ensuring the simulation sample achieves a stable energy state. The Conjugate Gradient method is utilized to minimize the energy of the model. Following this, a relaxation period of 30 ps is conducted within the constant pressure and constant (NPT) ensemble, maintaining a pressure of 0 MPa. This procedure aims to ascertain the stable energy state of the simulation sample. The alterations in temperature, pressure, and potential energy of the model after relaxation are depicted in Fig.2. This visualization illustrates that both the temperature and pressure of the model have attained the predetermined values, while the average potential energy of atoms has stabilized.\u003c/p\u003e\n\u003cp\u003eThe tensile load is applied to the model sample along the Y-axis direction through displacement loading. The procedure is detailed as follows: along the Y-axis direction, four layers of atoms situated above and below the grain boundaries are designated as boundaries. Under loading, the lower four layers of atoms remain fixed, while the upper four layers of atoms undergo gradual displacement to induce stretching.\u0026nbsp;The time step\u0026nbsp;∆t\u0026nbsp;is set to\u0026nbsp;0.005ps, the engineering strain rate of tensile loading is 1\u0026times;10\u003csup\u003e5\u0026nbsp;\u003c/sup\u003es\u003csup\u003e-1\u003c/sup\u003e, and the timestep in the calculation process is set to 1\u0026times;10\u003csup\u003e9\u003c/sup\u003e. The strain produced in the system can be expressed as:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 451px; height: 42.2812px;\" width=\"451\" height=\"42.2812\"\u003e\u003c/p\u003e\n\u003cp\u003eWherein, \u003cem\u003e\u0026epsilon;\u003c/em\u003e represents the strain of the system; \u003cem\u003eN\u003c/em\u003e denotes the number of timesteps for system simulation; ∆\u003cem\u003et\u003c/em\u003e signifies the timestep of system simulation; and \u003cem\u003e\u0026epsilon;\u003c/em\u003e\u003csub\u003ee\u003c/sub\u003e represents the engineering strain rate. It can be calculated that the strain produced by the system is 20%, that is, the simulated system stops stretching when the strain is 20%.\u003c/p\u003e"},{"header":"3. Simulation results and discussion","content":"\u003cp\u003e3.1 Effect of hydrogen atom concentrations on mechanical performance of polycrystalline Fe model\u003c/p\u003e\n\u003cp\u003eFig.3 presents the stress-strain curves of polycrystalline Fe with varying hydrogen atom concentrations subjected to tensile loading at a room temperature of 300 K. Observations reveal that the strain-stress curves exhibit analogous changing trends. Notably, as the concentration of hydrogen increases, there is a discernible reduction in peak stress across various extents, accompanied by a decrease in the strain required to reach this maximum peak stress. As the tensile strain escalates, the stress increases continuously; Upon the strain reaches a threshold, the stress attains the peak; When the stress exceeds the peak value, the system enters the fracture stage, during which defects emerge, and the stress precipitously declines to a stable level. Subsequently, as the strain continues to increase, the stress fluctuates around this equilibrium value. The stress-strain curves obtained from the simulation system during tension closely mirror those reported by Xu[27], thus further verifying the accuracy of the model.\u003c/p\u003e\n\u003cp\u003eCalculate the slope of each curve during the elastic stage to determine Young\u0026apos;s modulus for each model. The peak stress (tensile strength) and the corresponding strain for each stress-strain curve are also counted. These parameters serve to assess the strength and ductility of the polycrystalline Fe model respectively,\u0026nbsp;with higher values indicating superior material properties.\u0026nbsp;In the macroscopic experiments, the presence of numerous dislocations in the material typically results in lower stress levels compared to those of an ideal crystal.\u0026nbsp;Consequently, variations in stress levels are primarily attributed to dislocations and slips. Therefore, the peak stress observed in this paper is notably higher than that observed in the macroscopic experiment.\u003c/p\u003e\n\u003cp\u003eTab.1 Essential parameters of mechanical properties for polycrystalline Fe models with different hydrogen atom concentrations at 300 K\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eHydrogen atom concentration (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eYoung\u0026apos;s modulus (GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eTensile strength (GPa)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003eStrain at maximum stress (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e198.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e15.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e5.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e1.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e195.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e14.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e1.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e7.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e185.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e13.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e1.33\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e9.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e183.32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e9.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25%\"\u003e\n \u003cp\u003e2.14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe curves of tensile strength and Young\u0026apos;s modulus for these models under tensile loading have been plotted, as depicted in Fig. 4. At a hydrogen concentration of 0%, the polycrystalline Fe model exhibits an ultimate tensile strength of 15.29 GPa and Young\u0026apos;s modulus of 198.59 GPa. Conversely, when the hydrogen concentration increases to 9.2%, the tensile strength drops to a minimum of 9.98 GPa and Young\u0026apos;s modulus decreases to 183.32 GPa, reflecting reductions of 34.7% and 7.69% in tensile strength and Young\u0026apos;s modulus. These findings decisively demonstrate that the mechanical properties of polycrystalline Fe decrease significantly with the climb of the volume fraction of hydrogen atoms, which further verifies the destructive effect of hydrogen on the structure and mechanism of materials. Concurrently, both the tensile strength and Young\u0026apos;s modulus exhibit a decline with the rising hydrogen concentration. This shows that under the same conditions, a higher hydrogen concentration results in diminished tensile strength of the polycrystalline iron model, reducing its capacity to withstand deformation and increasing its susceptibility to failure. Their presence alters the interatomic forces among iron atoms, causing some to deviate from their original lattice positions and leading to lattice distortion. Such distortion impacts not only the microstructure of the material but also compromises its overall mechanical properties.\u003c/p\u003e\n\u003cp\u003e3.2 Influence of hydrogen atom concentration on microscopic phase transformation of polycrystalline Fe model\u003c/p\u003e\n\u003cp\u003eFig.5 illustrates the structural transformation process of the polycrystalline Fe model under tensile loading at varying hydrogen atom concentrations. Initially, within a small deformation range, the model largely retains the original atomic arrangement. However, as deformation progresses, distortion at the grain boundaries intensifies, vacancies proliferate, and grain boundary energy escalates. This sequence of changes results in the rupture of several metal bonds near the grain boundaries, initiating crack formation at these sites. The model then transitions into the plastic deformation stage, continuing until through-holes develop in the crystal, ultimately leading to its failure. Furthermore, atomic dislocations, hole nucleation, and crack propagation all originate from the grain boundary. This phenomenon occurs because the grain boundary acts as a transitional zone between different grains within the crystal, and the discontinuity and irregularity in its atomic arrangement result in notable differences in mechanical properties. Primarily, due to its structural discontinuity, the grain boundary frequently serves as the origin or accumulation point for dislocations. Additionally, stress concentration at these boundaries facilitates the formation and movement of dislocations. Secondly, the structural discontinuity of the grain boundary, coupled with the relative weakening of atomic bonding forces, predisposes these areas to hole nucleation. This tendency is particularly pronounced under tensile stress, where the formation and expansion of holes become more evident. Lastly, the inherent non-uniformity and weakened characteristics of grain boundaries facilitate the initial formation of cracks in these regions, which then propagate swiftly along the grain boundaries.\u003c/p\u003e\n\u003cp\u003eAccording to the classical dislocation transport theory, hydrogen atoms can migrate in the crystal with dislocation, which significantly accelerates its diffusion speed in the crystal and leads to the significant enrichment of hydrogen at the grain boundary. In addition, the existence of hydrogen atoms promotes the occurrence of coplanar slip, which further accelerates the spread and migration of hydrogen. Hydrogen atoms can also reduce the binding energy between atoms, thus weakening the mechanical strength of grain boundaries or phase boundaries. Grain boundary fractures arise as a result of the significant stress concentration at the grain boundary brought on by the acceleration of hydrogen atoms\u0026apos; collecting speed at the grain boundary caused by an increase in material deformation. The existence of these cracks significantly accelerates the brittle fracture process along the grain boundary.\u003c/p\u003e\n\u003cp\u003eFig. 6 depicts how hydrogen atoms promote the formation of holes and the evolution of the internal surface of the model during grain boundary. In addition, Fig. 6 provides statistical data on the total surface area of voids and fracture surfaces throughout the deformation process. It is evident from the depiction that as strain increases, the voids in the polycrystalline Fe model progressively enlarge due to the influence of hydrogen atoms, and cracking even occurs along the grain boundaries. The data show that in the polycrystalline Fe model with hydrogen atom segregation concentrations of 0.1 and 0.2, compared with the sample with higher hydrogen concentration, there are fewer voids and a smaller surface area of defects. Especially, in the polycrystalline Fe model with a hydrogen atom concentration of 0.3, there is a marked increase in surface area during the deformation, whereas models with the other two concentrations exhibit only minor changes in surface area. Although the polycrystalline Fe alloy with the highest concentration of hydrogen atom segregation displays the smallest defect surface area during the tensile process, which indicates that the existence of excessive hydrogen atoms may directly lead to the fracture of the polycrystalline Fe model, overall, the higher the concentration of hydrogen atoms, the more defect surface area is produced in the polycrystalline Fe model, which further proves the destructive effect of hydrogen atoms in the material.\u003c/p\u003e\n\u003cp\u003eFig.7 employs von Mises shear stress to delineate and analyze deformation, illustrating local deformation in areas undergoing phase transformation. Notably, substantial stress concentration was observed around voids, predominantly located in high-energy grain boundary regions. Although the presence of a modest quantity of hydrogen atoms does not suffice to alter the BCC phase transformation as the primary mechanism of plastic deformation, it does facilitate the early generation of dislocations. The slippage of these dislocations causes local plastic deformation around nano-holes, markedly altering their shape, enhancing the likelihood of void growth and coalescence, and potentially precipitating macroscopic hydrogen embrittlement. From a mechanical response perspective, dislocation slip necessitates increased shear stress. Consequently, the polycrystalline Fe model containing more hydrogen atoms exhibits a lower threshold for the initiation of plastic deformation. This indicates that hydrogen presence diminishes the material\u0026rsquo;s resistance to external loads, enabling plastic deformation under reduced stress, thereby hastening the material\u0026apos;s failure process.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eUtilizing molecular dynamics simulation, the failure behavior of polycrystalline Fe models with varying hydrogen concentrations has been investigated from a microscopic perspective, revealing the interactions between hydrogen and pure iron pipelines as well as the underlying failure mechanisms. The changes in crystal structure under tensile stress loading were observed and analyzed. The following is a summary of the main findings:\u003c/p\u003e\n\u003cp\u003e(1) The stress-strain curves of the polycrystalline Fe model with varying hydrogen concentrations exhibit similar trends, with tensile strength, Young\u0026apos;s modulus, and strain at maximum stress all decreasing as hydrogen atom concentration increases. Specifically, the maximum tensile strength and Young\u0026apos;s modulus are 15.29 GPa and 198.59 GPa, at 0% hydrogen concentration, while the minimum values are 9.98 GPa and 183.32 GPa at 9.2% hydrogen concentration, reflecting reductions of 34.7% and 7.69%.\u003c/p\u003e\n\u003cp\u003e(2) The infiltration and accumulation of hydrogen atoms at grain boundaries induce significant structural distortions and stress concentrations, leading to increased grain boundary energy, the rupture of metal bonds, and the initiation and propagation of cracks. These phenomena collectively facilitate plastic deformation under tensile load, the formation of through-holes, and expedite the brittle fracture process along grain boundaries.\u003c/p\u003e\n\u003cp\u003e(3) The presence of hydrogen atoms markedly lowers the trigger stress for plastic deformation in materials, indicating that hydrogen accumulation diminishes the material\u0026apos;s resistance to external loads and accelerates the failure process. This finding holds substantial scientific and engineering significance for understanding and preventing hydrogen embrittlement.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor contribution \u0026nbsp;\u003c/strong\u003eFeng Zhang designed the experiments. Youran Zhi, Qiaoyun Tang, and Deyong Wang investigated the traits. Youran Zhi and Qiaoyun Tang analyzed the data and wrote the manuscript; Feng Zhang and Liu Yang revised and edited the manuscript. All the authors have read and approved the fnal manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding \u0026nbsp;\u003c/strong\u003eThis project was supported by National Natural Science Foundation of China (51505212，52005248), Scientific research fund project of Nanjing Institute of Technology (CKJA202101), Natural Science Foundation of Jiangsu Province (BK20201031).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability \u0026nbsp;\u003c/strong\u003eAll data generated or analyzed in this study are included in this published article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests \u0026nbsp;\u003c/strong\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDirk Ponge, Franz Roters, Alisson Kwiatkowski Da Silva, Karo Sedighiani,Vitesh Shah (2020) Current Challenges and Opportunities in Microstructure-Related Properties of Advanced High-Strength Steels. 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American Physical Society 9:57. https://doi.org/10.1103/PHYSREVB.57.5140\u003c/li\u003e\n\u003cli\u003eXu T. H., Zhu Z. Q., Geng S. F.,Song H. Y. (2017) Molecular dynamics study of effect of hydrogen atoms on mechanical properties of \u0026alpha; -Fe nanowires. Physics Letters A 381:3222-3227. https://doi.org/https://doi.org/10.1016/j.physleta.2017.08.012\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Polycrystalline Fe, Hydrogen embrittlement, Grain boundary segregation, Mechanical performance","lastPublishedDoi":"10.21203/rs.3.rs-4303209/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4303209/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Molecular dynamics simulation method has been adopted to scrutinize the reactions of hydrogen atom segregation within the grain boundary affect zones of a polycrystalline Fe model. The primary focus is to discern the influence of varied hydrogen concentrations on the failure behaviors exhibited during plastic deformation. The investigation aims to straighten out the mechanical characteristics and failure mechanisms at the microscale in polycrystalline iron. Moreover, the study monitors and analyzes alterations in the crystal structure of the polycrystalline iron model under tensile loading, employing the common neighbor analysis technique. Findings indicate that tensile strength, Young's modulus, and strain when reaching the tensile strength diminish as hydrogen concentration increases, thereby heightening the propensity for failure in polycrystalline iron. In stress conditions, the congregation of hydrogen atoms tends to facilitate dislocation, void formation, and precipitate brittle fractures. The insights garnered from this investigation not only enhance our comprehension of micro-failure mechanisms in hydrogen-affected infrastructures but also furnish essential theoretical support for ensuring the reliability and safety of hydrogen transmission pipelines.","manuscriptTitle":"Simulation study on mechanical properties of nanocrystalline Fe with hydrogen atom segregated on grain boundaries","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-26 09:59:18","doi":"10.21203/rs.3.rs-4303209/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0e29725c-c2d9-41be-8046-3c6c42e74939","owner":[],"postedDate":"April 26th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-18T14:40:53+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-26 09:59:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4303209","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4303209","identity":"rs-4303209","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}