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Origin of hydrogen embrittlement in vanadium-based hydrogen separation membranes
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Origin of hydrogen embrittlement in vanadium-based hydrogen separation membranes Won-Seok Ko a, Jong Bae Jeon a, Jae-Hyeok Shim b, Byeong-Joo Lee a,c,* a
Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea b High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea c Division of Advanced Nuclear Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea
article info
abstract
Article history:
Hydrogen embrittlement in metals is a challenging technical issue in the proper use of
Received 9 May 2012
hydrogen energy. Despite extensive investigations, the underlying mechanism has not been
Received in revised form
clearly understood. Using atomistic simulations, we focused on the hydrogen embrittlement
14 June 2012
in vanadium-based hydrogen separation membrane. We found that, contrary to the
Accepted 15 June 2012
conventional reasoning for the embrittlement of vanadium, the hydrogen-enhanced local-
Available online 21 July 2012
ized plasticity (HELP) mechanism is the most promising mechanism. Hydrogen enhances the nucleation of dislocations near the crack tip, which leads to the localized plasticity, and
Keywords:
eventually enhances the void nucleation that leads to the failure. Those results provide an
Hydrogen separation membrane
insight into the complex atomic scale process of hydrogen embrittlement in vanadium and
Hydrogen embrittlement
also help us design a new alloy for hydrogen separation membranes.
Vanadiumehydrogen
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
Atomistic simulation
reserved.
Modified embedded-atom method
1.
Introduction
Hydrogen is one of the most favorable energy sources to replace limited fossil fuels, reduce pollution and minimize the threat of global climate change, because of its natural abundance and the nonpolluting nature of combustion products (H2O). With these advantages, materials employed in the manufacture, storage and transport of hydrogen also receive a great attention these days. However, metallic materials used in hydrogen environments often suffer from the degradation of mechanical properties [1]. This phenomenon named as hydrogen embrittlement and reported as early as 1875 [2], has been extensively studied over the
century, but the underlying mechanism is still poorly understood. One of the important materials groups that face a challenge to overcome the hydrogen embrittlement is metallic hydrogen separation membranes for an efficient manufacturing of hydrogen gas [3]. Palladium and its alloys are the most commonly used membrane materials because of their high hydrogen permeability, relatively good mechanical characteristics and highly catalytic surface. Unfortunately, the extremely high cost is dragging down their practical applications, and recent researches have been focused on the development of non-palladium based membranes using economically feasible metals [3]. Vanadium is a promising
* Corresponding author. Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea. Tel.: þ82 54 2792157; fax: þ82 54 2792399. E-mail address: [email protected] (B.-J. Lee). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2012.06.075
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Nomenclature C CNA G GCMC HEDE HELP KI KII LEFM MD
elastic constants, Pa common neighbor analysis shear modulus, Pa grand canonical Monte Carlo hydrogen-enhanced decohesion hydrogen-enhanced localized plasticity mode I stress intensity factor, Pa(m)0.5 mode II stress intensity factor, Pa(m)0.5 linear elastic fracture mechanics molecular dynamics
candidate because of not only its relatively low cost but also its high hydrogen permeability [4]. In spite of these advantages, the membranes based on vanadium usually suffer from severe hydrogen embrittlement during the hydrogen separation process. For the development of more accessible metallic hydrogen membranes and the facilitation of hydrogen economy, it is important to clarify the governing mechanism of hydrogen embrittlement in metallic membrane materials. The effect of hydrogen is difficult to analyze experimentally because its role in mechanical behavior of metals is related with highly localized atomic scale phenomena. Since hydrogen embrittlement was first reported, a great amount of research effort has been made to understand the hydrogenrelated degradation of metals, but resulted in an enormous number of sometimes controversial findings and/or interpretations. The inherent difficulty in experimental approaches to the hydrogen embrittlement presents an opportunity for atomistic simulations that provide clear information on the structural evolution on an atomic scale. First-principles calculations provide the most accurate results on the atomic scale. However, because of the size limit (number of atoms) it is often more efficient to consider atomistic simulations such as molecular statics (MS), molecular dynamics (MD) and Monte Carlo (MC) simulation combined with (semi-)empirical interatomic potentials that can deal with more atoms than first-principles calculations by several orders. In the present study, we performed a series of atomistic simulations using the Large-scale atomic/molecular massively parallel simulator (LAMMPS) [5] to find out the most dominant mechanism of hydrogen embrittlement in vanadium-based hydrogen separation membranes.
2. Mechanisms for the hydrogen embrittlement Several mechanisms have been suggested so far to explain the hydrogen embrittlement phenomenon and three candidates acquired much attention [6]. The first is the hydride formation mechanism which explains the embrittlement by the formation of brittle hydride precipitates [7,8]. The second is the hydrogen-enhanced decohesion (HEDE) mechanism which explains the embrittlement by the decrease of atomic bonding strength at crack tip or interfaces with the presence of hydrogen atoms [9,10]. The last mechanism is the hydrogen-
MEAM modified embedded-atom method MS molecular statics PCT pressureecomposition isotherms S elastic compliances, Pa1 VeH vanadiumehydrogen 2NN MEAM second nearest-neighbor modified embeddedatom method unstable stacking fault energy gus n Poisson’s ratio hydrostatic stress, Pa sm von Mises stress, Pa svon c stress triaxiality
enhanced localized plasticity (HELP) [11]. In the HELP mechanism, it is considered that the presence of hydrogen causes local instability associated with a plastic flow by either promoting the nucleation of dislocations [12,13] or increasing the mobility of dislocations [14,15]. The hydride formation has long been considered to be the governing mechanism of hydrogen embrittlement in vanadium and its alloys [16], since vanadium is a hydride-forming metal at ambient temperatures and high hydrogen concentrations [17]. If we only focus on the embrittlement behavior at relatively low temperature and high hydrogen concentrations, the explanation by hydride formation mechanism seems apparently reasonable. For example, Nishimura et al. [18] evaluated the effect of the alloying addition (Ni) in hopes of preventing the formation of brittle hydrides and decreasing the hydrogen solubility. According to their result, the membranes of Ve10 at%Ni and Ve15 at%Ni alloys without VeNi intermetallic compounds show strong resistance to the embrittlement. They explained the results by the depression of the miscibility gap toward lower temperatures due to the addition of nickel, showing no existence of plateau in pressureecomposition isotherms (PCT) curves. However, there are several experimental evidences that throw doubt on the hydride formation mechanism. Recently, Yukawa et al. [19] clearly showed that hydrogen embrittlement in vanadium occurs not only at ambient temperatures but also at the operation temperature of the hydrogen separation where the temperature is 200e300 K higher than the formation temperature of stable hydrides. According to their result, the embrittlement was observed while the PCT curve indicates no existence of plateau. Furthermore, Owen and Scott [20] disputed the proposition that the formation of hydrides is the main cause of the embrittlement, because a ductility drop occurred even in the absence of hydrides at high temperatures and lower hydrogen concentrations and there was no severe embrittlement at the very low temperature (77 K), although the volume fraction of hydride was large enough. From this result, they emphasized the effect of mobile hydrogen atoms in bcc solid solution on the embrittlement. It should be also mentioned here that the effect of nickel addition in Nishimura et al.’s work [18] could be explained not only by the depression of the miscibility gap but also by the decrease of the hydrogen solubility in bcc solid solution as shown in their paper. To summarize, the hydride formation mechanism is inadequate to explain the general embrittlement behavior at
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wide ranges of temperatures and hydrogen concentrations in vanadium alloys. Instead, the remaining possible mechanisms, HEDE and HELP are needed to be further investigated because these mechanisms are not associated with the hydrides but associated with hydrogen in bcc solid solution. Therefore, we intended to find out the most dominant mechanism of hydrogen embrittlement in vanadium-based hydrogen separation membranes focusing on the HEDE and HELP. We will discuss again the hydrides-related embrittlement behavior later on showing that it is well within the explanation by the above-mentioned candidate governing mechanisms, HEDE and HELP.
3.
Methodology
3.1.
Interatomic potential
All simulations performed in this study employed the second nearest-neighbor modified embedded-atom method (2NN MEAM) interatomic potential. To simulate the atomic interactions between vanadium and hydrogen in a semi-empirical way, an interatomic potential that can describe vanadium and hydrogen simultaneously using a common formalism is necessary. From this point of view, the modified embeddedatom method (MEAM) interatomic potential, proposed by Baskes [21], is highly applicable because it can describe a wide
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however, the present work focuses on the HEDE and HELP mechanisms which are not associated with hydrides but associated with hydrogen atoms in bcc vanadium. The other weakness of the potential is that the migration energy barrier of hydrogen in bcc vanadium is deviated from experimental values by about one order. However, if we are concerned only with the final equilibrium distribution of hydrogen for further simulations, the problems related to the transition state of hydrogen can be avoided by using the alternative simulation method such as equilibrium Monte Carlo simulation. Therefore, even with the incompleteness of the interatomic potential, by successfully describing the behaviors of bcc solid solution, it is believed that the use of this potential would be relevant for the investigation of the hydrogen embrittlement. Since the 2NN MEAM formalism includes up to second nearest-neighbor interactions, a radial cutoff distance should be at least larger than the second nearest-neighbor distance in structures under consideration. All calculations were per˚ which is larger formed with a radial cutoff distance of 4.2 A than the second nearest-neighbor distance of bcc vanadium.
3.2. Linear elastic fracture mechanics (LEFM) equations for the displacement near a crack tip Sih and Leibowitz [26] found a plane-strain solution for the anisotropic displacement field around a crack tip. Under the mode-I loading, the displacements are given by
rffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii r 1 h cos q þ m1 sin q þ m1 m22 S011 m2 S016 þ S012 cos q þ m2 sin q ; Re m2 m21 S011 m1 S016 þ S012 pffi m1 m2 rffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 1 1 0 1 0 uy ¼ KI m2 S22 S026 þ m1 S012 S22 S026 þ m2 S012 Re cos q þ m1 sin q þ m1 cos q þ m2 sin q p m1 m2 m1 m2 ux ¼ KI
(1)
and under the mode-II loading, the displacements are given by
rffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii r 1 h 2 0 cos q þ m1 sin q þ m2 S11 m2 S016 þ S012 cos q þ m2 sin q ; Re m1 S11 m1 S016 þ S012 pffi m1 m2 rffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 1 1 0 1 0 uy ¼ KII S22 S026 þ m1 S012 S22 S026 þ m2 S012 Re cos q þ m1 sin q þ cos q þ m2 sin q p m1 m2 m1 m2 ux ¼ KII
range of elements (fcc, bcc, hcp, diamond-structured and even gaseous elements) using a common mathematical formalism. Recently, the MEAM is modified again by Lee and Baskes [22] to partially consider second nearest-neighbor interactions overcoming some critical shortcomings of the original MEAM. Detailed formulation for 2NN MEAM formalism is available in literature [22e24]. In the present work, the 2NN MEAM potential for the VeH binary system by Shim et al. [25] was taken without any modification. The potential reasonably reproduces the fundamental physical properties (thermodynamic, elastic and volumetric properties) of V-rich bcc solid solution and some of vanadium hydride phases. The main weakness of this potential is that the heat of formation of b1-V2H hydride is too negative. As stated,
(2)
where KI and KII are stress intensity factors for the mode-I and mode-II loading, respectively, r and q are the cylindrical coordinates with the origin at the crack tip position, and m1 and m2 are roots of the following characteristic equation, S011 m4 2S016 m3 þ 2S012 þ S066 m2 2S026 m þ S022 ¼ 0
(3)
The reduced elastic constants S0ij in Voigt notation are derived from the elastic compliance matrix Sij as follows:
S0ij ¼ Sij
Si3 Si3 S33
(4)
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The plane-strain solution for the isotropic displacement field around a crack tip under the mode-I loading is given by,
3.4. Molecular statics simulation for mode-I fracture of bi-crystals
rffiffiffiffiffiffi r q 2 q cos 1 2n þ sin ; 2p 2 2 rffiffiffiffiffiffi KI r q q uy ¼ sin 2 2n cos2 G 2p 2 2
The purpose of this simulation is to investigate the effect of hydrogen on the fracture behavior of bcc vanadium bi-crystals, as a means to examine the validity of the HEDE mechanism on a grain boundary. The shape and size of the specimens used for mode-I fracture simulations on bi-crystals are the same as those of single crystals. The bi-crystal specimen used in this study has a grain boundary at the center as shown in Fig. 1(b). The grain boundary considered is a S33 symmetrical tilt boundary with ½110 axis of rotation, (118) boundary plane and misorientation angle of 20.0 . The equilibrium grain boundary structure is obtained considering a certain rigid-body translation of one grain relative to the other grain. This translation is performed without a crack, and the most stable configuration is selected for further simulations. The procedure for the crack propagation simulation, the division of the specimen into two regions and assigning displacement field to the outer boundary region, used for single crystals is also used for bi-crystals. However, the type of LEFM equations used for the calculation of displacement field and the way of generating hydrogen charged specimens are changed. It is natural to use the anisotropic solution for the displacement field (Eqs. (1), (3) and (4)) when performing simulations on single crystals. Isotropic solution (Eq. (5)) must be for polycrystalline specimens. However, since the solution for bi-crystals is not available in a simple analytical form, one should make a difficult choice between the two solutions. The use of anisotropic solution would yield different simulation results depending on the choice of coordinate in the solution. Based on this and the previous work [27] reporting that the use of the isotropic solution should be less problematic than the use of the anisotropic solution, we use the isotropic solution. The use of the isotropic solution may cause a computational error in absolute value of the stress intensity factor for the crack propagation. However, the purpose of the present study is not to estimate the absolute values of the critical stress
ux ¼
KI G
(5)
where KI is the stress intensity factor, r and q are the cylindrical coordinates with the origin at the crack tip position, G is the shear modulus, and n is the Poisson’s ratio.
3.3. Molecular statics simulation for mode-I fracture of single crystals The purpose of this simulation is to investigate the effect of hydrogen on the fracture behavior of bcc vanadium single crystals, as a means to examine the validity of the HEDE mechanism. Cylindrical specimens as shown in Fig. 1(a) are generated for mode-I fracture simulations. An atomically sharp crack is inserted into each specimen by applying the anisotropic displacement field calculated by the linear elastic fracture mechanics (LEFM) equations (Eqs. (1), (3) and (4)) with a given initial stress intensity factor value. Then, the specimen is divided into two regions. One is the outer boundary region where the atomic positions are fixed and the other is the inner region where a free evolution of atomic configuration is allowed under the constraint by the outer boundary region. The loading is applied by assigning an incremental displacement field to the outer boundary region. The amount of incremental displacement field is updated using the LEFM equations with an incremental stress intensity factor (DKI ¼ 0.008 MPa(m)0.5) and the position of the crack tip step by step. During the loading simulation, a periodic boundary condition is applied along the crack tip front (z direction in Fig. 1(a)) to simulate the plane strain condition and avoid unintended surface effects.
Fig. 1 e (a) Single crystal specimen for mode-I fracture simulation. (b) Bi-crystal specimen for mode-I fracture simulation, containing a S33 symmetrical tilt grain boundary. In the atomistic configuration, gray spheres represent vanadium atoms and dark brown (black) spheres represent hydrogen atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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intensity factor, but to compare the crack propagation behavior of pure vanadium and hydrogen charged vanadium bi-crystal specimens. For the comparison, the isotropic approximation is thought to be suitable enough to provide qualitatively meaningful results.
3.5. Molecular statics simulation for the nucleation of dislocations in single crystals The purpose of this simulation is to investigate the effect of hydrogen on the nucleation of {112}<111> edge dislocation in bcc vanadium, as a means to examine the validity of the HELP mechanism. Generally, bcc metals have two slip systems, {110}< 111> and {112}<111>. Considering that only the {112} slip plane shows a distortion in the presence of hydrogen, and that materials with the {112} slip not activated are less sensitive to hydrogen [28e30], we considered only the {112}<111> edge dislocation. The shape of specimens is similar to that for the mode-I simulation. The specimens are oriented so that the [111] and ½112 correspond to the direction of crack propagation and normal direction of the crack plane, respectively. To introduce ˚ a mode-II initial crack into the specimen, atoms within 4.5 A thickness of (111) layers are removed as shown in Fig. 2. The loading simulation is performed by imposing an increment of stress-intensity factor (DKII ¼ 0.008 MPa(m)0.5) to the pre-separated boundary region according to the anisotropic solution of Mode-II crack tip (Eqs. (2)e(4)). In the case of hydrogen charged specimens, 30 independent simulations at each hydrogen concentration are performed and the critical stress intensity factor for the nucleation of dislocations is determined by averaging the 30 resultant values to diminish the statistical error.
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connects the atomistic scale nucleation of dislocations and the macroscale ductile rupture. A cube type pure vanadium single crystal with about 250,000 atoms is prepared, and given amounts of hydrogen atoms are randomly distributed to generate hydrogen charged specimens. After equilibration at 650 K for 100 ps with a Nose/Hoover isobariceisothermal (NPT) ensemble, tensile loadings are applied into two different directions, [110] and [111], with three-dimensional periodic boundary condition. During the loading the sample dimensions perpendicular to the loading direction are kept constant to induce triaxial stress states. A constant strain rate of 5 108/s is introduced until voids start to nucleate and the atomic configurations are visualized using a common neighbor analysis (CNA) algorithm [31]. Three different quantities, the hydrostatic stress, the von Mises stress and the stress triaxiality, are calculated and compared for specimens with a wide range of hydrogen concentration. The hydrostatic stress is calculated using the following equation, 1 sm ¼ skk ; 3
(6)
where skk represents the diagonal components of stress tensor. The von Mises stress is calculated using svon ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ij s sm dij sij sm dij 2
(7)
and the stress triaxiality using c¼
sm : svon
(8)
4.
Results and discussion
3.6. Molecular dynamics simulation for the void nucleation in single crystals
4.1.
Hydrogen effect on the crack propagation
The purpose of this simulation is to investigate the effect of hydrogen on the void nucleation, a probable mechanism that
To examine the validity of the HEDE mechanism, we compared mode-I (tensile) crack propagation behaviors of
Fig. 2 e (a) Single crystal specimen of mode-II simulation of the nucleation of dislocations. (b) Snapshots of pure vanadium and hydrogen charged vanadium specimens before and after the nucleation of dislocations. The color of atoms is scaled according to sxx stress. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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pure vanadium and hydrogen charged vanadium using two different series of MS simulations, one using single crystals and the other using bi-crystal specimens. In the case of single crystals, simulation specimens with four different crack orientations were prepared as indicated in Table 1 [32]. The number of total atoms in pure vanadium specimen is around 200,000 and given amounts (5, 20 at%) of hydrogen atoms are randomly distributed into the tetrahedral interstitial sites to generate hydrogen charged specimens. No special effort is made to increase the hydrogen concentration in the vicinity of the crack tip as frequently has been done in simulations of hydrogen embrittlement, since the hydrogen content in practical vanadium-based hydrogen separation membranes and the present specimen is already high (up to 20 at%). Fig. 3 shows the deformation behavior near the crack tip of specimens with different crack orientations, hydrogen contents and stress levels. It is shown that pure vanadium specimens do not show a cleavage fracture but are associated with a formation of twins or dislocations. Similar deformation and crack tip blunting are observed also for all the hydrogen charged specimens without any evidence of the hydrogenenhanced decohesion. The second series of simulations were performed using bicrystals containing a S33 symmetrical tilt grain boundary with and without segregated hydrogen atoms. This was to investigate the effect of hydrogen on the grain boundary decohesion. When generating hydrogen charged specimens using single crystals, we randomly distribute given amounts of hydrogen atoms in a pure vanadium specimen, as already mentioned. However, in the case of bi-crystals that contain a grain boundary, we have to consider the probable grain boundary segregation of hydrogen atoms. The best way to distribute solute atoms in thermodynamically inhomogeneous specimens is to use a Grand Canonical Monte Carlo (GCMC) simulation [33]. Therefore, we use a GCMC simulation to distribute hydrogen atoms in the vanadium bi-crystal specimen. In order to focus on the effect of hydrogen atoms segregated on the grain boundary, the hydrogen contents in matrix are maintained relatively low compared to those in single crystal specimens. The selected hydrogen contents in matrix are 0.14, 1.05 and 1.74 at%, and the corresponding values for hydrogen contents on grain boundary are 16.8, 29.8 and 32.0 at%, respectively. The GCMC simulation is performed at 650 K and then quenched to 0 K for further MS simulations.
Table 1 e Summary of crack orientations considered for mode-I fracture simulations [32]. q is the angle between the direction of crack propagation and the slip direction. Orientation of specimen (Crack plane)[Crack direction] (001)[110] (110)[001] (111)½112
ð011Þ[011]
Slip system
q ( )
{112}<111> {110}<111> {112}<111> {112}<111> {112}<111> {112}<111> {110}<111> {110}<111>
35.3 90 54.7 125.3 90 19.5 35.3 90
In this case, we monitored the position of a crack tip during the crack propagation along the grain boundary as a function of stress intensity factor (KI). Fig. 4 shows the resultant crack resistance curves. The crack propagation distance in hydrogen charged vanadium is smaller than that in pure vanadium under the same stress intensity factor. This indicates that the segregation of hydrogen atoms does not cause any decohesion on the grain boundary.
4.2. Hydrogen effect on the nucleation behavior of dislocations With the results that indicate no validity of the HEDE mechanism, we focused on the validity of the HELP mechanism. We compared the nucleation behavior of dislocations in pure vanadium and hydrogen charged vanadium single crystal specimens using MS simulations of mode-II (shear) loading. Fig. 5(a) shows the change of critical stress intensity factor (KIIc) for the nucleation of an edge dislocation in a functional form of the hydrogen concentration. As the hydrogen concentration increases, KIIc for the nucleation of a dislocation decreases. This result indicates that the nucleation of dislocations is enhanced by hydrogen, supporting the HELP mechanism. It should be meaningful to compare the present result with a theoretical approach. Rice [34] proposed the critical stress intensity factor for the nucleation of an edge dislocation along the crack plane from a mode-II crack tip, as given in the following equation, KIIc
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Gslip gus ¼ 1n
Gslip ¼ ðC11 C12 þ C44 Þ=3
(9) (10)
where Gslip is the shear modulus along the slip plane, gus is the unstable stacking fault energy, n is the Poisson’s ratio and Cij is elastic constants. Fig. 5(b) shows the relation between the hydrogen concentration and elastic moduli calculated using the interatomic potential adopted in this study. The shear modulus (Gslip) calculated using Eq. (10) decreases as the hydrogen concentration increases. From Eq. (9), one can also expect that the KIIc for the emission of an edge dislocation decreases as the hydrogen concentration increases. This result is consistent with the present simulation given in Fig. 5(a) which was obtained by the direct observation of the nucleation event of a dislocation. It should be also mentioned here that Tal-Gutelmacher et al. [35] performed a nano-indentation test to examine the effect of hydrogen on the nucleation of dislocations in a vanadium (100) single crystal. They clearly showed that the homogeneous nucleation of dislocations is enhanced by the presence of hydrogen, which is generally consistent with the present finding.
4.3.
Hydrogen effect on the void nucleation process
Through the mode-I crack propagation and mode-II dislocation emission simulations, it can be concluded that the most promising mechanism of hydrogen embrittlement in
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vanadium is the HELP mechanism. However, an important issue remains unresolved: how is the hydrogen-enhanced dislocation emission, an atomic scale phenomenon, related with the fracture, a macroscale materials phenomenon? The most promising explanation may be that hydrogen induces a shear localization of the plastic flow and results in a highly localized ductile rupture [12,36]. It is widely accepted that the ductile rupture involves the nucleation, growth and coalescence of voids (or cracks). Also, it has been experimentally reported that hydrogen promotes void nucleation [37e39].
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However, it is not known how hydrogen atoms can promote the void nucleation. An effort to clarify the hydrogen-induced void nucleation process was made in the present study by using an MD simulation. The void nucleation typically occurs by decohesion of particleematrix interfaces or grain boundaries, but also occurs inside grains [40]. In the later case, the void nucleation is significantly facilitated by localized deformed structures such as shear band and triaxial stress state near the crack tip or second-phase particles. Therefore, a series of MD tensile
Fig. 3 e Deformation behavior of pure and hydrogen charged vanadium single crystal with different crack orientations, (a) (001)[110], (b) (110)[001], (c) (111)½112 and (d) ð011Þ[011], hydrogen content and stress level. The color of atoms is scaled according to sxx or syy stresses.
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Fig. 4 e Crack resistance curves obtained from MS simulations of pure vanadium and hydrogen segregated vanadium bicrystals containing a S33 symmetrical tilt grain boundary. The crack propagation directions are (a) ½441 and (b) ½441. In the atomistic configuration, gray spheres represent vanadium atoms and dark brown (black) spheres represent hydrogen atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
loading simulations were performed using single crystals of pure vanadium and hydrogen charged vanadium to study the triaxiality-driven void nucleation. Grain boundaries as the typical site for the void nucleation were not considered because the fracture path of the hydrogen charged vanadium was reported to be transgranular rather than intergranular [41], and the present MS simulation using bi-crystal specimens showed no sign of the grain boundary decohesion due to hydrogen. Fig. 6 shows the void nucleation process of pure vanadium single crystals, obtained by using the MD tensile loading simulations. The specimens were subjected to a continuous tensile loading at 650 K, the usual operation temperature of metallic hydrogen separation membranes. The calculated hydrostatic stress, von Mises stress and stress triaxiality are also illustrated. Initially, the specimen is deformed elastically. As the loading increases, the deformation mode is switched to
be plastic and the von Mises stress starts to decrease, leaving a maximum peak on the stress curve. This point can be defined as the “yield point”. After the yield point, the hydrostatic stress continues increasing until the void nucleation starts. Once the void nucleation starts, the hydrostatic stress decreases abruptly leaving a maximum peak on the stress curve. Concerning the void formation, the main finding of the present study is that the stress level necessary for the nucleation of voids is significantly lowered in hydrogen charged vanadium compared to pure vanadium. Fig. 7(a),(b) shows tensile stressestrain response of pure vanadium and hydrogen charged vanadium. One can see that the critical tensile stress and strain for the void nucleation decrease as the amount of hydrogen increases. Fig. 7(c),(d) shows the von Mises stressestrain response of pure vanadium and hydrogen charged vanadium. The yield stress and strain decrease as the
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Fig. 5 e (a) Relationship between the concentration of hydrogen and the critical stress intensity factor (KIIc) for the nucleation of dislocations. The KIIc values are averaged values of 30 independent simulations for each hydrogen concentration. (b) Relationship between hydrogen concentration and elastic constants or shear modulus.
amount of hydrogen increases, which leads to a conclusion that hydrogen makes the nucleation of dislocations and thus the nucleation of voids easier. This result is qualitatively consistent with the result given in Fig. 5(a), the decrease of KIIc with increasing hydrogen concentration in the Mode-II simulation for the nucleation of dislocations.
4.4. A suggestion for an alloy design to reduce the hydrogen embrittlement Through the investigation by atomistic simulations, it can be thought that the easiness of the void nucleation by hydrogen in bcc solid solution via the HELP mechanism can explain reasonably well the embrittlement of vanadium membranes. It should be also meaningful to discuss the embrittlement behavior at relatively low temperature and high hydrogen concentration where hydrides are reported to form. In general, the void nucleation can be significantly facilitated by the presence of the second-phase particles because of the local triaxial stress state easily developed near the particles [42]. Therefore, in the presence of hydrides as a kind of
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Fig. 6 e The void nucleation process of pure vanadium single crystals subjected to a continuous tensile loading along (a) [110] and (b) [111] directions at 650 K. The snapshots of the atomistic configuration before the void nucleation are visualized using a common neighbor analysis (CNA) algorithm and the snapshots after the void nucleation are visualized using the potential energy of individual atoms. In CNA snapshots, yellow (gray) atoms are in a perfect bcc structure and brown (black) atoms are in an unknown lattice structure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
second-phase particles, it is expected that the void nucleation would be facilitated with the help of hydrogen in bcc solid solution. Nonetheless, it is hard to say that the hydride formation is the governing mechanism of the embrittlement. An experimental work by Owen and Scott [20] indicates that the alloy with hydrides and without hydrogen in bcc solid solution does not cause severe embrittlement. According to their result, there is no severe embrittlement unless the volume fraction of hydride is large enough at very low temperature, 77 K. At this temperature, the hydrogen presumably exists only in the form of the hydride as can be seen in the phase diagram [17]. In the alloy design of metallic membrane materials, it is strongly recommended to avoid the formation of secondphase particles for better resistance to the embrittlement. During the above-mentioned void nucleation, the characteristic of second-phase particles has less importance because the void nucleation is not resulted from the break of particles
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Fig. 7 e (a), (b): The tensile stressestrain response and (c), (d): the von Mises stressestrain response of pure vanadium and hydrogen charged vanadium under triaxial stress states where tensile loadings are imposed along (a)(c)[110] and (b)(d)[111] directions and the sample dimensions perpendicular to the loading direction are kept constant.
but resulted from the triaxial stress state of matrix near the particles. In other words, the presence of the second-phase particle causes the embrittlement whether it is hydrides or not. This feature can well explain an interesting aspect of the experimental work by Nishimura et al. [18], according to which, the membranes of quenched Ve10 at%Ni and Ve15 at %Ni alloys without VeNi intermetallic compounds show relatively strong resistance to the embrittlement, while the same alloys with VeNi intermetallic compounds show severe embrittlement.
5.
Conclusion
Our results strongly support the HELP mechanism as the governing mechanism to explain the hydrogen embrittlement in vanadium-based hydrogen separation membranes. We could not observe any sign for the hydrogen enhanced decohesion (HEDE) inside a grain or on grain boundary. Instead, we could clearly observe that hydrogen enhances the nucleation of dislocations near the crack tip and eventually the localized plasticity. We also observed that hydrogen decreases the stress and strain level necessary for the nucleation of voids, which consequently enhances the ductile rupture. Our results provide an insight into the complex atomic scale process of
hydrogen embrittlement in vanadium-based hydrogen separation membranes. The result can also be used as a guidance of further experimental studies on the macroscopic hydrogen embrittlement phenomenon and the further development of suitable metallic hydrogen separation membranes.
Acknowledgments This work has been supported by Korea Institute of Science and Technology (2E22742).
references
[1] Louthan Jr MR, Swanson RE. Material defects, gas purity and hydrogen embrittlement. Int J Hydrogen Energy 1985;10: 551e4. [2] Johnson WH. On some remarkable changes produced in iron and steels by the action of hydrogen acids. Proc R Soc Lond 1875;23:168e75. [3] Dolan MD. Non-Pd BCC alloy membranes for industrial hydrogen separation. J Membr Sci 2010;362:12e28. [4] Steward SA. Review of hydrogen isotope permeability through materials. Lawrence Livermore National Laboratory Report; 1983. UCRL-53441.
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[5] Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 1995;117:1e19. [6] Myers SM, Baskes MI, Birnbaum HK, Corbett JW, DeLeo GG, Estreicher SK, et al. Hydrogen interactions with defects in crystalline solids. Rev Mod Phys 1992;64:559e617. [7] Westlake DG. Generalized model for hydrogen embrittlement. Trans ASM 1969;62:1000e6. [8] Shih DS, Robertson IM, Birnbaum HK. Hydrogen embrittlement of a titanium: in situ tem studies. Acta Metall 1988;36:111e24. [9] Troiano AR. The role of hydrogen and other interstitials in the mechanical behavior of metals. Trans ASM 1960;52: 54e80. [10] Kimura A, Birnbaum HK. Hydrogen induced grain boundary fracture in high purity nickel and its alloys-enhanced hydrogen diffusion along grain boundaries. Acta Metall 1988; 36:757e66. [11] Beachem CD. New model for hydrogen-assisted cracking (“hydrogen embrittlement”). Metall Trans 1972;3:437e51. [12] Robertson IM, Birnbaum HK. An HVEM study of hydrogen effects on the deformation and fracture of nickel. Acta Metall 1986;34:353e66. [13] Lynch SP. Environmentally assisted cracking: overview of evidence for an adsorption-induced localised-slip process. Acta Metall 1988;36:2639e61. [14] Sirois E, Birnbaum HK. Effects of hydrogen and carbon on thermally activated deformation in nickel. Acta Metall Mater 1992;40:1377e85. [15] Birnbaum HK, Sofronis P. Hydrogen-enhanced localized plasticity e a mechanism for hydrogen-related fracture. Mater Sci Eng A 1994;176:191e202. [16] Takano S, Suzuki T. An electron-optical study of b-hydride and hydrogen embrittlement of vanadium. Acta Metall 1974; 22:265e74. [17] Manchester FD, editor. Phase diagrams of binary hydrogen alloys. Materials Park, OH: ASM International; 2000. [18] Nishimura C, Komaki M, Amano M. Hydrogen permeation characteristics of vanadiumenickel alloys. Mater Trans JIM 1991;32:501e7. [19] Yukawa H, Nambu T, Matsumoto Y. VeW alloy membranes for hydrogen purification. J Alloys Compd 2011;509:S881e4. [20] Owen CV, Scott TE. Relation between hydrogen embrittlement and the formation of hydride in the group V transition metals. Metall Trans 1972;3:1715e26. [21] Baskes MI. Modified embedded-atom potentials for cubic materials and impurities. Phys Rev B 1992;46:2727e42. [22] Lee B-J, Baskes MI. Second nearest-neighbor modified embedded-atom-method potential. Phys Rev B 2000;62: 8564e7. [23] Lee B-J, Baskes MI, Kim H, Cho YK. Second nearest-neighbor modified embedded atom method potentials for bcc transition metals. Phys Rev B 2001;64:184102.
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[24] Lee B-J, Jang J-W. A modified embedded-atom method interatomic potential for the FeeH system. Acta Mater 2007; 55:6779e88. [25] Shim J-H, Lee Y-S, Fleury E, Cho YW, Ko W-S, Lee B-J. A modified embedded-atom method interatomic potential for the VH system. CALPHAD 2011;35:302e7. [26] Sih GC, Leibowitz H. Fracture, vol. 2. New York: Academic Press; 1968. [27] Farkas D. Bulk and intergranular fracture behaviour of NiAl. Philos Mag A 2000;80:1425e44. [28] Bastien P, Azou P. Influence l’e´crouissage sur le frottement inte´rieur du fer et de l’acier charge´s ou non en hydroge`ne. Compt Rend Acad Sci 1951;232:1845e8. [29] Taketomi S, Matsumoto R, Miyazaki N. Atomistic study of hydrogen distribution and diffusion around a {112}<111> edge dislocation in alpha iron. Acta Mater 2008;56:3761e9. [30] Matsumoto R, Taketomi S, Matsumoto S, Miyazaki N. Atomistic simulations of hydrogen embrittlement. Int J Hydrogen Energy 2009;34:9576e84. [31] Faken D, Jo´nsson H. Systematic analysis of local atomic structure combined with 3D computer graphics. Comput Mater Sci 1994;2:279e86. [32] Gordon PA, Neeraj T, Luton MJ, Farkas D. Crack-tip deformation mechanisms in a-Fe and binary Fe alloys: an atomistic study on single crystals. Metall Mater Trans A 2007; 38A:2191e202. [33] Frenkel D, Smit B. Understanding molecular simulation: from algorithms to applications. New York: Academic Press; 1996. [34] Rice JR. Dislocation nucleation from a crack tip: an analysis based on the Peierls concept. J Mech Phys Solids 1992;40: 239e71. [35] Tal-Gutelmacher E, Gemma R, Volkert CA, Kirchheim R. Hydrogen effect on dislocation nucleation in a vanadium (100) single crystal as observed during nanoindentation. Scripta Mater 2010;63:1032e5. [36] Liang Y, Sofronis P, Aravas N. The effect of hydrogen on plastic instabilities in metals. Acta Meter 2003;51:2717e30. [37] Louthan Jr MR, Caskey Jr GR, Donovan JA, Rawl Jr DE. Hydrogen embrittlement of metals. Mater Sci Eng 1972;10: 357e68. [38] Oriani RA, Josephic PH. Hydrogen-enhanced load relaxation in a deformed medium-carbon steel. Acta Metall 1979;27: 997e1005. [39] Thompson AW. Hydrogen-assisted fracture in single-phase nickel alloys. Scripta Metall 1982;16:1189e92. [40] Garrison Jr WM, Moody NR. Ductile fracture. J Phys Chem Solids 1987;48:1035e74. [41] Chung DW, Stoloff NS. Effect of hydrogen on fatigue crack propagation in vanadium. Metall Trans A 1978;9:71e8. [42] Horstemeyer MF, Gokhale AM. A void-crack nucleation model for ductile metals. Int J Solids Struct 1999;36:5029e55.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/he
Origin of hydrogen embrittlement in vanadium-based hydrogen separation membranes Won-Seok Ko a, Jong Bae Jeon a, Jae-Hyeok Shim b, Byeong-Joo Lee a,c,* a
Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea b High Temperature Energy Materials Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea c Division of Advanced Nuclear Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea
article info
abstract
Article history:
Hydrogen embrittlement in metals is a challenging technical issue in the proper use of
Received 9 May 2012
hydrogen energy. Despite extensive investigations, the underlying mechanism has not been
Received in revised form
clearly understood. Using atomistic simulations, we focused on the hydrogen embrittlement
14 June 2012
in vanadium-based hydrogen separation membrane. We found that, contrary to the
Accepted 15 June 2012
conventional reasoning for the embrittlement of vanadium, the hydrogen-enhanced local-
Available online 21 July 2012
ized plasticity (HELP) mechanism is the most promising mechanism. Hydrogen enhances the nucleation of dislocations near the crack tip, which leads to the localized plasticity, and
Keywords:
eventually enhances the void nucleation that leads to the failure. Those results provide an
Hydrogen separation membrane
insight into the complex atomic scale process of hydrogen embrittlement in vanadium and
Hydrogen embrittlement
also help us design a new alloy for hydrogen separation membranes.
Vanadiumehydrogen
Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
Atomistic simulation
reserved.
Modified embedded-atom method
1.
Introduction
Hydrogen is one of the most favorable energy sources to replace limited fossil fuels, reduce pollution and minimize the threat of global climate change, because of its natural abundance and the nonpolluting nature of combustion products (H2O). With these advantages, materials employed in the manufacture, storage and transport of hydrogen also receive a great attention these days. However, metallic materials used in hydrogen environments often suffer from the degradation of mechanical properties [1]. This phenomenon named as hydrogen embrittlement and reported as early as 1875 [2], has been extensively studied over the
century, but the underlying mechanism is still poorly understood. One of the important materials groups that face a challenge to overcome the hydrogen embrittlement is metallic hydrogen separation membranes for an efficient manufacturing of hydrogen gas [3]. Palladium and its alloys are the most commonly used membrane materials because of their high hydrogen permeability, relatively good mechanical characteristics and highly catalytic surface. Unfortunately, the extremely high cost is dragging down their practical applications, and recent researches have been focused on the development of non-palladium based membranes using economically feasible metals [3]. Vanadium is a promising
* Corresponding author. Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang 790-784, Republic of Korea. Tel.: þ82 54 2792157; fax: þ82 54 2792399. E-mail address: [email protected] (B.-J. Lee). 0360-3199/$ e see front matter Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2012.06.075
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Nomenclature C CNA G GCMC HEDE HELP KI KII LEFM MD
elastic constants, Pa common neighbor analysis shear modulus, Pa grand canonical Monte Carlo hydrogen-enhanced decohesion hydrogen-enhanced localized plasticity mode I stress intensity factor, Pa(m)0.5 mode II stress intensity factor, Pa(m)0.5 linear elastic fracture mechanics molecular dynamics
candidate because of not only its relatively low cost but also its high hydrogen permeability [4]. In spite of these advantages, the membranes based on vanadium usually suffer from severe hydrogen embrittlement during the hydrogen separation process. For the development of more accessible metallic hydrogen membranes and the facilitation of hydrogen economy, it is important to clarify the governing mechanism of hydrogen embrittlement in metallic membrane materials. The effect of hydrogen is difficult to analyze experimentally because its role in mechanical behavior of metals is related with highly localized atomic scale phenomena. Since hydrogen embrittlement was first reported, a great amount of research effort has been made to understand the hydrogenrelated degradation of metals, but resulted in an enormous number of sometimes controversial findings and/or interpretations. The inherent difficulty in experimental approaches to the hydrogen embrittlement presents an opportunity for atomistic simulations that provide clear information on the structural evolution on an atomic scale. First-principles calculations provide the most accurate results on the atomic scale. However, because of the size limit (number of atoms) it is often more efficient to consider atomistic simulations such as molecular statics (MS), molecular dynamics (MD) and Monte Carlo (MC) simulation combined with (semi-)empirical interatomic potentials that can deal with more atoms than first-principles calculations by several orders. In the present study, we performed a series of atomistic simulations using the Large-scale atomic/molecular massively parallel simulator (LAMMPS) [5] to find out the most dominant mechanism of hydrogen embrittlement in vanadium-based hydrogen separation membranes.
2. Mechanisms for the hydrogen embrittlement Several mechanisms have been suggested so far to explain the hydrogen embrittlement phenomenon and three candidates acquired much attention [6]. The first is the hydride formation mechanism which explains the embrittlement by the formation of brittle hydride precipitates [7,8]. The second is the hydrogen-enhanced decohesion (HEDE) mechanism which explains the embrittlement by the decrease of atomic bonding strength at crack tip or interfaces with the presence of hydrogen atoms [9,10]. The last mechanism is the hydrogen-
MEAM modified embedded-atom method MS molecular statics PCT pressureecomposition isotherms S elastic compliances, Pa1 VeH vanadiumehydrogen 2NN MEAM second nearest-neighbor modified embeddedatom method unstable stacking fault energy gus n Poisson’s ratio hydrostatic stress, Pa sm von Mises stress, Pa svon c stress triaxiality
enhanced localized plasticity (HELP) [11]. In the HELP mechanism, it is considered that the presence of hydrogen causes local instability associated with a plastic flow by either promoting the nucleation of dislocations [12,13] or increasing the mobility of dislocations [14,15]. The hydride formation has long been considered to be the governing mechanism of hydrogen embrittlement in vanadium and its alloys [16], since vanadium is a hydride-forming metal at ambient temperatures and high hydrogen concentrations [17]. If we only focus on the embrittlement behavior at relatively low temperature and high hydrogen concentrations, the explanation by hydride formation mechanism seems apparently reasonable. For example, Nishimura et al. [18] evaluated the effect of the alloying addition (Ni) in hopes of preventing the formation of brittle hydrides and decreasing the hydrogen solubility. According to their result, the membranes of Ve10 at%Ni and Ve15 at%Ni alloys without VeNi intermetallic compounds show strong resistance to the embrittlement. They explained the results by the depression of the miscibility gap toward lower temperatures due to the addition of nickel, showing no existence of plateau in pressureecomposition isotherms (PCT) curves. However, there are several experimental evidences that throw doubt on the hydride formation mechanism. Recently, Yukawa et al. [19] clearly showed that hydrogen embrittlement in vanadium occurs not only at ambient temperatures but also at the operation temperature of the hydrogen separation where the temperature is 200e300 K higher than the formation temperature of stable hydrides. According to their result, the embrittlement was observed while the PCT curve indicates no existence of plateau. Furthermore, Owen and Scott [20] disputed the proposition that the formation of hydrides is the main cause of the embrittlement, because a ductility drop occurred even in the absence of hydrides at high temperatures and lower hydrogen concentrations and there was no severe embrittlement at the very low temperature (77 K), although the volume fraction of hydride was large enough. From this result, they emphasized the effect of mobile hydrogen atoms in bcc solid solution on the embrittlement. It should be also mentioned here that the effect of nickel addition in Nishimura et al.’s work [18] could be explained not only by the depression of the miscibility gap but also by the decrease of the hydrogen solubility in bcc solid solution as shown in their paper. To summarize, the hydride formation mechanism is inadequate to explain the general embrittlement behavior at
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wide ranges of temperatures and hydrogen concentrations in vanadium alloys. Instead, the remaining possible mechanisms, HEDE and HELP are needed to be further investigated because these mechanisms are not associated with the hydrides but associated with hydrogen in bcc solid solution. Therefore, we intended to find out the most dominant mechanism of hydrogen embrittlement in vanadium-based hydrogen separation membranes focusing on the HEDE and HELP. We will discuss again the hydrides-related embrittlement behavior later on showing that it is well within the explanation by the above-mentioned candidate governing mechanisms, HEDE and HELP.
3.
Methodology
3.1.
Interatomic potential
All simulations performed in this study employed the second nearest-neighbor modified embedded-atom method (2NN MEAM) interatomic potential. To simulate the atomic interactions between vanadium and hydrogen in a semi-empirical way, an interatomic potential that can describe vanadium and hydrogen simultaneously using a common formalism is necessary. From this point of view, the modified embeddedatom method (MEAM) interatomic potential, proposed by Baskes [21], is highly applicable because it can describe a wide
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however, the present work focuses on the HEDE and HELP mechanisms which are not associated with hydrides but associated with hydrogen atoms in bcc vanadium. The other weakness of the potential is that the migration energy barrier of hydrogen in bcc vanadium is deviated from experimental values by about one order. However, if we are concerned only with the final equilibrium distribution of hydrogen for further simulations, the problems related to the transition state of hydrogen can be avoided by using the alternative simulation method such as equilibrium Monte Carlo simulation. Therefore, even with the incompleteness of the interatomic potential, by successfully describing the behaviors of bcc solid solution, it is believed that the use of this potential would be relevant for the investigation of the hydrogen embrittlement. Since the 2NN MEAM formalism includes up to second nearest-neighbor interactions, a radial cutoff distance should be at least larger than the second nearest-neighbor distance in structures under consideration. All calculations were per˚ which is larger formed with a radial cutoff distance of 4.2 A than the second nearest-neighbor distance of bcc vanadium.
3.2. Linear elastic fracture mechanics (LEFM) equations for the displacement near a crack tip Sih and Leibowitz [26] found a plane-strain solution for the anisotropic displacement field around a crack tip. Under the mode-I loading, the displacements are given by
rffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii r 1 h cos q þ m1 sin q þ m1 m22 S011 m2 S016 þ S012 cos q þ m2 sin q ; Re m2 m21 S011 m1 S016 þ S012 pffi m1 m2 rffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 1 1 0 1 0 uy ¼ KI m2 S22 S026 þ m1 S012 S22 S026 þ m2 S012 Re cos q þ m1 sin q þ m1 cos q þ m2 sin q p m1 m2 m1 m2 ux ¼ KI
(1)
and under the mode-II loading, the displacements are given by
rffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii r 1 h 2 0 cos q þ m1 sin q þ m2 S11 m2 S016 þ S012 cos q þ m2 sin q ; Re m1 S11 m1 S016 þ S012 pffi m1 m2 rffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 1 1 0 1 0 uy ¼ KII S22 S026 þ m1 S012 S22 S026 þ m2 S012 Re cos q þ m1 sin q þ cos q þ m2 sin q p m1 m2 m1 m2 ux ¼ KII
range of elements (fcc, bcc, hcp, diamond-structured and even gaseous elements) using a common mathematical formalism. Recently, the MEAM is modified again by Lee and Baskes [22] to partially consider second nearest-neighbor interactions overcoming some critical shortcomings of the original MEAM. Detailed formulation for 2NN MEAM formalism is available in literature [22e24]. In the present work, the 2NN MEAM potential for the VeH binary system by Shim et al. [25] was taken without any modification. The potential reasonably reproduces the fundamental physical properties (thermodynamic, elastic and volumetric properties) of V-rich bcc solid solution and some of vanadium hydride phases. The main weakness of this potential is that the heat of formation of b1-V2H hydride is too negative. As stated,
(2)
where KI and KII are stress intensity factors for the mode-I and mode-II loading, respectively, r and q are the cylindrical coordinates with the origin at the crack tip position, and m1 and m2 are roots of the following characteristic equation, S011 m4 2S016 m3 þ 2S012 þ S066 m2 2S026 m þ S022 ¼ 0
(3)
The reduced elastic constants S0ij in Voigt notation are derived from the elastic compliance matrix Sij as follows:
S0ij ¼ Sij
Si3 Si3 S33
(4)
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The plane-strain solution for the isotropic displacement field around a crack tip under the mode-I loading is given by,
3.4. Molecular statics simulation for mode-I fracture of bi-crystals
rffiffiffiffiffiffi r q 2 q cos 1 2n þ sin ; 2p 2 2 rffiffiffiffiffiffi KI r q q uy ¼ sin 2 2n cos2 G 2p 2 2
The purpose of this simulation is to investigate the effect of hydrogen on the fracture behavior of bcc vanadium bi-crystals, as a means to examine the validity of the HEDE mechanism on a grain boundary. The shape and size of the specimens used for mode-I fracture simulations on bi-crystals are the same as those of single crystals. The bi-crystal specimen used in this study has a grain boundary at the center as shown in Fig. 1(b). The grain boundary considered is a S33 symmetrical tilt boundary with ½110 axis of rotation, (118) boundary plane and misorientation angle of 20.0 . The equilibrium grain boundary structure is obtained considering a certain rigid-body translation of one grain relative to the other grain. This translation is performed without a crack, and the most stable configuration is selected for further simulations. The procedure for the crack propagation simulation, the division of the specimen into two regions and assigning displacement field to the outer boundary region, used for single crystals is also used for bi-crystals. However, the type of LEFM equations used for the calculation of displacement field and the way of generating hydrogen charged specimens are changed. It is natural to use the anisotropic solution for the displacement field (Eqs. (1), (3) and (4)) when performing simulations on single crystals. Isotropic solution (Eq. (5)) must be for polycrystalline specimens. However, since the solution for bi-crystals is not available in a simple analytical form, one should make a difficult choice between the two solutions. The use of anisotropic solution would yield different simulation results depending on the choice of coordinate in the solution. Based on this and the previous work [27] reporting that the use of the isotropic solution should be less problematic than the use of the anisotropic solution, we use the isotropic solution. The use of the isotropic solution may cause a computational error in absolute value of the stress intensity factor for the crack propagation. However, the purpose of the present study is not to estimate the absolute values of the critical stress
ux ¼
KI G
(5)
where KI is the stress intensity factor, r and q are the cylindrical coordinates with the origin at the crack tip position, G is the shear modulus, and n is the Poisson’s ratio.
3.3. Molecular statics simulation for mode-I fracture of single crystals The purpose of this simulation is to investigate the effect of hydrogen on the fracture behavior of bcc vanadium single crystals, as a means to examine the validity of the HEDE mechanism. Cylindrical specimens as shown in Fig. 1(a) are generated for mode-I fracture simulations. An atomically sharp crack is inserted into each specimen by applying the anisotropic displacement field calculated by the linear elastic fracture mechanics (LEFM) equations (Eqs. (1), (3) and (4)) with a given initial stress intensity factor value. Then, the specimen is divided into two regions. One is the outer boundary region where the atomic positions are fixed and the other is the inner region where a free evolution of atomic configuration is allowed under the constraint by the outer boundary region. The loading is applied by assigning an incremental displacement field to the outer boundary region. The amount of incremental displacement field is updated using the LEFM equations with an incremental stress intensity factor (DKI ¼ 0.008 MPa(m)0.5) and the position of the crack tip step by step. During the loading simulation, a periodic boundary condition is applied along the crack tip front (z direction in Fig. 1(a)) to simulate the plane strain condition and avoid unintended surface effects.
Fig. 1 e (a) Single crystal specimen for mode-I fracture simulation. (b) Bi-crystal specimen for mode-I fracture simulation, containing a S33 symmetrical tilt grain boundary. In the atomistic configuration, gray spheres represent vanadium atoms and dark brown (black) spheres represent hydrogen atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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intensity factor, but to compare the crack propagation behavior of pure vanadium and hydrogen charged vanadium bi-crystal specimens. For the comparison, the isotropic approximation is thought to be suitable enough to provide qualitatively meaningful results.
3.5. Molecular statics simulation for the nucleation of dislocations in single crystals The purpose of this simulation is to investigate the effect of hydrogen on the nucleation of {112}<111> edge dislocation in bcc vanadium, as a means to examine the validity of the HELP mechanism. Generally, bcc metals have two slip systems, {110}< 111> and {112}<111>. Considering that only the {112} slip plane shows a distortion in the presence of hydrogen, and that materials with the {112} slip not activated are less sensitive to hydrogen [28e30], we considered only the {112}<111> edge dislocation. The shape of specimens is similar to that for the mode-I simulation. The specimens are oriented so that the [111] and ½112 correspond to the direction of crack propagation and normal direction of the crack plane, respectively. To introduce ˚ a mode-II initial crack into the specimen, atoms within 4.5 A thickness of (111) layers are removed as shown in Fig. 2. The loading simulation is performed by imposing an increment of stress-intensity factor (DKII ¼ 0.008 MPa(m)0.5) to the pre-separated boundary region according to the anisotropic solution of Mode-II crack tip (Eqs. (2)e(4)). In the case of hydrogen charged specimens, 30 independent simulations at each hydrogen concentration are performed and the critical stress intensity factor for the nucleation of dislocations is determined by averaging the 30 resultant values to diminish the statistical error.
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connects the atomistic scale nucleation of dislocations and the macroscale ductile rupture. A cube type pure vanadium single crystal with about 250,000 atoms is prepared, and given amounts of hydrogen atoms are randomly distributed to generate hydrogen charged specimens. After equilibration at 650 K for 100 ps with a Nose/Hoover isobariceisothermal (NPT) ensemble, tensile loadings are applied into two different directions, [110] and [111], with three-dimensional periodic boundary condition. During the loading the sample dimensions perpendicular to the loading direction are kept constant to induce triaxial stress states. A constant strain rate of 5 108/s is introduced until voids start to nucleate and the atomic configurations are visualized using a common neighbor analysis (CNA) algorithm [31]. Three different quantities, the hydrostatic stress, the von Mises stress and the stress triaxiality, are calculated and compared for specimens with a wide range of hydrogen concentration. The hydrostatic stress is calculated using the following equation, 1 sm ¼ skk ; 3
(6)
where skk represents the diagonal components of stress tensor. The von Mises stress is calculated using svon ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 ij s sm dij sij sm dij 2
(7)
and the stress triaxiality using c¼
sm : svon
(8)
4.
Results and discussion
3.6. Molecular dynamics simulation for the void nucleation in single crystals
4.1.
Hydrogen effect on the crack propagation
The purpose of this simulation is to investigate the effect of hydrogen on the void nucleation, a probable mechanism that
To examine the validity of the HEDE mechanism, we compared mode-I (tensile) crack propagation behaviors of
Fig. 2 e (a) Single crystal specimen of mode-II simulation of the nucleation of dislocations. (b) Snapshots of pure vanadium and hydrogen charged vanadium specimens before and after the nucleation of dislocations. The color of atoms is scaled according to sxx stress. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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pure vanadium and hydrogen charged vanadium using two different series of MS simulations, one using single crystals and the other using bi-crystal specimens. In the case of single crystals, simulation specimens with four different crack orientations were prepared as indicated in Table 1 [32]. The number of total atoms in pure vanadium specimen is around 200,000 and given amounts (5, 20 at%) of hydrogen atoms are randomly distributed into the tetrahedral interstitial sites to generate hydrogen charged specimens. No special effort is made to increase the hydrogen concentration in the vicinity of the crack tip as frequently has been done in simulations of hydrogen embrittlement, since the hydrogen content in practical vanadium-based hydrogen separation membranes and the present specimen is already high (up to 20 at%). Fig. 3 shows the deformation behavior near the crack tip of specimens with different crack orientations, hydrogen contents and stress levels. It is shown that pure vanadium specimens do not show a cleavage fracture but are associated with a formation of twins or dislocations. Similar deformation and crack tip blunting are observed also for all the hydrogen charged specimens without any evidence of the hydrogenenhanced decohesion. The second series of simulations were performed using bicrystals containing a S33 symmetrical tilt grain boundary with and without segregated hydrogen atoms. This was to investigate the effect of hydrogen on the grain boundary decohesion. When generating hydrogen charged specimens using single crystals, we randomly distribute given amounts of hydrogen atoms in a pure vanadium specimen, as already mentioned. However, in the case of bi-crystals that contain a grain boundary, we have to consider the probable grain boundary segregation of hydrogen atoms. The best way to distribute solute atoms in thermodynamically inhomogeneous specimens is to use a Grand Canonical Monte Carlo (GCMC) simulation [33]. Therefore, we use a GCMC simulation to distribute hydrogen atoms in the vanadium bi-crystal specimen. In order to focus on the effect of hydrogen atoms segregated on the grain boundary, the hydrogen contents in matrix are maintained relatively low compared to those in single crystal specimens. The selected hydrogen contents in matrix are 0.14, 1.05 and 1.74 at%, and the corresponding values for hydrogen contents on grain boundary are 16.8, 29.8 and 32.0 at%, respectively. The GCMC simulation is performed at 650 K and then quenched to 0 K for further MS simulations.
Table 1 e Summary of crack orientations considered for mode-I fracture simulations [32]. q is the angle between the direction of crack propagation and the slip direction. Orientation of specimen (Crack plane)[Crack direction] (001)[110] (110)[001] (111)½112
ð011Þ[011]
Slip system
q ( )
{112}<111> {110}<111> {112}<111> {112}<111> {112}<111> {112}<111> {110}<111> {110}<111>
35.3 90 54.7 125.3 90 19.5 35.3 90
In this case, we monitored the position of a crack tip during the crack propagation along the grain boundary as a function of stress intensity factor (KI). Fig. 4 shows the resultant crack resistance curves. The crack propagation distance in hydrogen charged vanadium is smaller than that in pure vanadium under the same stress intensity factor. This indicates that the segregation of hydrogen atoms does not cause any decohesion on the grain boundary.
4.2. Hydrogen effect on the nucleation behavior of dislocations With the results that indicate no validity of the HEDE mechanism, we focused on the validity of the HELP mechanism. We compared the nucleation behavior of dislocations in pure vanadium and hydrogen charged vanadium single crystal specimens using MS simulations of mode-II (shear) loading. Fig. 5(a) shows the change of critical stress intensity factor (KIIc) for the nucleation of an edge dislocation in a functional form of the hydrogen concentration. As the hydrogen concentration increases, KIIc for the nucleation of a dislocation decreases. This result indicates that the nucleation of dislocations is enhanced by hydrogen, supporting the HELP mechanism. It should be meaningful to compare the present result with a theoretical approach. Rice [34] proposed the critical stress intensity factor for the nucleation of an edge dislocation along the crack plane from a mode-II crack tip, as given in the following equation, KIIc
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Gslip gus ¼ 1n
Gslip ¼ ðC11 C12 þ C44 Þ=3
(9) (10)
where Gslip is the shear modulus along the slip plane, gus is the unstable stacking fault energy, n is the Poisson’s ratio and Cij is elastic constants. Fig. 5(b) shows the relation between the hydrogen concentration and elastic moduli calculated using the interatomic potential adopted in this study. The shear modulus (Gslip) calculated using Eq. (10) decreases as the hydrogen concentration increases. From Eq. (9), one can also expect that the KIIc for the emission of an edge dislocation decreases as the hydrogen concentration increases. This result is consistent with the present simulation given in Fig. 5(a) which was obtained by the direct observation of the nucleation event of a dislocation. It should be also mentioned here that Tal-Gutelmacher et al. [35] performed a nano-indentation test to examine the effect of hydrogen on the nucleation of dislocations in a vanadium (100) single crystal. They clearly showed that the homogeneous nucleation of dislocations is enhanced by the presence of hydrogen, which is generally consistent with the present finding.
4.3.
Hydrogen effect on the void nucleation process
Through the mode-I crack propagation and mode-II dislocation emission simulations, it can be concluded that the most promising mechanism of hydrogen embrittlement in
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vanadium is the HELP mechanism. However, an important issue remains unresolved: how is the hydrogen-enhanced dislocation emission, an atomic scale phenomenon, related with the fracture, a macroscale materials phenomenon? The most promising explanation may be that hydrogen induces a shear localization of the plastic flow and results in a highly localized ductile rupture [12,36]. It is widely accepted that the ductile rupture involves the nucleation, growth and coalescence of voids (or cracks). Also, it has been experimentally reported that hydrogen promotes void nucleation [37e39].
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However, it is not known how hydrogen atoms can promote the void nucleation. An effort to clarify the hydrogen-induced void nucleation process was made in the present study by using an MD simulation. The void nucleation typically occurs by decohesion of particleematrix interfaces or grain boundaries, but also occurs inside grains [40]. In the later case, the void nucleation is significantly facilitated by localized deformed structures such as shear band and triaxial stress state near the crack tip or second-phase particles. Therefore, a series of MD tensile
Fig. 3 e Deformation behavior of pure and hydrogen charged vanadium single crystal with different crack orientations, (a) (001)[110], (b) (110)[001], (c) (111)½112 and (d) ð011Þ[011], hydrogen content and stress level. The color of atoms is scaled according to sxx or syy stresses.
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Fig. 4 e Crack resistance curves obtained from MS simulations of pure vanadium and hydrogen segregated vanadium bicrystals containing a S33 symmetrical tilt grain boundary. The crack propagation directions are (a) ½441 and (b) ½441. In the atomistic configuration, gray spheres represent vanadium atoms and dark brown (black) spheres represent hydrogen atoms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
loading simulations were performed using single crystals of pure vanadium and hydrogen charged vanadium to study the triaxiality-driven void nucleation. Grain boundaries as the typical site for the void nucleation were not considered because the fracture path of the hydrogen charged vanadium was reported to be transgranular rather than intergranular [41], and the present MS simulation using bi-crystal specimens showed no sign of the grain boundary decohesion due to hydrogen. Fig. 6 shows the void nucleation process of pure vanadium single crystals, obtained by using the MD tensile loading simulations. The specimens were subjected to a continuous tensile loading at 650 K, the usual operation temperature of metallic hydrogen separation membranes. The calculated hydrostatic stress, von Mises stress and stress triaxiality are also illustrated. Initially, the specimen is deformed elastically. As the loading increases, the deformation mode is switched to
be plastic and the von Mises stress starts to decrease, leaving a maximum peak on the stress curve. This point can be defined as the “yield point”. After the yield point, the hydrostatic stress continues increasing until the void nucleation starts. Once the void nucleation starts, the hydrostatic stress decreases abruptly leaving a maximum peak on the stress curve. Concerning the void formation, the main finding of the present study is that the stress level necessary for the nucleation of voids is significantly lowered in hydrogen charged vanadium compared to pure vanadium. Fig. 7(a),(b) shows tensile stressestrain response of pure vanadium and hydrogen charged vanadium. One can see that the critical tensile stress and strain for the void nucleation decrease as the amount of hydrogen increases. Fig. 7(c),(d) shows the von Mises stressestrain response of pure vanadium and hydrogen charged vanadium. The yield stress and strain decrease as the
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Fig. 5 e (a) Relationship between the concentration of hydrogen and the critical stress intensity factor (KIIc) for the nucleation of dislocations. The KIIc values are averaged values of 30 independent simulations for each hydrogen concentration. (b) Relationship between hydrogen concentration and elastic constants or shear modulus.
amount of hydrogen increases, which leads to a conclusion that hydrogen makes the nucleation of dislocations and thus the nucleation of voids easier. This result is qualitatively consistent with the result given in Fig. 5(a), the decrease of KIIc with increasing hydrogen concentration in the Mode-II simulation for the nucleation of dislocations.
4.4. A suggestion for an alloy design to reduce the hydrogen embrittlement Through the investigation by atomistic simulations, it can be thought that the easiness of the void nucleation by hydrogen in bcc solid solution via the HELP mechanism can explain reasonably well the embrittlement of vanadium membranes. It should be also meaningful to discuss the embrittlement behavior at relatively low temperature and high hydrogen concentration where hydrides are reported to form. In general, the void nucleation can be significantly facilitated by the presence of the second-phase particles because of the local triaxial stress state easily developed near the particles [42]. Therefore, in the presence of hydrides as a kind of
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Fig. 6 e The void nucleation process of pure vanadium single crystals subjected to a continuous tensile loading along (a) [110] and (b) [111] directions at 650 K. The snapshots of the atomistic configuration before the void nucleation are visualized using a common neighbor analysis (CNA) algorithm and the snapshots after the void nucleation are visualized using the potential energy of individual atoms. In CNA snapshots, yellow (gray) atoms are in a perfect bcc structure and brown (black) atoms are in an unknown lattice structure. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
second-phase particles, it is expected that the void nucleation would be facilitated with the help of hydrogen in bcc solid solution. Nonetheless, it is hard to say that the hydride formation is the governing mechanism of the embrittlement. An experimental work by Owen and Scott [20] indicates that the alloy with hydrides and without hydrogen in bcc solid solution does not cause severe embrittlement. According to their result, there is no severe embrittlement unless the volume fraction of hydride is large enough at very low temperature, 77 K. At this temperature, the hydrogen presumably exists only in the form of the hydride as can be seen in the phase diagram [17]. In the alloy design of metallic membrane materials, it is strongly recommended to avoid the formation of secondphase particles for better resistance to the embrittlement. During the above-mentioned void nucleation, the characteristic of second-phase particles has less importance because the void nucleation is not resulted from the break of particles
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Fig. 7 e (a), (b): The tensile stressestrain response and (c), (d): the von Mises stressestrain response of pure vanadium and hydrogen charged vanadium under triaxial stress states where tensile loadings are imposed along (a)(c)[110] and (b)(d)[111] directions and the sample dimensions perpendicular to the loading direction are kept constant.
but resulted from the triaxial stress state of matrix near the particles. In other words, the presence of the second-phase particle causes the embrittlement whether it is hydrides or not. This feature can well explain an interesting aspect of the experimental work by Nishimura et al. [18], according to which, the membranes of quenched Ve10 at%Ni and Ve15 at %Ni alloys without VeNi intermetallic compounds show relatively strong resistance to the embrittlement, while the same alloys with VeNi intermetallic compounds show severe embrittlement.
5.
Conclusion
Our results strongly support the HELP mechanism as the governing mechanism to explain the hydrogen embrittlement in vanadium-based hydrogen separation membranes. We could not observe any sign for the hydrogen enhanced decohesion (HEDE) inside a grain or on grain boundary. Instead, we could clearly observe that hydrogen enhances the nucleation of dislocations near the crack tip and eventually the localized plasticity. We also observed that hydrogen decreases the stress and strain level necessary for the nucleation of voids, which consequently enhances the ductile rupture. Our results provide an insight into the complex atomic scale process of
hydrogen embrittlement in vanadium-based hydrogen separation membranes. The result can also be used as a guidance of further experimental studies on the macroscopic hydrogen embrittlement phenomenon and the further development of suitable metallic hydrogen separation membranes.
Acknowledgments This work has been supported by Korea Institute of Science and Technology (2E22742).
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