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Modeling of hydrogen embrittlement in single crystal Ni
Computational Materials Science 30 (2004) 202–211 www.elsevier.com/locate/commatsci
Modeling of hydrogen embrittlement in single crystal Ni Mao Wen, Xue-Jun Xu, Yuki Omura, Seiji Fukuyama, Kiyoshi Yokogawa
*
Research Institute of Instrumentation Frontier, National Institute of Advanced Industrial Science and Technology (AIST), AIST-Chugoku, Kure 737-0197, Japan Received 12 December 2003; received in revised form 15 February 2004; accepted 16 February 2004
Abstract A large-scale molecular dynamics simulation by the embedded atom method was carried out on hydrogen embrittlement of a single crystal containing 1,021,563 nickel atoms. The details of the deformation in the specimen were identified by a new method of the deformation analysis. Plenty of slip deformation occurred around the crack tip and in the bulk of the hydrogen-free specimen. Hydrogen embrittlement was most serious in the specimen hydrogen-charged in the notched area. Serious embrittlement was also observed in the specimen hydrogen-charged in the slip planes, in which dislocation emission was localized at the crack tip and enhanced on the planes where hydrogen atoms were located. It is considered that the fracture process is due to the hydrogen-enhanced decohesion mechanism. 2004 Elsevier B.V. All rights reserved. PACS: 07.05.T; 71.15.D; 81.40.N; 62.20.M Keywords: Computer simulation; Molecular dynamics; Embedded atom method; Hydrogen embrittlement; Nickel
1. Introduction Environmentally assisted fracture, hydrogen embrittlement (HE), is known to be a serious problem in nickel and nickel-based alloys used for high-temperature devices; thus, extensive experimental studies of HE in those materials have been conducted to clarify the process. Although many experimental studies have been carried out, the influence of hydrogen on the mechanical properties is very complicated, and thus, definite HE * Corresponding author. Tel.: +81-823-72-1947; fax: +81823-73-3284. E-mail address: [email protected] (K. Yokogawa).
mechanisms of nickel have not been established yet [1–3]. By using computer simulations together with the embedded atom method (EAM), the above processes can be discussed at the atomistic level. The EAM was firstly applied to HE of nickel [4–11]. Daw and Baskes [4–6] investigated the influence of hydrogen on the fracture of nickel. It was observed that hydrogen reduced the fracture stress of nickel in the absence of plasticity, due to the weakening of the metallic bonds. In these simulations, the hydrogen-enhanced decohesion mechanism with brittle fracture was well proven. However, all of the models used were small and two-dimensional, which made the system brittle in nature and cross slip impossible, so that the real situation was not well reproduced.
0927-0256/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2004.02.047
M. Wen et al. / Computational Materials Science 30 (2004) 202–211
In this study, a large-scale 3D crack tip model of one million nickel atoms, whose size is visible by transmission electron microscopy, was used in the simulation. A large-scale model can address the long-range character of crack strain field without complicated boundary treatments. MD simulations with the EAM were carried out to study the uniaxial tensile processes of single crystals of nickel at room temperature. The details of the deformation in the specimen were identified by a new method of the deformation analysis. The effects of hydrogen distribution and content on dislocation emission and slip deformation were examined. The mechanism of HE was discussed based on the simulation results.
2. Molecular dynamics simulation MD with the EAM was applied for the simulation. We used the velocity form of the Verlet algorithm to evolve the system, and the simple velocity scaling method to keep the temperature fixed at room temperature (293.15 K). The time increment for each MD step was chosen to be 1.0 · 1015 s. The EAM potentials for the nickelhydrogen system proposed by Baskes and coworkers [10,12,13] were used in the simulation. This set of potentials was successfully applied to our previous simulation on HE of nickel [8]. Experiments revealed that the notched shape enhanced hydrogen-assisted crack nucleation [14]. Thus, a 3D model of a single crystal of nickel with a crack tip was designed for the simulation, as shown inpFig. ffiffiffi 1. The pffiffiffigeometric size of the model is 80a 40 2a 40 2a in the X–Y–Z direction, with a total number of 1,021,563 nickel atoms. The influence of hydrogen was studied by precharging a different number of hydrogen atoms into the model with various distributions before simulation to avoid simulating the long time process of diffusion that cannot be achieved by the conventional MD. Four types of hydrogen distribution were arranged to examine the effect of hydrogen distribution on HE, as shown in Fig. 2. The cross-section of the model along the (0 1 1) plane is shown in the figure. The hydrogen atoms were assumed to occupy the octahedral interstitial
203
Fig. 1. Three-dimensional crack tip model containing 1,021,563 nickel atoms.
sites of nickel in the notched (1 0 0) planes ahead of the crack tip as NA specimen in Fig. 2(a), along the (1 1 1) and (1 1 1) slip planes intersecting the crack tip as SP specimen in Fig. 2(b), near the crack tip as CT specimen in Fig. 2(c) and homogeneously in the upper part of the model as UP specimen in Fig. 2(d). A displacement-boundary condition was applied along X , and free boundary conditions were applied along Y and Z to simulate the tensile behavior of the specimen. To avoid sudden tensile loading, the magnitude of the displacement SX at time step n was calculated using the following equation [8,15] 4 3 n nr n nr SX ðnÞ ¼ S0 þ 2S0 nt nt nr 6 n 6 nr þ n t ; n nr nt ðS1 S0 Þ SX ðnÞ ¼ S0 þ nc
ð1Þ
nr þ nt < n 6 nr þ n t þ nc ; where nr ¼ 10,000, nt ¼ 20,000 and nc ¼ 380,000 are the time steps for relaxation, transition and constant-strain-rate tension, respectively. S1 ¼ 26:048 nm is the total amount of displacement for 200% elongation and S0 ¼ S1 nt =ðnt þ 2nc Þ. This corresponds to a strain rate of 5.1282 · 109 /s. In order to interpret the results of the MD simulations, we developed a new method of deformation analysis for the specimens. The details of the method are given elsewhere [16], so we
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Fig. 2. Cross-sectional views of hydrogen distribution on (0 1 1) plane of NA specimen in (a), CT specimen in (b), UP specimen in (c) and SP specimen in (d). (Nickel atoms: large blue spheres, hydrogen atoms: small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.).
described briefly as follows. We defined the deformation index (DI) of nickel atom i, ui , as the maximum absolute value of the relative displacements between atom i and its nearest neighbors j, in unit of the magnitude of the Burgers vector 1/2Æ1 1 0æ: *
*0
ui ¼ maxðj r ij r ij jÞ=b;
ð2Þ
*
where r ij is the relative position vector of atoms i *0 and j, and r ij is the vector in the reference lattice. Thus for the slipped areas by 1=6h1 1 2iui ¼ 0:58, and for the slipped areas by 1=2h1 1 0iui ¼ 1. Following DI, the slip activities can thus be traced and analyzed, and dislocations can be located immediately ahead of the slipped area. Any lattice imperfections, torsion and structure changes can also be displayed clearly by this method.
of 5.1%, is analyzed in Fig. 3 using this new method. A general view is shown in Fig. 3(a). Cyan and green areas near the crack tip indicate slipped areas and blue areas indicate deform-free areas. The mark of dislocation, ?, indicates the emergent site of dislocation on the surface. The deformed atoms by excluding non-deformed area near the crack tip, where ui is above 0.5 are shown in Fig. 3(b). Partial dislocations in pairs, with stacking faults between the pairs, emit from the crack tip clearly. The emission of the dislocations that are on the two main slip planes of (1 1 1) and (1 1 1) causes crack blunting. The emission of the dislocations on the (1 1 1) plane, which is oblique to the crack front, causes jogging and forms a step in the crack front. We can also see that the jogging dislocations on the (1 1 1) plane interact with the blunting dislocations on (1 1 1) and (1 1 1), and impede their slip motion.
3. Results 3.1. Dislocation emission and dislocation structure of hydrogen-free specimen Deformation of the hydrogen-free specimen at the MD step of 30,000, corresponding to a strain
3.2. Effect of hydrogen distribution on dislocation emission and cracking The effect of hydrogen on dislocation emission analyzed by this method is shown in Fig. 4. General views of the hydrogen-charged specimens with
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together with the hydrogen-free specimen at the MD step of 100,000, corresponding to a strain of 41.0%, are shown in the figure. Heavy slip deformation occurred at the areas displayed yellow. All of the specimens except the SP specimen show that extensive slip deformation occurred along four {1 1 1} planes. It is evident that of all types of specimens with same number of hydrogen atoms, hydrogen exerted the most serious effect on the NA specimen, a considerably serious effect on the SP specimen, a significant effect on the CT specimen, and a minor effect on the UP specimen. 3.3. Deformation of SP specimens
Fig. 3. Deformation analysis in the hydrogen-free specimen at the MD step of 30,000. (General view of atomic arrangement in (a) and deformed atoms near the crack tip in (b).) (Nickel atoms are represented by spheres colored according to the DI, ui , indicated by the color bar. ? indicates the emergent site of dislocation on the surface in (a). Black lines mark dislocations and the arrows also demonstrate the atoms on the crack plane as reference in (b). For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
8000 hydrogen atoms at the MD step of 30,000, corresponding to a strain of 5.1%, are shown in the figure. Dislocation emission was localized at the crack tip in the hydrogen-charged NA, CT and UP specimens, as shown in Fig. 4(a–c), respectively. The CT specimen shows that a dislocation emitted from the crack tip and then cross-slipped onto the (1 1 1) plane. The SP specimen shows that dislocation emission was enhanced on the (1 1 1) and (1 1 1) planes where hydrogen atoms were located, as shown in Fig. 4(d). The effect of hydrogen distribution on cracking is shown in Fig. 5. General views of the specimens charged with 8000 hydrogen atoms
General views of the hydrogen-free specimen and the SP specimens with 8000, 18,281 and 29,302 hydrogen atoms at the MD step of 60,000, corresponding to a strain of 20.5%, are shown in Fig. 6. Slip deformation was highly localized along the (1 1 1) and (1 1 1) planes and decreased with increasing hydrogen content in the SP specimens. Cross-sectional views of the (1 1 1) plane of the specimen pre-charged with 8000 hydrogen atoms are shown in Fig. 7. Microvoid formation was observed in association with the formation of hydrogen molecules, as identified by the potentials of the hydrogen atoms. A microvoid was observed at the MD step of 50,000. The microvoid nucleated at the site where the slip plane meets the left tension end. This site is of high stress concentration, and thus favors microvoid formation. New microvoid formation also was observed at the MD step of 60,000 and 95,000. 3.4. Deformation of NA specimens General views of the hydrogen-free specimen and the NA specimens with 2000 and 8000 hydrogen atoms at the MD step of 100,000, corresponding to a strain of 41.0%, and 16,402 hydrogen atoms at the MD step of 50,000, corresponding to a strain of 15.4%, are shown in Fig. 8. The hydrogen-free specimen showed good ductility. The crack tip opening angle decreased with increasing hydrogen content. Brittle fracture had already occurred on the (1 0 0) plane perpendicular
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Fig. 4. Dislocation emission of the specimens charged with 8000 hydrogen atoms: NA specimen in (a), CT specimen in (b), UP specimen in (c) and SP specimen in (d), at the MD step of 30,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. ? indicates the emergent site of dislocation on the surface. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. General views of the hydrogen-free specimen in (a), the specimens charged with 8000 hydrogen atoms: NA specimen in (b), CT specimen in (c), UP specimen in (d), and SP specimen in (e), at the MD step of 100,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. General views of the hydrogen-free specimen in (a), and the SP specimens with 8000 hydrogen atoms in (b), 18,281 hydrogen atoms in (c) and 29,302 hydrogen atoms in (d) at the MD step of 60,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Cross-sectional views of the middle (1 1 1) plane of the SP specimens with 8000 hydrogen atoms at the MD step of 50,000 in (a), 60,000 in (b) and 95,000 in (c). (Nickel atoms: large spheres, hydrogen atoms: small spheres. Atoms are colored according to their potentials indicated by the color bar. An arrow shows a microvoid. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. General views of the hydrogen-free specimen in (a), and the NA specimens with 2000 hydrogen atoms in (b) and 8000 hydrogen atoms in (c) at the MD step of 100,000 and 16,402 hydrogen atoms in (d) at the MD step of 50,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
to the tensile axis with little plastic deformation in the specimen with 16,402 hydrogen atoms. Cross-sectional views of the middle (1 0 0) plane of the specimens pre-charged with 8000 hydrogen atoms in the notched (1 0 0) planes are shown in Fig. 9. A microvoid was observed at the MD step of 50,000. The microvoid linked with the crack tip and two new microvoids formed at the MD step of 60,000. Microvoid growth and linkage, and new microvoid formation were observed at the MD step of 65,000. It is obvious that fracture was due
to microvoid formation and subsequent microvoid growth and linkage at such high hydrogen content. Microvoid formation increased with increasing hydrogen content. Fracture occurred with a dominant feature of brittleness due to significant microvoid formation and subsequent microvoid growth and linkage at the early stage of deformation in the case of the specimen containing a thin layer of hydride with 16,402 hydrogen atoms, and the hydride decomposed during fracture. No microvoid formation was found until fracture
Fig. 9. Cross-sectional views of the middle (1 0 0) plane of the NA specimens with 8000 hydrogen atoms at the MD step of 50,000 in (a), 60,000 in (b) and 65,000 in (c). (Nickel atoms: large spheres, hydrogen atoms: small spheres. Atoms are colored according to their potentials indicated by the color bar. An arrow shows a microvoid. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.).
M. Wen et al. / Computational Materials Science 30 (2004) 202–211
Fig. 10. Effect of hydrogen concentration on the elongation at the fracture of the NA specimen.
occurred in the specimen charged with 2000 hydrogen atoms. The effect of hydrogen content on the elongation at the fracture of the NA specimen is shown in Fig. 10. The result of our recent simulation of a moderate-scale model containing 163,311 nickel atoms [8] is also shown for comparison. Hydrogen concentration is defined only in the notched area. The elongation decreases with increasing hydrogen concentration. It is evident that the large-scale model is much more ductile than the moderatescale model, owing to the smaller restriction of the large model on dislocation motions. However, at a hydrogen content of 1.0, where a thin layer of NiH exists in the notched plane ahead of the crack tip, the plasticity of the two models is almost same, since brittle fracture occurred in the two models with nearly no dislocation activities.
4. Discussion The present simulations revealed that HE of the NA specimen was the most serious. This is in
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agreement with the mechanism proposed by Troiano [14] that HE occurs in the notched area slightly ahead of the crack tip, where the most severe triaxial-stress state exists and a sufficiently high hydrogen concentration is obtained via stressinduced diffusion of hydrogen. Boniszewski and Smith [17] found that nickel could form an FCC metal hydride phase called b hydride, which decomposed during fracture. Vehoff [3] recently estimated that hydrogen-assisted crack growth occurred in the fracture process zone several nanometers ahead of the crack tip, where an extremely high hydrogen concentration could be obtained by diffusion, based on the experimental data on nickel single crystal. Therefore, our model with high hydrogen content is consistent with the above results. By pre-charging a sufficient number of hydrogen atoms into such a notched area region ahead of the crack tip, we avoided simulating longdistance hydrogen diffusion, and thereby successfully simulated the brittle fracture by hydrogen without hydrogen diffusion. For the NA specimen, hydrogen was charged in the notched area ahead of the crack tip. Hydrogen localized dislocation emission at the crack tip and fracture occurred macroscopically on the (1 0 0) pre-crack plane perpendicular to the tensile direction in this case. The crack tip opening angle decreased with increasing hydrogen content. At low hydrogen content, extensive plastic deformation was observed by the motion of dislocations. This result cannot be attributed to the impeded dislocation motion mechanism [1,3], because hydrogen atoms were charged only in the notched area ahead of the crack tip and the motion of the blunting dislocations on the (1 1 1) and (1 1 1) planes was thus not impeded to increase the local stresses at the crack tip. Hydrogen only weakened the bonds between nickel atoms at the crack tip, and thus induced the crack to propagate along where hydrogen atoms were pre-charged. At high hydrogen content, hydrogen induced microvoid formation due to bond breaking of the seriously weakened metallic bonds ahead of the crack tip, and a significant reduction in the ductility of the specimen was observed. Fracture occurred after the subsequent microvoid growth and linkage.
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In the case of the CT specimen, hydrogen was charged around the crack tip. The emission of dislocations from the crack tip and crack propagation were thus localized at the earlier stage of deformation. After the crack propagation outside the hydrogen-charged area, however, there were insufficient hydrogen atoms near the crack tip. Thus, further deformation of the specimen was almost not affected by hydrogen. This result implies that hydrogen atoms at the crack tip are required to induce HE. In the UP specimen, hydrogen was charged homogeneously in the upper part of the specimen where deformation takes place. Hydrogen slightly localized dislocation emission at the crack tip at the beginning of plastic deformation, but did not affect deformation afterwards. This result also indicates that a very high hydrogen content at the crack tip is required for significant HE. In the case of the SP specimen, hydrogen was charged along the (1 1 1) and ( 11 1) slip planes intersecting the crack tip. Slip deformation was mainly along the two slip planes, and decreased with increasing hydrogen content. Microvoid formed at the site where stress concentration is high and failure along the slip planes was observed finally. This is in accordance with the observations of the TEM foils [3,18,19]. It seems that the failure is due to the hydrogen-enhanced dislocation motion mechanism. In the present simulations, however, the strain rate is so high and the deformation period is so short that it is impossible for hydrogen atoms to diffuse to positions of lowest energy and to form atmospheres surrounding dislocations which produce the ‘‘elastic shielding’’ effect, as proposed by Sirois and Birnbaum [20]. Therefore, we rationalized that this result was also due to hydrogen weakening the bonds of nickel atoms between the slip planes. When hydrogen atoms are located on these planes, the cohesion energy is reduced, and then dislocation emission and motion along these planes become easy. Following the above discussion, the present results support the hydrogen-enhanced decohesion mechanism with localized deformation and brittle fracture depending on the hydrogen content and distribution.
5. Conclusions A large-scale MD simulation with the EAM was carried out on HE of a single crystal of nickel. The details of the deformation in the specimen were identified by a new method of the deformation analysis. The influence of hydrogen was examined by pre-charging a different number of hydrogen atoms into the model with various distributions. It was found that the present results support the hydrogen-enhanced decohesion mechanism with localized deformation and brittle fracture depending on the hydrogen content and distribution.
References [1] H.G. Nelson, Treatise on Materials Science and Technology, Academic Press, London, 1983, pp. 275–359. [2] S.M. Myers, M.I. Baskes, H.K. Birnbaum, J.W. Corbett, G.G. Deleo, S.K. Estreicher, E.E. Haller, S.J. Pearton, Rev. Mod. Phys. 64 (1992) 559–617. [3] H. Vehoff, Hydrogen in metals III, in: Wipf (Ed.), Topics in Applied Physics, Springer, Berlin, 1997, pp. 215–278. [4] M.S. Daw, M.I. Baskes, Phys. Rev. Lett. 50 (1983) 1285– 1288. [5] M.S. Daw, M.I. Baskes, Phys. Rev. B 29 (1984) 6443–6453. [6] M.S. Daw, M.I. Baskes, NATO ASI Ser. E 130 (1987) 196– 218. [7] R.G. Hoagland, H.L. Heinisch, J. Mater. Res. 7 (1992) 2080–2088. [8] X. Xu, M. Wen, S. Fukuyama, K. Yokogawa, Mater. Trans. JIM 42 (2001) 2283–2289. [9] M.S. Daw, M.I. Baskes, C.L. Bisson, W.G. Wolfer, in: R.H. Jones, W.W. Gerberich (Eds.), Conf. Modeling Environmental Effects on Crack Growth Processes, Metallurgical Society of AIME, New York, 1986, pp. 99–124. [10] J.E. Angelo, N.R. Moody, M.I. Baskes, Model. Simul. Mater. Sci. Eng. 3 (1995) 289–307. [11] J.E. Angelo, N.R. Moody, M.I. Baskes, in: N.R. Moody, A.W. Thompson (Eds.), Hydrogen Effects in Materials, The Minerals, Metals and Materials Society, Warrendale, PA, 1996, pp. 161–170. [12] M.I. Baskes, J.E. Angelo, N.R. Moody, in: N.R. Moody, A.W. Thompson (Eds.), Hydrogen Effects in Materials, The Minerals, Metals and Materials Society, Warrendale, PA, 1996, pp. 77–90. [13] M.I. Baskes, X. Sha, J.E. Angelo, N.R. Moody, Model. Simul. Mater. Sci. Eng. 5 (1997) 651–652. [14] A.R. Troiano, Trans. ASM 52 (1960) 54–80. [15] Z. Hu, S. Fukuyama, K. Yokogawa, S. Okamoto, Model. Simul. Mater. Sci. Eng. 7 (1999) 541–551. [16] M. Wen, S. Fukuyama, K. Yokogawa, in preparation.
M. Wen et al. / Computational Materials Science 30 (2004) 202–211 [17] J. Boniszewski, G.C. Smith, J. Phys. Chem. Solids 21 (1961) 115–118. [18] I.M. Robertson, H.K. Birnbaum, Acta Metall. 34 (1986) 353–366.
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[19] P. Rozenak, I.M. Robertson, H.K. Birnbaum, Acta Metall. 38 (1990) 2031–2040. [20] E. Sirois, H.K. Birnbaum, Acta Metall. 40 (1992) 1377– 1385.
Modeling of hydrogen embrittlement in single crystal Ni Mao Wen, Xue-Jun Xu, Yuki Omura, Seiji Fukuyama, Kiyoshi Yokogawa
*
Research Institute of Instrumentation Frontier, National Institute of Advanced Industrial Science and Technology (AIST), AIST-Chugoku, Kure 737-0197, Japan Received 12 December 2003; received in revised form 15 February 2004; accepted 16 February 2004
Abstract A large-scale molecular dynamics simulation by the embedded atom method was carried out on hydrogen embrittlement of a single crystal containing 1,021,563 nickel atoms. The details of the deformation in the specimen were identified by a new method of the deformation analysis. Plenty of slip deformation occurred around the crack tip and in the bulk of the hydrogen-free specimen. Hydrogen embrittlement was most serious in the specimen hydrogen-charged in the notched area. Serious embrittlement was also observed in the specimen hydrogen-charged in the slip planes, in which dislocation emission was localized at the crack tip and enhanced on the planes where hydrogen atoms were located. It is considered that the fracture process is due to the hydrogen-enhanced decohesion mechanism. 2004 Elsevier B.V. All rights reserved. PACS: 07.05.T; 71.15.D; 81.40.N; 62.20.M Keywords: Computer simulation; Molecular dynamics; Embedded atom method; Hydrogen embrittlement; Nickel
1. Introduction Environmentally assisted fracture, hydrogen embrittlement (HE), is known to be a serious problem in nickel and nickel-based alloys used for high-temperature devices; thus, extensive experimental studies of HE in those materials have been conducted to clarify the process. Although many experimental studies have been carried out, the influence of hydrogen on the mechanical properties is very complicated, and thus, definite HE * Corresponding author. Tel.: +81-823-72-1947; fax: +81823-73-3284. E-mail address: [email protected] (K. Yokogawa).
mechanisms of nickel have not been established yet [1–3]. By using computer simulations together with the embedded atom method (EAM), the above processes can be discussed at the atomistic level. The EAM was firstly applied to HE of nickel [4–11]. Daw and Baskes [4–6] investigated the influence of hydrogen on the fracture of nickel. It was observed that hydrogen reduced the fracture stress of nickel in the absence of plasticity, due to the weakening of the metallic bonds. In these simulations, the hydrogen-enhanced decohesion mechanism with brittle fracture was well proven. However, all of the models used were small and two-dimensional, which made the system brittle in nature and cross slip impossible, so that the real situation was not well reproduced.
0927-0256/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2004.02.047
M. Wen et al. / Computational Materials Science 30 (2004) 202–211
In this study, a large-scale 3D crack tip model of one million nickel atoms, whose size is visible by transmission electron microscopy, was used in the simulation. A large-scale model can address the long-range character of crack strain field without complicated boundary treatments. MD simulations with the EAM were carried out to study the uniaxial tensile processes of single crystals of nickel at room temperature. The details of the deformation in the specimen were identified by a new method of the deformation analysis. The effects of hydrogen distribution and content on dislocation emission and slip deformation were examined. The mechanism of HE was discussed based on the simulation results.
2. Molecular dynamics simulation MD with the EAM was applied for the simulation. We used the velocity form of the Verlet algorithm to evolve the system, and the simple velocity scaling method to keep the temperature fixed at room temperature (293.15 K). The time increment for each MD step was chosen to be 1.0 · 1015 s. The EAM potentials for the nickelhydrogen system proposed by Baskes and coworkers [10,12,13] were used in the simulation. This set of potentials was successfully applied to our previous simulation on HE of nickel [8]. Experiments revealed that the notched shape enhanced hydrogen-assisted crack nucleation [14]. Thus, a 3D model of a single crystal of nickel with a crack tip was designed for the simulation, as shown inpFig. ffiffiffi 1. The pffiffiffigeometric size of the model is 80a 40 2a 40 2a in the X–Y–Z direction, with a total number of 1,021,563 nickel atoms. The influence of hydrogen was studied by precharging a different number of hydrogen atoms into the model with various distributions before simulation to avoid simulating the long time process of diffusion that cannot be achieved by the conventional MD. Four types of hydrogen distribution were arranged to examine the effect of hydrogen distribution on HE, as shown in Fig. 2. The cross-section of the model along the (0 1 1) plane is shown in the figure. The hydrogen atoms were assumed to occupy the octahedral interstitial
203
Fig. 1. Three-dimensional crack tip model containing 1,021,563 nickel atoms.
sites of nickel in the notched (1 0 0) planes ahead of the crack tip as NA specimen in Fig. 2(a), along the (1 1 1) and (1 1 1) slip planes intersecting the crack tip as SP specimen in Fig. 2(b), near the crack tip as CT specimen in Fig. 2(c) and homogeneously in the upper part of the model as UP specimen in Fig. 2(d). A displacement-boundary condition was applied along X , and free boundary conditions were applied along Y and Z to simulate the tensile behavior of the specimen. To avoid sudden tensile loading, the magnitude of the displacement SX at time step n was calculated using the following equation [8,15] 4 3 n nr n nr SX ðnÞ ¼ S0 þ 2S0 nt nt nr 6 n 6 nr þ n t ; n nr nt ðS1 S0 Þ SX ðnÞ ¼ S0 þ nc
ð1Þ
nr þ nt < n 6 nr þ n t þ nc ; where nr ¼ 10,000, nt ¼ 20,000 and nc ¼ 380,000 are the time steps for relaxation, transition and constant-strain-rate tension, respectively. S1 ¼ 26:048 nm is the total amount of displacement for 200% elongation and S0 ¼ S1 nt =ðnt þ 2nc Þ. This corresponds to a strain rate of 5.1282 · 109 /s. In order to interpret the results of the MD simulations, we developed a new method of deformation analysis for the specimens. The details of the method are given elsewhere [16], so we
204
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Fig. 2. Cross-sectional views of hydrogen distribution on (0 1 1) plane of NA specimen in (a), CT specimen in (b), UP specimen in (c) and SP specimen in (d). (Nickel atoms: large blue spheres, hydrogen atoms: small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.).
described briefly as follows. We defined the deformation index (DI) of nickel atom i, ui , as the maximum absolute value of the relative displacements between atom i and its nearest neighbors j, in unit of the magnitude of the Burgers vector 1/2Æ1 1 0æ: *
*0
ui ¼ maxðj r ij r ij jÞ=b;
ð2Þ
*
where r ij is the relative position vector of atoms i *0 and j, and r ij is the vector in the reference lattice. Thus for the slipped areas by 1=6h1 1 2iui ¼ 0:58, and for the slipped areas by 1=2h1 1 0iui ¼ 1. Following DI, the slip activities can thus be traced and analyzed, and dislocations can be located immediately ahead of the slipped area. Any lattice imperfections, torsion and structure changes can also be displayed clearly by this method.
of 5.1%, is analyzed in Fig. 3 using this new method. A general view is shown in Fig. 3(a). Cyan and green areas near the crack tip indicate slipped areas and blue areas indicate deform-free areas. The mark of dislocation, ?, indicates the emergent site of dislocation on the surface. The deformed atoms by excluding non-deformed area near the crack tip, where ui is above 0.5 are shown in Fig. 3(b). Partial dislocations in pairs, with stacking faults between the pairs, emit from the crack tip clearly. The emission of the dislocations that are on the two main slip planes of (1 1 1) and (1 1 1) causes crack blunting. The emission of the dislocations on the (1 1 1) plane, which is oblique to the crack front, causes jogging and forms a step in the crack front. We can also see that the jogging dislocations on the (1 1 1) plane interact with the blunting dislocations on (1 1 1) and (1 1 1), and impede their slip motion.
3. Results 3.1. Dislocation emission and dislocation structure of hydrogen-free specimen Deformation of the hydrogen-free specimen at the MD step of 30,000, corresponding to a strain
3.2. Effect of hydrogen distribution on dislocation emission and cracking The effect of hydrogen on dislocation emission analyzed by this method is shown in Fig. 4. General views of the hydrogen-charged specimens with
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together with the hydrogen-free specimen at the MD step of 100,000, corresponding to a strain of 41.0%, are shown in the figure. Heavy slip deformation occurred at the areas displayed yellow. All of the specimens except the SP specimen show that extensive slip deformation occurred along four {1 1 1} planes. It is evident that of all types of specimens with same number of hydrogen atoms, hydrogen exerted the most serious effect on the NA specimen, a considerably serious effect on the SP specimen, a significant effect on the CT specimen, and a minor effect on the UP specimen. 3.3. Deformation of SP specimens
Fig. 3. Deformation analysis in the hydrogen-free specimen at the MD step of 30,000. (General view of atomic arrangement in (a) and deformed atoms near the crack tip in (b).) (Nickel atoms are represented by spheres colored according to the DI, ui , indicated by the color bar. ? indicates the emergent site of dislocation on the surface in (a). Black lines mark dislocations and the arrows also demonstrate the atoms on the crack plane as reference in (b). For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
8000 hydrogen atoms at the MD step of 30,000, corresponding to a strain of 5.1%, are shown in the figure. Dislocation emission was localized at the crack tip in the hydrogen-charged NA, CT and UP specimens, as shown in Fig. 4(a–c), respectively. The CT specimen shows that a dislocation emitted from the crack tip and then cross-slipped onto the (1 1 1) plane. The SP specimen shows that dislocation emission was enhanced on the (1 1 1) and (1 1 1) planes where hydrogen atoms were located, as shown in Fig. 4(d). The effect of hydrogen distribution on cracking is shown in Fig. 5. General views of the specimens charged with 8000 hydrogen atoms
General views of the hydrogen-free specimen and the SP specimens with 8000, 18,281 and 29,302 hydrogen atoms at the MD step of 60,000, corresponding to a strain of 20.5%, are shown in Fig. 6. Slip deformation was highly localized along the (1 1 1) and (1 1 1) planes and decreased with increasing hydrogen content in the SP specimens. Cross-sectional views of the (1 1 1) plane of the specimen pre-charged with 8000 hydrogen atoms are shown in Fig. 7. Microvoid formation was observed in association with the formation of hydrogen molecules, as identified by the potentials of the hydrogen atoms. A microvoid was observed at the MD step of 50,000. The microvoid nucleated at the site where the slip plane meets the left tension end. This site is of high stress concentration, and thus favors microvoid formation. New microvoid formation also was observed at the MD step of 60,000 and 95,000. 3.4. Deformation of NA specimens General views of the hydrogen-free specimen and the NA specimens with 2000 and 8000 hydrogen atoms at the MD step of 100,000, corresponding to a strain of 41.0%, and 16,402 hydrogen atoms at the MD step of 50,000, corresponding to a strain of 15.4%, are shown in Fig. 8. The hydrogen-free specimen showed good ductility. The crack tip opening angle decreased with increasing hydrogen content. Brittle fracture had already occurred on the (1 0 0) plane perpendicular
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Fig. 4. Dislocation emission of the specimens charged with 8000 hydrogen atoms: NA specimen in (a), CT specimen in (b), UP specimen in (c) and SP specimen in (d), at the MD step of 30,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. ? indicates the emergent site of dislocation on the surface. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. General views of the hydrogen-free specimen in (a), the specimens charged with 8000 hydrogen atoms: NA specimen in (b), CT specimen in (c), UP specimen in (d), and SP specimen in (e), at the MD step of 100,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. General views of the hydrogen-free specimen in (a), and the SP specimens with 8000 hydrogen atoms in (b), 18,281 hydrogen atoms in (c) and 29,302 hydrogen atoms in (d) at the MD step of 60,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
Fig. 7. Cross-sectional views of the middle (1 1 1) plane of the SP specimens with 8000 hydrogen atoms at the MD step of 50,000 in (a), 60,000 in (b) and 95,000 in (c). (Nickel atoms: large spheres, hydrogen atoms: small spheres. Atoms are colored according to their potentials indicated by the color bar. An arrow shows a microvoid. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 8. General views of the hydrogen-free specimen in (a), and the NA specimens with 2000 hydrogen atoms in (b) and 8000 hydrogen atoms in (c) at the MD step of 100,000 and 16,402 hydrogen atoms in (d) at the MD step of 50,000. (Nickel atoms are represented by spheres colored according to the deformation index (DI), ui , indicated by the color bar and hydrogen atoms are represented by small red spheres. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.)
to the tensile axis with little plastic deformation in the specimen with 16,402 hydrogen atoms. Cross-sectional views of the middle (1 0 0) plane of the specimens pre-charged with 8000 hydrogen atoms in the notched (1 0 0) planes are shown in Fig. 9. A microvoid was observed at the MD step of 50,000. The microvoid linked with the crack tip and two new microvoids formed at the MD step of 60,000. Microvoid growth and linkage, and new microvoid formation were observed at the MD step of 65,000. It is obvious that fracture was due
to microvoid formation and subsequent microvoid growth and linkage at such high hydrogen content. Microvoid formation increased with increasing hydrogen content. Fracture occurred with a dominant feature of brittleness due to significant microvoid formation and subsequent microvoid growth and linkage at the early stage of deformation in the case of the specimen containing a thin layer of hydride with 16,402 hydrogen atoms, and the hydride decomposed during fracture. No microvoid formation was found until fracture
Fig. 9. Cross-sectional views of the middle (1 0 0) plane of the NA specimens with 8000 hydrogen atoms at the MD step of 50,000 in (a), 60,000 in (b) and 65,000 in (c). (Nickel atoms: large spheres, hydrogen atoms: small spheres. Atoms are colored according to their potentials indicated by the color bar. An arrow shows a microvoid. For interpretation of the references in color in this figure legend, the reader is referred to the web version of this article.).
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Fig. 10. Effect of hydrogen concentration on the elongation at the fracture of the NA specimen.
occurred in the specimen charged with 2000 hydrogen atoms. The effect of hydrogen content on the elongation at the fracture of the NA specimen is shown in Fig. 10. The result of our recent simulation of a moderate-scale model containing 163,311 nickel atoms [8] is also shown for comparison. Hydrogen concentration is defined only in the notched area. The elongation decreases with increasing hydrogen concentration. It is evident that the large-scale model is much more ductile than the moderatescale model, owing to the smaller restriction of the large model on dislocation motions. However, at a hydrogen content of 1.0, where a thin layer of NiH exists in the notched plane ahead of the crack tip, the plasticity of the two models is almost same, since brittle fracture occurred in the two models with nearly no dislocation activities.
4. Discussion The present simulations revealed that HE of the NA specimen was the most serious. This is in
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agreement with the mechanism proposed by Troiano [14] that HE occurs in the notched area slightly ahead of the crack tip, where the most severe triaxial-stress state exists and a sufficiently high hydrogen concentration is obtained via stressinduced diffusion of hydrogen. Boniszewski and Smith [17] found that nickel could form an FCC metal hydride phase called b hydride, which decomposed during fracture. Vehoff [3] recently estimated that hydrogen-assisted crack growth occurred in the fracture process zone several nanometers ahead of the crack tip, where an extremely high hydrogen concentration could be obtained by diffusion, based on the experimental data on nickel single crystal. Therefore, our model with high hydrogen content is consistent with the above results. By pre-charging a sufficient number of hydrogen atoms into such a notched area region ahead of the crack tip, we avoided simulating longdistance hydrogen diffusion, and thereby successfully simulated the brittle fracture by hydrogen without hydrogen diffusion. For the NA specimen, hydrogen was charged in the notched area ahead of the crack tip. Hydrogen localized dislocation emission at the crack tip and fracture occurred macroscopically on the (1 0 0) pre-crack plane perpendicular to the tensile direction in this case. The crack tip opening angle decreased with increasing hydrogen content. At low hydrogen content, extensive plastic deformation was observed by the motion of dislocations. This result cannot be attributed to the impeded dislocation motion mechanism [1,3], because hydrogen atoms were charged only in the notched area ahead of the crack tip and the motion of the blunting dislocations on the (1 1 1) and (1 1 1) planes was thus not impeded to increase the local stresses at the crack tip. Hydrogen only weakened the bonds between nickel atoms at the crack tip, and thus induced the crack to propagate along where hydrogen atoms were pre-charged. At high hydrogen content, hydrogen induced microvoid formation due to bond breaking of the seriously weakened metallic bonds ahead of the crack tip, and a significant reduction in the ductility of the specimen was observed. Fracture occurred after the subsequent microvoid growth and linkage.
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In the case of the CT specimen, hydrogen was charged around the crack tip. The emission of dislocations from the crack tip and crack propagation were thus localized at the earlier stage of deformation. After the crack propagation outside the hydrogen-charged area, however, there were insufficient hydrogen atoms near the crack tip. Thus, further deformation of the specimen was almost not affected by hydrogen. This result implies that hydrogen atoms at the crack tip are required to induce HE. In the UP specimen, hydrogen was charged homogeneously in the upper part of the specimen where deformation takes place. Hydrogen slightly localized dislocation emission at the crack tip at the beginning of plastic deformation, but did not affect deformation afterwards. This result also indicates that a very high hydrogen content at the crack tip is required for significant HE. In the case of the SP specimen, hydrogen was charged along the (1 1 1) and ( 11 1) slip planes intersecting the crack tip. Slip deformation was mainly along the two slip planes, and decreased with increasing hydrogen content. Microvoid formed at the site where stress concentration is high and failure along the slip planes was observed finally. This is in accordance with the observations of the TEM foils [3,18,19]. It seems that the failure is due to the hydrogen-enhanced dislocation motion mechanism. In the present simulations, however, the strain rate is so high and the deformation period is so short that it is impossible for hydrogen atoms to diffuse to positions of lowest energy and to form atmospheres surrounding dislocations which produce the ‘‘elastic shielding’’ effect, as proposed by Sirois and Birnbaum [20]. Therefore, we rationalized that this result was also due to hydrogen weakening the bonds of nickel atoms between the slip planes. When hydrogen atoms are located on these planes, the cohesion energy is reduced, and then dislocation emission and motion along these planes become easy. Following the above discussion, the present results support the hydrogen-enhanced decohesion mechanism with localized deformation and brittle fracture depending on the hydrogen content and distribution.
5. Conclusions A large-scale MD simulation with the EAM was carried out on HE of a single crystal of nickel. The details of the deformation in the specimen were identified by a new method of the deformation analysis. The influence of hydrogen was examined by pre-charging a different number of hydrogen atoms into the model with various distributions. It was found that the present results support the hydrogen-enhanced decohesion mechanism with localized deformation and brittle fracture depending on the hydrogen content and distribution.
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