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Effect of grain boundary segregation of Co or Ti on cyclic deformation of aluminium bi-crystals
Accepted Manuscript Effect of grain boundary segregation of Co or Ti on cyclic deformation of aluminium bi-crystals Rita I. Babicheva, Sergey V. Dmitriev, Dmitry V. Bachurin, Narasimalu Srikanth, Ying Zhang, Shaw Wei Kok, Kun Zhou PII: DOI: Reference:
S0142-1123(17)30044-0 http://dx.doi.org/10.1016/j.ijfatigue.2017.01.038 JIJF 4228
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
20 October 2016 23 January 2017 25 January 2017
Please cite this article as: Babicheva, R.I., Dmitriev, S.V., Bachurin, D.V., Srikanth, N., Zhang, Y., Kok, S.W., Zhou, K., Effect of grain boundary segregation of Co or Ti on cyclic deformation of aluminium bi-crystals, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue.2017.01.038
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Effect of grain boundary segregation of Co or Ti on cyclic deformation of aluminium bi-crystals Rita I. Babicheva1, Sergey V. Dmitriev2,3, Dmitry V. Bachurin2,4, Narasimalu Srikanth5, Ying Zhang6, Shaw Wei Kok6, Kun Zhou1 1
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore 2 Institute for Metals Superplasticity Problems of Russian Academy of Sciences, 39 Khalturin St., Ufa 450001, Russia 3 Research Laboratory for Mechanics of New Nanomaterials, Peter the Great St. Petersburg Polytechnical University, St. Petersburg 195251, Russia 4 Institute for Applied Materials – Applied Materials Physics, Karlsruhe Institute of Technology, Hermann-vonHelmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany 5 Energy Research Institute @NTU, Nanyang Technological University, Singapore 637141, Singapore 6 Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075, Singapore
Abstract There exist many factors affecting fatigue behavior of metallic materials, among them the effect of grain boundary (GB) segregation of alloying elements remains largely unexplored. To exploit this factor, an atomistic simulation is performed to investigate the cyclic behavior of Al bi-crystals with GB segregation of Co or Ti during their mode I cyclic loading perpendicular to GB plane. Results are given in comparison with the case of pure Al bi-crystal. Detailed analysis of the structure evolution during cyclic loading for the considered bi-crystals is presented. It is found that during the cycling, plastic deformation of the pure Al bi-crystal occurs through perfect dislocation sliding followed by twinning, while the GB segregations inhibit the formation of both perfect dislocations and twins in an Al matrix leading to decrease in ductility of the bi-crystals and intergranular crack propagation rate. The cyclic loading of the samples with GB segregation is accompanied with a generation of plenty of Shockley partials. Both the alloying elements in GBs can improve the fatigue lifetime of the Al bicrystals. The ability of GB segregations in bi-crystalline and polycrystalline Al to retard the dislocation emission from GBs that has been first revealed in the study could be successfully used to improve fatigue characteristics of metals, especially nanocrystalline metals with a dense GB network. Keywords Aluminum alloys; cracks; cyclic stress/strain curve; dislocations; molecular dynamics. Corresponding author: K. Zhou, E-mail address: [email protected]
1. Introduction Fatigue is a progressive structural damage of a material that can be observed when it is subjected to repeated loading and unloading. It is the most common source behind failures of mechanical structures and therefore crucial for the application of metals and alloys [1]. Understanding of the fatigue behavior of metallic materials is an important issue in material science. Investigation of structure evolution and crack growth in a material during its cyclic loading, as well as an estimation of its lifespan, are the main tasks scientists aim to solve in this framework. Due to the ability of metallic bulk ultra-fine grain (UFG) and nanocrystalline (NC) materials to demonstrate very high strength and superplastic behavior caused by a dense grain boundary (GB) network, such materials are of significant scientific and technological interest [2-7]. According to the experimental studies, the fatigue endurance of the UFG alloys is higher as compared to the alloys with coarse-grained microstructure [8-12]. The main reason for this is a high ultimate strength of UFG materials, which favors an increased fatigue endurance limit [13] (with exceptions [14]). A large number of GBs and/or twins in NC or nanotwinned metallic materials can impede fatigue crack propagation [15-17]. The effect of high-angle GBs and a twin boundary on fatigue cracking behavior of Cu coaxial bi-crystals was studied experimentally [18]. Mechanisms of defect-interface interactions were analyzed in a recent review [19]. Grain refinement of a polycrystalline material down to the nanoscale level can improve also its various functional properties [2,3,20,21]. According to the literature, the main fatigue-crack propagation mechanisms are a coalescence of cracks, vacancies and voids caused by an emission and absorption of dislocations at a crack tip or by fatigue cleavage of atomic bonds in a crack plane [15,22-27]. Due to dislocation activity usually, the crack tip undergoes blunting during sample loading and re-sharpening when stresses are released [15]. Crack nucleation and propagation ultimately involves the rupture of atomic bonds [27]. Nishimura and Miyazaki observed that cyclic loading of Fe can be accompanied with not only
emission and absorption of edge dislocations and vacancy generation but also with phase transition to release stress concentration around a crack tip [22]. Similar structural change near the crack tip during cyclic loading of body-centered cubic (bcc) Fe was observed in [28]. Such structural behavior looks very close to that observed in intermetallic alloys during their uniaxial tension when domains having different elastic strains coexist in the structure [29-34]. Recently, Rupert and Schuh revealed that cyclic loading of NC Ni leads to relaxation of non-equilibrium GB structure through dissipation of energy and reduction of the average atomic energy and additional strengthening of the material [35]. It was shown that, under certain conditions, GB segregation can result in additional strengthening and have a positive effect on ductility and structural stability of bulk NC materials [3643]. On the other hand, major of works devoted to the fatigue crack growth were devoted to single element materials, for example, pure Cu [15,23], Ni [23,44,45], Al [46], Mg [47] and Fe [28,48,49]. A series of theoretical studies was conducted earlier on the effect of GB segregation of various alloying elements in NC and bi-crystalline Al samples subjected to quasi-static loading in mode I and mode II [50-54]. At the same time, there is a lack of works devoted to fatigue behavior of bulk NC materials having GB segregations. From the abovementioned literature, it is seen that the fatigue behavior of different metallic materials, especially single-crystalline and bi-crystalline metals, has been studied quite extensively by molecular dynamics (MD). At the same time, to the best of our knowledge, there are no theoretical studies dealing with deformation behavior, analyses of structure evolution and crack propagation in metallic materials having GB segregations during their cyclic loading. Given this, the current study is devoted to a comparison of deformation behavior and mechanisms of bi-crystals of pure Al and Al with GB segregation of Co or Ti when they are subjected to cyclic loading perpendicular to GB planes.
2. Modeling A computational cell having almost 70000 atoms of Al is in the form of a rectangular parallelepiped of 21×18×3 nm size, i.e. quasi-two-dimensional geometry, is chosen for simulation (Fig. 1 (a)). The atoms form two differently oriented face-centered cubic (fcc) crystals. The crystallographic orientation of the upper grain is shown in Fig. 1 (a), the orientation of the lower grain is obtained by clockwise rotation of the upper grain around the [011] direction by the angle of 30º forming an asymmetric tilt GB. In both the grains, the [011] direction is parallel to the z-axis. The planes of the two tilt GBs existing in the computational cell are parallel to the xz-plane. One of them is located in the middle of the computational cell, while another one is formed by the upper and lower faces of the cell due to the use of periodic boundary conditions along the three orthogonal directions. The crystallographic orientations of the crystals are chosen to promote the generation of dislocations and further ease of their visualization. The maximal Schmid factor, m, is equal to 0.408 and 0.241 for the upper and lower grains, respectively. In both the grains, there exists only one slip system with the maximal m. In order to create GB segregation, two rows of Al atoms at GBs are replaced by Co or Ti atoms. According to our previous numerical studies [50-54], NC Al with these additional elements in GBs can be very promising for practical application because they can lead to enhanced ductility and strength of the material. The segregated atoms are shown in blue in Fig.1 (b). Though such high concentration of Co and Ti in GBs is far from being observed experimentally, but it is applied for observation of the prominent effect of their addition and an ease of computational reproducibility. To speed up the deformation process and failure of the samples under cyclic loading, a microcrack of 2.5×0.7×3 nm size along the x, y and z directions, respectively, is initially introduced in the bi-crystals. For analyzing the possible effect of GB segregation on structure evolution of the bicrystals, the microcrack is created right under an interlayer of segregated atoms in the middle of the computational cell (Fig. 1 (a)).
The large-scale atomic/molecular massively parallel simulator (LAMMPS) program package is used for the atomistic simulation [55]. In the considered systems, as force-field potentials of atom interaction the many-body embedded-atom method (EAM) potentials [56] are chosen. A motion of atoms in the Al-Co and Al-Ti bi-crystals is described by interatomic potentials developed by Purja Pun et al. [57] and Zope et al. [58], respectively. For simulation of the pure Al, either the interatomic potential for Al-Co or for Al-Ti is used. Therefore hereinafter, throughout the paper, the corresponding Al structures are denoted as “Al_Al-Co base” and “Al_Al-Ti base”, respectively, depending on the interatomic potential used. For visualizing an atomic structure and for dislocation analysis (the dislocation extraction algorithm), open source OVITO software is adopted [59,60].
Fig. 1. (a) MD model geometry. In (b), simulation cell for Al-X bi-crystal (X can be Co or Ti) after relaxation and equilibration at 300 K within 10 ps. Al atoms are shown in red, while X atoms segregated in the tilt GBs in blue. In (c), schematic illustration of the cyclic loading with gradually increasing amplitude imposed on the bi-crystals is given.
Prior to cycling, the studied materials are relaxed at zero temperature to obtain the state of the minimum potential energy and then equilibrated for 10 ps at 300 K. The isothermal-isobaric (NPT) ensemble is employed in the simulations. During the cyclic loading of the bi-crystals, the stresscontrolled tensile loading-unloading in mode I at the temperature of 300 K along the y-axis is applied at a constant stress rate of dyy/dt = 7×109 GPa/sec. All the strain components except yy are controlled to be zero in order to avoid collapsing of the microcrack due to deformation of the computational cell along the x and z-axes perpendicular to the direction of applied loading. Figure 1 (c) schematically shows the cycling loading imposed on the bi-crystals as the dependence of stresses, yy , vs. number of cycles, N. The minimal stress (σmin) corresponds to the unloaded state and equals to 0 GPa. The initial maximal applied stress for the cyclic loading (σmax) is defined as 85 % of the ultimate strength obtained during the quasi-static uniaxial tension which is about 3.52, 3.44, 3.57 and 3.4 GPa for the “Al_Al-Co base”, “Al_Al-Ti base”, Al-Co and Al-Ti bicrystals, respectively. The stress ratio R = σmin/σmax is equal to 0. Since modeling of cyclic deformation is a very time-consuming process and, as a result of repeated loading and unloading, normally material accumulates defects leading to its hardening, it is decided to gradually increase σmax by 20 MPa per cycle to speed up the development of fracture.
3. Results 3.1. Cyclic stress-strain curves Figure 2 shows the stress-strain curves obtained for the “Al_Al-Co base” (a), “Al_Al-Ti base” (b), Al-Co (c), and Al-Ti (d) bi-crystals during their cyclic loading. The stress-strain hysteresis loops for the “Al_Al-Co base” bi-crystal gradually shift to the right cycle-by-cycle up to its failure (Fig. 2 (a)). Very similar behavior for the “Al_Al-Ti base” bi-crystal is observed (Fig. 2 (b)). It is clearly seen that stress-strain response for the pure Al, for both the considered interatomic potentials, is quite identical in terms of residual strain (Fig. 2 (a) and (b)). However, it differs noticeably from their
counterparts having the GB segregation. The curves for the Al-Co and Al-Ti bi-crystals are arranged more densely (Fig. 2 (c) and (d)). Interestingly, in the case of Al-Co, the stress-strain loops almost merge, while deformation of the Al-Ti bi-crystal along the y-axis at unloaded condition does not exceed 0.4 %.
Fig. 2. Stress-strain curves obtained during cyclic loading of the bi-crystals: (a) Al_Al-Co base; (b) Al_Al-Ti base, (c) Al-Co and (d) Al-Ti.
In Fig. 3, the time dependence of the potential energy per atom, Ep, is given for the considered bi-crystals. It is common for all the bi-crystals that loading is accompanied by an increase in the energy while unloading results in decreasing its value. Therefore from these curves, one can easily count the maximal number of cycles to failure, Nmax, sample endures during cyclic loading. For the
“Al_Al-Co base”, “Al-Al-Ti base”, Al-Co and Al-Ti bi-crystals, Nmax is 25, 13, 26 and 14, respectively. Thus, an introduction of the GB segregation of Co or Ti in Al bi-crystal increases Nmax by one cycle. It is seen that the average energy per atom for the systems having atoms segregated to GBs is higher than that for the pure Al. It is valid for both the interatomic potentials used for the pure Al. For the Al-Co and Al-Ti bi-crystals, Ep is around of -3.40 and -3.39 eV, while for the pure Al bicrystal Ep is close to -3.31 eV.
Fig. 3. Potential energy per atom, Ep, as the function of time, t, during cyclic loading of the “Al_Al-Co base” (a), “Al_Al-Ti base” (b), Al-Co (c) and Al-Ti (d) bi-crystals.
In Fig. 4, the dependence of residual strain along the y-axis after unloading of the bi-crystals as a function of the cycle number is presented. A change of the strain for the pure Al bi-crystals can be
divided into three stages. At the first stage, the residual strain slightly increases or even does not change. At the second stage, a sharp increase of the strain during two loading-unloading cycles is observed. At the third stage, before sample failure, a continuous but not rapid increase in its size occurs. Quite different behavior for the Al-Co and Al-Ti bi-crystals is revealed: almost no increase in the residual strain for the Al-Co and only insignificant elongation after ten loading-unloading cycles for the Al-Ti bi-crystal.
Fig. 4. Residual strain along the y axis vs. cycle number after unloading of the bi-crystals.
3.2. Effect of grain boundary segregation on crack growth Recall that in order to speed up the bi-crystal failure during its cycling, the microcrack is introduced at GB in the middle of the computational cell (Fig. 1 (a) and (b)). Therefore it would be interesting to study the effect of GB segregation on the crack growth during the cyclic loading. In Fig. 5, the dependence of crack length and its maximal opening as a function of the cycle number, N, is given for the considered bi-crystals. Slopes of the crack length curves and the maximal crack opening curves are different for the bi-crystals. Overall, it is clearly seen that in the pure Al, the crack growth rate is higher than that in the Al-Co and Al-Ti bi-crystals. During the cycling, before the last full cycle, the crack length for the “Al_Al-Co base” and “Al_Al-Ti base” bi-crystals increases
from ~ 27 and 30 Å to ~ 40 and 45 Å demonstrating an abrupt change in the size at N = 10 and N = 4, respectively. With further cycling, up to the samples’ failure, the crack grows gradually undergoes some oscillations but without any sufficient changes. At the same time, the crack growth rate during the cycling of the bi-crystals with GB segregation is lower. Thus, for the Al-Ti bi-crystal, with the exception of the last full cycle, the crack propagates gradually from ~ 27 to 35 Å. It is interesting that in the case of the Al-Co bi-crystal, its value almost does not change upon the cycling. Another important difference is that, unlike the pure Al, the bi-crystals with GB segregation do not demonstrate any abrupt changes of the crack size during the cycling. The maximal crack opening curves behave in a similar way (Fig. 5 (b)). With the increase in cycle number, the cracks for the “Al_Al-Co base” and “Al_Al-Ti base” bi-crystals open up to ~18 and 17 Å at N = 25 and N = 13, respectively. Like for the crack length curves, the bi-crystals demonstrate an abrupt increase in the crack opening value at N = 4 and N = 10. In the case of the Al-Co bi-crystal, similar to the crack length, the sample does not show any significant changes in its opening. As for the Al-Ti bi-crystal, the maximal crack opening value gradually increases (up to ~ 13 Å), but the slope of the curve is much lower than for the corresponding pure Al bi-crystal.
Fig. 5. Crack length (a) and maximal crack opening (b) vs. cycle number, N.
4. Discussion In order to understand the effect of Co and Ti addition to GBs on the deformation behavior of Al bi-crystals, the analysis of structure evolution in the pure Al, Al-Co and Al-Ti bi-crystals during their cyclic loading is carried out. In Figs. 6 to 9, the common neighbor analysis results are presented for the “Al_Al-Co base”, “Al_Al-Ti base”, Al-Co and Al-Ti bi-crystals, respectively. Here, single and double rows of hexagonal close-packed (hcp) crystal atoms refer to twin boundaries and stacking faults, respectively. Atoms of bcc and disordered structures are mostly located along microcrack surfaces, GBs and near point defects. For all the samples, the presence of multiple atomic-scale disordered regions can be observed, especially in the loaded state. Some of such regions are encircled in Fig. 6 for the first cycle. These areas represent localized large-amplitude thermal fluctuations of atoms and point defects. It is seen that the pure Al samples deform by twinning during the cycling loading (Figs. 6 and 7). The formation of first twins in the “Al_Al-Co base” bi-crystal can be observed at N = 11, while in the “Al_Al-Ti base” bi-crystal this process takes place earlier at N = 5. The appearance of twin plates is preceded by the formation of stacking faults crossing the grains from one GB to another that can be seen at an early stage of the cycling. The Shockley partials, which are precursors to the formation of stacking faults, are emitted from the internal free surface of the microcrack or nearby. Similar observation was made in Ref. [61], where the authors found that free surface facilitates the nucleation of dislocations from GBs. As a consequence of such dislocation emission, an appearance of atomic steps on the microcrack surface and its growth are observed (Figs. 6 and 7). The latter finding is consistent with the models suggesting void growth by an emission of dislocations [62-65].
Fig. 6. Structure evolution of the “Al_Al-Co base” bi-crystal during cyclic loading (N is cycle number). The common neighbour analysis is given: red color represents hcp atoms, dark blue – bcc atoms and light blue – atoms of the disordered structure. To avoid cluttering, atoms of the fcc structure are made invisible. Loaded and unloaded structures are indicated on the left by “σmax” and “σmin”, respectively.
The first twin appears in the upper grain of the bi-crystals with the higher Schmid factor. It is worth noting that the distance between the neighbouring twin boundaries increases in the loaded state and decreases after unloading. During unloading, twins can again transform into stacking faults or completely disappear (Fig. 7), i.e. detwinning process takes place. Twin boundary migration occurs via partial dislocation gliding along a twin boundary on the adjacent {111} plane [66-68]. Due to very fast movement of perfect dislocations their cores are not seen in the snapshots presented in Figs. 6 to 9. Normally in conventional coarse-grained metals with high stacking fault energy such as Al, perfect dislocations do not split into partials. In the case of NC Al, the splitting distance is quite small, i.e. emission of trailing Shockley partial follows right after the nucleation of leading partial forming a short stacking fault in between [69-71]. Such perfect dislocations after travelling through the entire grain do not leave stacking faults and therefore cannot be detected by the common neighbour analysis. At the same time, it is known that conventional fcc metals normally deform by dislocation sliding and have a little contribution from twinning. Therefore, in order to evaluate perfect and partial dislocation activity in the bi-crystals’ structure subjected to the cyclic loading, the dislocation extraction algorithm is used [60]. Figure 10 shows the dependence of the number of the 1/2<110> perfect and the 1/6<112> Shockley partial dislocations vs. cycle number in the loaded and unloaded states. The other type of dislocations, such as the 1/3<111> Frank and 1/6<110> stair-rod dislocations, are also present in the bi-crystals’ structure, but their percentage is insignificant from the total number of defects, and therefore they are not taken into consideration.
Fig. 7. Same as in Fig. 6 but for the “Al_Al-Ti base” bi-crystal.
For both the pure Al bi-crystals, at the early stage of the cycling, the number of perfect dislocations detected in the GB regions is higher than the Shockley partials (Figs. 10 (a) and (b)). Their amount decreases with increase in a number of cycles that can be easily seen especially in the case of the “Al_Al-Co base” bi-crystal (Fig. 10 (a)). Given this, in the pure Al bi-crystal at the early stage of the cycling, the main deformation mechanism is the perfect dislocation sliding. Further cycling and consequently higher internal stresses lead to a reduction of perfect dislocation activity and switching-on of the twinning mechanism, i.e. when Shockley partials emitted on adjacent glide plane travel through an entire grain. A similar transition from one deformation mechanism to another in NC materials was revealed earlier [72]. Such tendency to twinning in NC metals can be explained by the fact that their deformation requires considerably higher stresses in comparison with conventional coarse-grained materials [73]. It is noticeable that the cyclic stress-strain curves for the “Al_Al-Co base” and “Al_Al-Ti base” bi-crystals are getting denser with an increase in the number of cycles (Figs. 3 (a) and (b)), wherein the residual strain tends to saturation (Fig. 4). This is presumably related to the change in deformation mechanism from the perfect dislocation sliding to twinning. Such deformation behavior is accompanied by an abrupt increase in the crack length and its opening at N = 4 and N = 10 for the “Al_Al-Co base” and “Al_Al-Ti” bi-crystals, respectively (Fig. 5 (a) and (b)). The “Al_Al-Co base” and “Al_Al-Ti” bi-crystals demonstrate different maximal number of cycles to failure, 25 and 13, respectively (Fig. 3(a) and (b)). This oddity can be explained by the fact that the Al-Ti interatomic potential gives for pure Al approximately 30 % lower surface energy than in the case of the Al-Co potential. The latter means that the formation of free surfaces in the “Al_Al-Ti” bi-crystal occurs easier and, as a consequence, it results in an earlier fracture in comparison with the “Al_Al-Co base” bi-crystal.
Fig. 8. Same as in Fig. 6 but for the Al-Co bi-crystal. The arrows show examples of Shockley partials.
Fig. 9. Same as in Fig. 6 but for the Al-Ti bi-crystal.
The deformation behavior of the Al bi-crystals with GB segregation significantly differs from that of the pure Al. It is revealed that the Al-Co bi-crystal does not undergo any twin formation (Fig. 8). Unlike the pure Al (Figs. 6 and 7), an increase in cycle number does not lead to significant crack growth as well as to rise in the residual strain up to sample failure (Figs. 4 and 5). The dislocation analysis shows only minor perfect dislocation activity, while the number of Shockley partials is higher than in the case of the pure Al in the whole range of cycling that especially evident in the loaded state (Fig. 10 (c)). Partial dislocations, as well as stacking faults, can be observed in the highly defected layer near GBs and mostly in the upper grain having the higher Schmid factor. A few examples of a Shockley dislocation location are indicated by the arrows in Fig. 8 for N = 1. Obviously, an absence of the perfect dislocation sliding and twinning results in merging of cyclic stress-strain curves for the AlCo bi-crystal (Fig. 3 (c)). Apparently, in this case, the plastic deformation of the bi-crystal occurs via sliding of the partial dislocations. Such remarkable difference in deformation behavior of the pure Al and Al-Co bi-crystals is due to highly defected regions formed near GBs that caused by the presence of Co atoms (Fig. 8). This is in agreement with the observation that the formation of GB segregations suppresses a dislocation initiation at GBs due to a solute drag [42]. Apparently, due to the weaker drag force of Ti, compared to Co, its GB segregation cannot stop the GB migration during deformation process that has been also observed earlier in [50]. Thus, it is clearly seen that the position of the crack, which was initially introduced under the GB (Fig. 1 (a)), after equilibration procedure, is located directly in it (Fig. 9) that explained by insignificant migration of the GB down to the microcrack level. For the Al-Ti bi-crystal, similar to the previous case, the twinning process does not take place during the cyclic loading (Fig. 9). Twins can be observed only in the last cycle right before the fracture, while stacking faults appear in the structure already at first cycles. The number of Shockley partials in the structure is noticeably higher than the number of perfect dislocations (Fig. 10). In this case, the main deformation mechanism is the partial dislocation sliding with less pronounced the perfect dislocation slip. The stress-strain loops, even though look
dense, do not merge as in the case of the Al-Co bi-crystal (Fig. 3 (c) and (d)). It can be explained by the contribution of perfect dislocations into the total plastic strain which is also reflected in a slight increase of the residual strain (Fig. 4). This is probably also associated with the weak drag force of Ti and some migration of the GB mentioned earlier. At the last cycle in the upper grain, the switching-on of additional slip systems with the lower Schmid factor can be observed (Fig. 9). All the studied bicrystals undergo failure at the corresponding cycle right after reaching σmax (see Figs. 6-9).
Fig. 10. Dependence of a number of dislocation segments vs. cycle number for the “Al_Al-Co base” (a), “Al_Al-Ti base” (b), Al-Co (c) and Al-Ti (d) bi-crystals. In the remarks, the symbols “l” and “unl” denote the loaded and unloaded states, respectively.
Another interesting effect is that the number of Shockley partials in both the Al-Co and Al-Ti bicrystals practically does not change with the cycle number in contrast to the number of perfect
dislocations in the pure Al structure which drastically decreases (Fig. 10). At first cycles, the release of internal stresses in the pure Al bi-crystals takes place via perfect dislocation sliding and, as a consequence, the wider stress-strain loops are observed (Fig. 2 (a) and (b)). At further cycles, an activity of all dislocations significantly decreases and the loops become denser, i.e. high internal stresses cannot be removed via dislocation slip that finally leads to failure. Unlike the pure Al, the bicrystals of Al-Co and Al-Ti demonstrate high partial dislocation activity during the whole cycling. Nevertheless, such amount of Shockley partials still cannot provide full structure relaxation and accommodation of plastic strain to prevent premature fracture of the samples. Based on the aforesaid, from the atomistic point of view, polycrystalline materials stable to cyclic loading should provide constantly high dislocation activity during cycling. The reduction of dislocation activity must be compensated by increasing the role of accommodation processes, such as GB sliding, GB migration, grain rotation etc., similar to those found in NC materials [72,74,75]. Another way to increase the partial dislocation activity in a material is through lowering stacking fault energy, which can be achieved by alloying.
5. Summary In summary, the stress-strain behavior and deformation mechanisms in the bi-crystals of pure Al and Al with GB segregation of Co or Ti during their cyclic loading were studied by means of the MD simulation. The results showed that during the cycling, the pure Al undergoes plastic deformation trough perfect dislocation sliding followed by twinning. An addition of Co or Ti atoms in GBs inhibits the perfect dislocation slip as well as the twin formation, thus decreasing plastic flow and residual strain after sample unloading. The main contribution to the deformation in the binary systems is from the slip of Shockley partials, while perfect dislocation activity is very low. The difference in the deformation behavior of the pure Al and its counterparts having GB segregation can be explained by the change of GB structure due to the presence of additional elements
that promotes splitting of the perfect dislocations on Shockley partials in the NC material with the high stacking fault energy. It was shown also that the emission of perfect dislocations from GBs and the twin formation promote crack propagation. Therefore, in Al bi-crystals with GB segregation, the crack grows slower in comparison with that in pure Al samples. As a result, an addition of both the considered alloying elements has the positive effect on the fatigue behavior of Al bi-crystals. The results of the present study suggest that GB segregation can improve fatigue properties of UFG and NC metallic materials, and therefore more studies in this direction, theoretical and experimental, are needed.
Acknowledgements R.I. Babicheva acknowledges the Singapore International Graduate Award (SINGA) for providing her PhD scholarship. The work was supported by the SIMTech-NTU Joint Lab on Reliability (Singapore) and the Russian Foundation for Basic Research (RFBR) [16-32-00618 mol_a]. S.V. Dmitriev acknowledges financial support from the Russian Science Foundation [14-13-00982].
References 1. P. Chowdhury, H. Sehitoglu, Mechanisms of fatigue crack growth – a critical digest of theoretical developments. Fatigue Fract. Engng. Mater. Struct. 39 (2016) 652–674. 2. R.Z. Valiev, A.P. Zhilyaev, T.G. Langdon, Bulk Nanostructured Materials: Fundamentals and Applications, (Hoboken, New Jersey: Wiley, 2014) 440 p. 3. A.P. Zhilyaev, T.G. Langdon, Using high-pressure torsion for metal processing: fundamentals and applications. Prog. Mater. Sci. 53 (2008) 893–979. 4. M. Zehetbauer, R. Grössinger, H. Krenn, M. Krystian, R. Pippan, P. Rogl, T. Waitz, R. Würschum, Bulk nanostructured functional materials by severe plastic deformation. Adv. Eng. Mater. 12(8) (2010) 692–700. 5. Y. Estrin, A. Vinogradov, Extreme grain refinement by severe plastic deformation: A wealth of challenging science. Acta Mater. 61 (2013) 782–817. 6. O. Sitdikov, E. Avtokratova, R. Babicheva, T. Sakai, K. Tsuzaki, Y. Watanabe, Influence of processing regimes on fine-grained microstructure development in an AlMgSc alloy by hot equal-channel angular pressing. Mater. Trans. 53(1) (2012) 56–62. 7. O.Sh. Sitdikov, E.V. Avtokratova, R.I. Babicheva, Effect of temperature on the formation of a microstructure upon equal-channel angular pressing of the Al-Mg-Sc 1570 alloy. Phys. Met. Metallogr. 110(2) (2010) 153–161. 8. I.P. Semenova, A.V. Polyakov, V.V. Polyakova, Y. Huang, R.Z. Valiev and T.G. Langdon, High-cycle fatigue behavior of an ultrafine-grained Ti–6Al–4V alloy processed by ECAP and extrusion. Adv. Eng. Mater. 18(12) (2016) 2057–2062. 9. S. Zherebtsov, G. Salishchev, R. Galeyev, K. Maekawa, Mechanical properties of Ti-6Al-4V titanium alloy with submicrocrystalline structure produced by severe plastic deformation. Mater. Trans. 46 (2005) 2020–2025. 10. L.R. Saitova, H.W. Höppel, M. Göken, I.P. Semenova, G.I. Raab, R.Z. Valiev, Fatigue behavior of ultrafine-grained Ti-6Al-4V 'ELI' alloy for medical applications. Mater. Sci. Eng. A 503 (2009) 145–147. 11. I.P. Semenova, E.B. Yakushina, V.V. Nurgaleeva, R.Z. Valiev, Nanostructuring of Ti-alloys by SPD processing to achieve superior fatigue properties. Int. J. Mater. Res. 100 (2009) 1691– 1696. 12. A. V. Polyakov, I. P. Semenova, Y. Huang, R. Z. Valiev, T. G. Langdon, Fatigue life and failure characteristics of an ultrafine-grained Ti-6Al-4V alloy processed by ECAP and extrusion. Adv. Eng. Mater. 16 (2014) 1038-1043.
13. H. W. Höppel, M. Kautz, C. Xu, M. Murashkin, T. G. Langdon, R. Z. Valiev, H. Mughrabi, An overview: Fatigue behaviour of ultrafine-grained metals and alloys. Int. J. Fatigue 28 (2006) 1001-1010. 14. R. Liu, Y. Tian, Z. Zhang, X. An, P. Zhang, Z. Zhang, Exceptional high fatigue strength in Cu15at.%Al alloy with moderate grain size. Sci. Rep. 6 (2016), 27433, DOI: 10.1038/srep27433 15. X. Zhou, X. Li, C. Chen. Atomistic mechanisms of fatigue in nanotwinned metals. Acta Mater. 99 (2015) 77–86. 16. K.S. Kumar, H. Van Swygenhoven, S. Suresh, Mechanical behavior of nanocrystalline metals and alloys. Acta Mater. 51 (2003) 5743. 17. P.B. Chowdhury, H. Sehitoglu, R.G. Rateick, H.J. Maier, Modeling fatigue crack growth resistance of nanocrystalline alloys. Acta Mater. Volume 61, Issue 7, (2013), Pages 2531– 2547. 18. L.L. Li, P. Zhang, Z.J. Zhang, Z.F. Zhang, Effect of crystallographic orientation and grain boundary character on fatigue cracking behaviors of coaxial copper bicrystals. Acta Mater. 61 (2013) 425–438. 19. I.J. Beyerlein, M.J. Demkowicz, A. Misra, B.P. Uberuaga, Defect-interface interactions. Prog. Mater. Sci. 74 (2015) 125–210. 20. R.I. Babicheva, K.Y. Mulyukov, Thermomechanical treatment to achieve stable two-way shape memory strain without training in Ti-49.8 at.% Ni alloy. Appl. Phys. A 116(4) (2014) 1857-1865. 21. R.I. Babicheva, K.Y. Mulyukov, I.Z. Sharipov, I.M. Safarov, Influence of the structure of the Ti-49.8 at % Ni alloy on its thermal expansion during the martensitic phase transformation. Phys. Solid State 54(7) (2012) 1480-1485. 22. K. Nishimura, N. Miyazaki, Molecular dynamics simulation of crack growth under cyclic loading. Comput. Mater. Sci. 31 (2004) 269–278. 23. G.P. Potirniche, M.F. Horstemeyer, P.M. Gullett, B. Jelinek, Atomistic modelling of fatigue crack growth and dislocation structuring in FCC crystals. Proc. R. Soc. A 462 (2006) 3707– 3731. 24. D. Farkas, M. Willemann, B. Hyde, Atomistic Mechanisms of Fatigue in Nanocrystalline Metals. PRL 94 (2005) 165502 (4 pages). 25. M.F. Horstemeyer, D. Farkas, S. Kim, T. Tang, G. Potirniche, Nanostructurally small cracks (NSC): A review on atomistic modeling of fatigue. Int. J. Fatigue 32 (2010) 1473–1502. 26. K.L. Baker, D.H. Warner, An atomistic investigation into the nature of near threshold fatigue crack growth in aluminum alloys. Eng. Fract. Mech. 115 (2014) 111–121.
27. E. Bitzek, J.R. Kermode, P. Gumbsch, Atomistic aspects of fracture. Int. J. Fracture. 191 (2015) 13–30. 28. L. Ma, S. Xiao, H. Deng, W. Hu, Molecular dynamics simulation of fatigue crack propagation in bcc iron under cyclic loading. Int. J. Fatigue 68 (2014) 253–259. 29. K.A. Bukreeva, R.I. Babicheva, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, A.I. Potekaev, Nonuniform elastic deformation of nanofilms formed from NiAl and FeAl alloys. Russian Physics Journal 57(1) (2014) 69-78. 30. R.I. Babicheva, K.A. Bukreeva, S.V. Dmitriev, R.R. Mulyukov, K. Zhou, Strengthening of NiAl nanofilms by introducing internal stresses. Intermetallics 43 (2013) 171-176. 31. R.I. Babicheva, K.A. Bukreeva, S.V. Dmitriev, K. Zhou, Discontinuous elastic strain observed during stretching of NiAl single crystal nanofilms. Comput. Mater. Sci. 79 (2013) 52-55. 32. K.A. Bukreeva, R.I. Babicheva, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, Inhomogeneous elastic deformation of nanofilms and nanowires of NiAl and FeAl alloys. JETP Letters 98 (2) (2013) 91-95. 33. K.A. Bukreeva, R.I. Babicheva, A.B. Sultanguzhina, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, Effect of temperature on inhomogeneous elastic deformation and negative stiffness of NiAl and FeAl alloy nanofilms. Phys. Solid State 56(6) (2014) 1157-1162. 34. K.A. Bukreeva, R.I. Babicheva, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, Negative stiffness of the FeAl intermetallic nanofilm. Phys. Solid State 55(9) (2013) 1963-1967. 35. T.J. Rupert, C.A. Schuh, Mechanically driven grain boundary relaxation: A mechanism for cyclic hardening in nanocrystalline Ni. Phil. Mag. Letters 92(1) (2012) 20-28. 36. A.J. Detor, C.A. Schuh, Grain boundary segregation, chemical ordering and stability of nanocrystalline alloys: Atomistic computer simulations in the Ni-W system. Acta Mater. 55 (2007) 4221–4232. 37. T. Frolov, K.A. Darling, L.J. Kecskes, Y. Mishin, Stabilization and strengthening of nanocrystalline copper by alloying with tantalum. Acta Mater. 60 (2012) 2158–2168. 38. N.Q. Vo, J. Schaefer, R.S. Averback, K. Albe, Y. Ashkenazy, P. Bellon, Reaching theoretical strengths in nanocrystalline Cu by grain boundary doping. Scripta Mater. 65 (2011) 660–663. 39. S. Özerinç, K. Tai, N.Q. Vo, P. Bellon, R.S. Averback, W.P. King, Grain boundary doping strengthens nanocrystalline copper alloys. Scripta Mater. 67 (2012) 720–723. 40. L. Kurmanaeva, Y. Ivanisenko, J. Markmann, K. Yang, H.J. Fecht, J. Weissmuller, Work hardening and inherent plastic instability of nanocrystalline metals. Phys. Status Solidi (RRL) 4 (2010) 130–132.
41. J. Schafer, A. Stukowski, K. Albe, Plastic deformation of nanocrystalline Pd-Au alloys: On the interplay of grain boundary solute segregation, fault energies and grain size. Acta Mater. 59 (2011) 2957–2968. 42. R.Z. Valiev, N.A. Enikeev, M.Yu. Murashkin, V.U. Kazykhanov, X. Sauvage, On the origin of the extremely high strength of ultrafine-grained Al alloys produced by severe plastic deformation. Scripta Mater. 63(9) (2010) 949–952. 43. K. Tugcu, G. Sha, X.Z. Liao, P. Trimby, J.H. Xia, M.Y. Murashkin, Y. Xie, R.Z. Valiev, S.P. Ringer, Enhanced grain refinement of an Al-Mg-Si alloy by high-pressure torsion processing at 100ºC. Mater. Sci. Eng. A552 (2012) 415–418. 44. W.-P. Wu, Y.-L. Li, X.-Y. Sun, Molecular dynamics simulation-based cohesive zone representation of fatigue crack growth in a single crystal nickel. Comput. Mater. Sci. 109 (2015) 66–75. 45. W.P. Wu, N.L. Li, Y.L. Li, Molecular dynamics-based cohesive zone representation of microstructure and stress evolutions of nickel intergranular fracture process: Effects of temperature. Comput. Mater. Sci. 113 (2016) 203–210. 46. P. White, Molecular dynamic modelling of fatigue crack growth in aluminium using LEFM boundary conditions. Int. J. Fatigue 44 (2012) 141–150. 47. T. Tang, S. Kim, M.F. Horstemeyer, Fatigue crack growth in magnesium single crystals under cyclic loading: Molecular dynamics simulation. Comput. Mater. Sci. 48 (2010) 426–439. 48. A. Machová, J. Pokluda, A. Uhnáková, P. Hora, 3D atomistic studies of fatigue behaviour of edge crack (001) in bcc iron loaded in mode I and II. Int. J. Fatigue 66 (2014) 11–19. 49. A. Uhnáková, J. Pokluda, A. Machová, P. Hora, 3D atomistic simulation of fatigue behavior of a ductile crack in bcc iron loaded in mode II. Comput. Mater. Sci. 61 (2012) 12–19. 50. R.I. Babicheva, S.V. Dmitriev, Y. Zhang, S.W. Kok, N. Srikanth, B. Liu, K. Zhou, Effect of grain boundary segregations of Fe, Co, Cu, Ti, Mg and Pb on small plastic deformation of nanocrystalline Al. Comput. Mater. Sci. 98 (2015) 410-416. 51. R.I. Babicheva, S.V. Dmitriev, L. Bai, Y. Zhang, S.W. Kok, G. Kang, K. Zhou, Effect of grain boundary segregation on the deformation mechanisms and mechanical properties of nanocrystalline binary aluminum alloys. Comput. Mater. Sci. 117 (2016) 445-454. 52. R. Babicheva, S. Dmitriev, Y. Zhang, S.W. Kok, K. Zhou, Effect of grain boundary segregation on shear deformation of nanocrystalline binary aluminum alloys at room temperature. Mater. Sci. Forum 838-839 (2016) 89-94.
53. R.I. Babicheva, D.V. Bachurin, S.V. Dmitriev, Y. Zhang, S.W. Kok, L. Bai, K. Zhou, Elastic moduli of nanocrystalline binary Al alloys with Fe, Co, Ti, Mg and Pb alloying elements. Phil. Mag. 96(15) (2016) 1598-1612. 54. R. Babicheva, S. Dmitriev, Y. Zhang, S.W. Kok, K. Zhou, Effect of Co distribution on plastic deformation of nanocrystalline Al-10.2 at.% Co alloy. Journal of Nanomaterials 2015, 2015. 55. S. Plimpton. Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117 (1995) 1–19. 56. M.S. Daw, M.I. Baskes, Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29(12) (1984) 6443–6453. 57. G.P. Purja Pun, V. Yamakov, Y. Mishin, Interatomic potential for the ternary Ni–Al–Co system and application to atomistic modeling of the B2–L10 martensitic transformation. Modelling Simul. Mater. Sci. Eng. 23 (2015) 065006. 58. R.R. Zope and Y. Mishin, Interatomic potentials for atomistic simulations of the Ti-Al system. Phys. Rev. B 68, 024102 (2003). DOI: 10.1103/PhysRevB.68.024102. 59. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO – the Open Visualization Tool. Modelling Simul. Mater. Sci. Eng. 18 (2010), 015012. 60. A. Stukowski, V. V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces. Modelling Simul. Mater. Sci. Eng. 20 (2012), 085007. 61. D.V. Bachurin, D. Weygand, P. Gumbsch, Dislocation-grain boundary interaction in <111> textured thin metal films. Acta Mater. 58 (2010) 5232–5241. 62. V.A. Lubarda, M.S. Schneider, D.H. Kalantar, B.A. Remington, M.A. Meyers, Void growth by dislocation emission. Acta Mater. 52 (2004) 1397–1408. 63. I.A. Ovid'ko, A.G. Sheinerman, Dislocation emission from nanovoids in single-phase and composite nanocrystalline materials. Rev. Adv. Mater. Sci. 11 (2006) 46–55. 64. D.C. Ahn, P. Sofronis, M. Kumar, J. Belak, R. Minich, Void growth by dislocation-loop emission. J. Appl. Phys. 101 (2007) 063514. 65. L. Wang, J.Q. Zhou, Y.G. Liu, S. Zhang, Y. Wang, W. Xing, Nanovoid growth in nanocrystalline metal by dislocation shear loop emission. Mater. Sci. Eng A 528 (2011) 5428– 5434. 66. J. Wang, N. Li, O. Anderoglu, X. Zhang, A. Misra, J.Y. Huang, J.P. Hirth, Detwinning Mechanisms for Growth Twins in Face Centered Cubic Metals. Acta Mater. 58 (2010) 2262– 2270.
67. H. Mirkhani, S.P. Joshi, Mechanism-Based Crystal Plasticity Modeling of Twin Boundary Migration in Nanotwinned Face-Centered Cubic Metals. J. Mech. Phys. Solids 68 (2014) 107– 133. 68. Y. Wei, The Kinetics and Energetics of Dislocation Mediated De-Twinning in NanoTwinned Face-Centered Cubic Metals. Mater. Sci. Eng. A 528(3) (2011) 1558–1566. 69. A. Froseth, H. Van Swygenhoven, P.M. Derlet, The influence of twins on the mechanical properties of nc-Al. Acta Mater. 52 (2004) 2259–2268. 70. A.G. Froseth, P.M. Derlet, H. Van Swygenhoven, Dislocations emitted from nanocrystalline grain boundaries: nucleation and splitting distance. Acta Mater. 52 (2004) 5863–5870. 71. H. Van Swygenhoven, P.M. Derlet, A.G. Froseth, Nucleation and propagation of dislocations in nanocrystalline fcc metals. Acta Mater. 54 (2006) 1975–1983. 72. D.V. Bachurin, P. Gumbsch, Accommodation processes during deformation of nanocrystalline palladium. Acta Mater. 58 (2010) 5491–5501. 73. Y.T. Zhu, X.Z. Liao, X.L. Wu, Deformation twinning in nanocrystalline materials. Prog. Mater. Sci. 57 (2012) 1–62. 74. H. Van Swygenhoven, P.A. Derlet, Grain-boundary sliding in nanocrystalline fcc metals. Phys. Rev. B 64(22) (2001) 224105. 75. N.Q. Vo, R.S. Averback, P. Bellon, S. Odunuga, A. Caro, Quantitative description of plastic deformation in nanocrystalline Cu: Dislocation glide versus grain boundary sliding. Phys. Rev. B 77(13) (2008) 134108.
Highlights
• Cycling of Al bi-crystal leads to perfect dislocation sliding followed by twinning. • Co and Ti in GBs of Al inhibit formation of perfect dislocations and twins. • Co and Ti in GBs promote partial dislocation slip during cycling of Al bi-crystal. • GB segregation can decrease ductility and cracking rate during nanomaterial cycling.
S0142-1123(17)30044-0 http://dx.doi.org/10.1016/j.ijfatigue.2017.01.038 JIJF 4228
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
20 October 2016 23 January 2017 25 January 2017
Please cite this article as: Babicheva, R.I., Dmitriev, S.V., Bachurin, D.V., Srikanth, N., Zhang, Y., Kok, S.W., Zhou, K., Effect of grain boundary segregation of Co or Ti on cyclic deformation of aluminium bi-crystals, International Journal of Fatigue (2017), doi: http://dx.doi.org/10.1016/j.ijfatigue.2017.01.038
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Effect of grain boundary segregation of Co or Ti on cyclic deformation of aluminium bi-crystals Rita I. Babicheva1, Sergey V. Dmitriev2,3, Dmitry V. Bachurin2,4, Narasimalu Srikanth5, Ying Zhang6, Shaw Wei Kok6, Kun Zhou1 1
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore 2 Institute for Metals Superplasticity Problems of Russian Academy of Sciences, 39 Khalturin St., Ufa 450001, Russia 3 Research Laboratory for Mechanics of New Nanomaterials, Peter the Great St. Petersburg Polytechnical University, St. Petersburg 195251, Russia 4 Institute for Applied Materials – Applied Materials Physics, Karlsruhe Institute of Technology, Hermann-vonHelmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany 5 Energy Research Institute @NTU, Nanyang Technological University, Singapore 637141, Singapore 6 Singapore Institute of Manufacturing Technology, 71 Nanyang Drive, Singapore 638075, Singapore
Abstract There exist many factors affecting fatigue behavior of metallic materials, among them the effect of grain boundary (GB) segregation of alloying elements remains largely unexplored. To exploit this factor, an atomistic simulation is performed to investigate the cyclic behavior of Al bi-crystals with GB segregation of Co or Ti during their mode I cyclic loading perpendicular to GB plane. Results are given in comparison with the case of pure Al bi-crystal. Detailed analysis of the structure evolution during cyclic loading for the considered bi-crystals is presented. It is found that during the cycling, plastic deformation of the pure Al bi-crystal occurs through perfect dislocation sliding followed by twinning, while the GB segregations inhibit the formation of both perfect dislocations and twins in an Al matrix leading to decrease in ductility of the bi-crystals and intergranular crack propagation rate. The cyclic loading of the samples with GB segregation is accompanied with a generation of plenty of Shockley partials. Both the alloying elements in GBs can improve the fatigue lifetime of the Al bicrystals. The ability of GB segregations in bi-crystalline and polycrystalline Al to retard the dislocation emission from GBs that has been first revealed in the study could be successfully used to improve fatigue characteristics of metals, especially nanocrystalline metals with a dense GB network. Keywords Aluminum alloys; cracks; cyclic stress/strain curve; dislocations; molecular dynamics. Corresponding author: K. Zhou, E-mail address: [email protected]
1. Introduction Fatigue is a progressive structural damage of a material that can be observed when it is subjected to repeated loading and unloading. It is the most common source behind failures of mechanical structures and therefore crucial for the application of metals and alloys [1]. Understanding of the fatigue behavior of metallic materials is an important issue in material science. Investigation of structure evolution and crack growth in a material during its cyclic loading, as well as an estimation of its lifespan, are the main tasks scientists aim to solve in this framework. Due to the ability of metallic bulk ultra-fine grain (UFG) and nanocrystalline (NC) materials to demonstrate very high strength and superplastic behavior caused by a dense grain boundary (GB) network, such materials are of significant scientific and technological interest [2-7]. According to the experimental studies, the fatigue endurance of the UFG alloys is higher as compared to the alloys with coarse-grained microstructure [8-12]. The main reason for this is a high ultimate strength of UFG materials, which favors an increased fatigue endurance limit [13] (with exceptions [14]). A large number of GBs and/or twins in NC or nanotwinned metallic materials can impede fatigue crack propagation [15-17]. The effect of high-angle GBs and a twin boundary on fatigue cracking behavior of Cu coaxial bi-crystals was studied experimentally [18]. Mechanisms of defect-interface interactions were analyzed in a recent review [19]. Grain refinement of a polycrystalline material down to the nanoscale level can improve also its various functional properties [2,3,20,21]. According to the literature, the main fatigue-crack propagation mechanisms are a coalescence of cracks, vacancies and voids caused by an emission and absorption of dislocations at a crack tip or by fatigue cleavage of atomic bonds in a crack plane [15,22-27]. Due to dislocation activity usually, the crack tip undergoes blunting during sample loading and re-sharpening when stresses are released [15]. Crack nucleation and propagation ultimately involves the rupture of atomic bonds [27]. Nishimura and Miyazaki observed that cyclic loading of Fe can be accompanied with not only
emission and absorption of edge dislocations and vacancy generation but also with phase transition to release stress concentration around a crack tip [22]. Similar structural change near the crack tip during cyclic loading of body-centered cubic (bcc) Fe was observed in [28]. Such structural behavior looks very close to that observed in intermetallic alloys during their uniaxial tension when domains having different elastic strains coexist in the structure [29-34]. Recently, Rupert and Schuh revealed that cyclic loading of NC Ni leads to relaxation of non-equilibrium GB structure through dissipation of energy and reduction of the average atomic energy and additional strengthening of the material [35]. It was shown that, under certain conditions, GB segregation can result in additional strengthening and have a positive effect on ductility and structural stability of bulk NC materials [3643]. On the other hand, major of works devoted to the fatigue crack growth were devoted to single element materials, for example, pure Cu [15,23], Ni [23,44,45], Al [46], Mg [47] and Fe [28,48,49]. A series of theoretical studies was conducted earlier on the effect of GB segregation of various alloying elements in NC and bi-crystalline Al samples subjected to quasi-static loading in mode I and mode II [50-54]. At the same time, there is a lack of works devoted to fatigue behavior of bulk NC materials having GB segregations. From the abovementioned literature, it is seen that the fatigue behavior of different metallic materials, especially single-crystalline and bi-crystalline metals, has been studied quite extensively by molecular dynamics (MD). At the same time, to the best of our knowledge, there are no theoretical studies dealing with deformation behavior, analyses of structure evolution and crack propagation in metallic materials having GB segregations during their cyclic loading. Given this, the current study is devoted to a comparison of deformation behavior and mechanisms of bi-crystals of pure Al and Al with GB segregation of Co or Ti when they are subjected to cyclic loading perpendicular to GB planes.
2. Modeling A computational cell having almost 70000 atoms of Al is in the form of a rectangular parallelepiped of 21×18×3 nm size, i.e. quasi-two-dimensional geometry, is chosen for simulation (Fig. 1 (a)). The atoms form two differently oriented face-centered cubic (fcc) crystals. The crystallographic orientation of the upper grain is shown in Fig. 1 (a), the orientation of the lower grain is obtained by clockwise rotation of the upper grain around the [011] direction by the angle of 30º forming an asymmetric tilt GB. In both the grains, the [011] direction is parallel to the z-axis. The planes of the two tilt GBs existing in the computational cell are parallel to the xz-plane. One of them is located in the middle of the computational cell, while another one is formed by the upper and lower faces of the cell due to the use of periodic boundary conditions along the three orthogonal directions. The crystallographic orientations of the crystals are chosen to promote the generation of dislocations and further ease of their visualization. The maximal Schmid factor, m, is equal to 0.408 and 0.241 for the upper and lower grains, respectively. In both the grains, there exists only one slip system with the maximal m. In order to create GB segregation, two rows of Al atoms at GBs are replaced by Co or Ti atoms. According to our previous numerical studies [50-54], NC Al with these additional elements in GBs can be very promising for practical application because they can lead to enhanced ductility and strength of the material. The segregated atoms are shown in blue in Fig.1 (b). Though such high concentration of Co and Ti in GBs is far from being observed experimentally, but it is applied for observation of the prominent effect of their addition and an ease of computational reproducibility. To speed up the deformation process and failure of the samples under cyclic loading, a microcrack of 2.5×0.7×3 nm size along the x, y and z directions, respectively, is initially introduced in the bi-crystals. For analyzing the possible effect of GB segregation on structure evolution of the bicrystals, the microcrack is created right under an interlayer of segregated atoms in the middle of the computational cell (Fig. 1 (a)).
The large-scale atomic/molecular massively parallel simulator (LAMMPS) program package is used for the atomistic simulation [55]. In the considered systems, as force-field potentials of atom interaction the many-body embedded-atom method (EAM) potentials [56] are chosen. A motion of atoms in the Al-Co and Al-Ti bi-crystals is described by interatomic potentials developed by Purja Pun et al. [57] and Zope et al. [58], respectively. For simulation of the pure Al, either the interatomic potential for Al-Co or for Al-Ti is used. Therefore hereinafter, throughout the paper, the corresponding Al structures are denoted as “Al_Al-Co base” and “Al_Al-Ti base”, respectively, depending on the interatomic potential used. For visualizing an atomic structure and for dislocation analysis (the dislocation extraction algorithm), open source OVITO software is adopted [59,60].
Fig. 1. (a) MD model geometry. In (b), simulation cell for Al-X bi-crystal (X can be Co or Ti) after relaxation and equilibration at 300 K within 10 ps. Al atoms are shown in red, while X atoms segregated in the tilt GBs in blue. In (c), schematic illustration of the cyclic loading with gradually increasing amplitude imposed on the bi-crystals is given.
Prior to cycling, the studied materials are relaxed at zero temperature to obtain the state of the minimum potential energy and then equilibrated for 10 ps at 300 K. The isothermal-isobaric (NPT) ensemble is employed in the simulations. During the cyclic loading of the bi-crystals, the stresscontrolled tensile loading-unloading in mode I at the temperature of 300 K along the y-axis is applied at a constant stress rate of dyy/dt = 7×109 GPa/sec. All the strain components except yy are controlled to be zero in order to avoid collapsing of the microcrack due to deformation of the computational cell along the x and z-axes perpendicular to the direction of applied loading. Figure 1 (c) schematically shows the cycling loading imposed on the bi-crystals as the dependence of stresses, yy , vs. number of cycles, N. The minimal stress (σmin) corresponds to the unloaded state and equals to 0 GPa. The initial maximal applied stress for the cyclic loading (σmax) is defined as 85 % of the ultimate strength obtained during the quasi-static uniaxial tension which is about 3.52, 3.44, 3.57 and 3.4 GPa for the “Al_Al-Co base”, “Al_Al-Ti base”, Al-Co and Al-Ti bicrystals, respectively. The stress ratio R = σmin/σmax is equal to 0. Since modeling of cyclic deformation is a very time-consuming process and, as a result of repeated loading and unloading, normally material accumulates defects leading to its hardening, it is decided to gradually increase σmax by 20 MPa per cycle to speed up the development of fracture.
3. Results 3.1. Cyclic stress-strain curves Figure 2 shows the stress-strain curves obtained for the “Al_Al-Co base” (a), “Al_Al-Ti base” (b), Al-Co (c), and Al-Ti (d) bi-crystals during their cyclic loading. The stress-strain hysteresis loops for the “Al_Al-Co base” bi-crystal gradually shift to the right cycle-by-cycle up to its failure (Fig. 2 (a)). Very similar behavior for the “Al_Al-Ti base” bi-crystal is observed (Fig. 2 (b)). It is clearly seen that stress-strain response for the pure Al, for both the considered interatomic potentials, is quite identical in terms of residual strain (Fig. 2 (a) and (b)). However, it differs noticeably from their
counterparts having the GB segregation. The curves for the Al-Co and Al-Ti bi-crystals are arranged more densely (Fig. 2 (c) and (d)). Interestingly, in the case of Al-Co, the stress-strain loops almost merge, while deformation of the Al-Ti bi-crystal along the y-axis at unloaded condition does not exceed 0.4 %.
Fig. 2. Stress-strain curves obtained during cyclic loading of the bi-crystals: (a) Al_Al-Co base; (b) Al_Al-Ti base, (c) Al-Co and (d) Al-Ti.
In Fig. 3, the time dependence of the potential energy per atom, Ep, is given for the considered bi-crystals. It is common for all the bi-crystals that loading is accompanied by an increase in the energy while unloading results in decreasing its value. Therefore from these curves, one can easily count the maximal number of cycles to failure, Nmax, sample endures during cyclic loading. For the
“Al_Al-Co base”, “Al-Al-Ti base”, Al-Co and Al-Ti bi-crystals, Nmax is 25, 13, 26 and 14, respectively. Thus, an introduction of the GB segregation of Co or Ti in Al bi-crystal increases Nmax by one cycle. It is seen that the average energy per atom for the systems having atoms segregated to GBs is higher than that for the pure Al. It is valid for both the interatomic potentials used for the pure Al. For the Al-Co and Al-Ti bi-crystals, Ep is around of -3.40 and -3.39 eV, while for the pure Al bicrystal Ep is close to -3.31 eV.
Fig. 3. Potential energy per atom, Ep, as the function of time, t, during cyclic loading of the “Al_Al-Co base” (a), “Al_Al-Ti base” (b), Al-Co (c) and Al-Ti (d) bi-crystals.
In Fig. 4, the dependence of residual strain along the y-axis after unloading of the bi-crystals as a function of the cycle number is presented. A change of the strain for the pure Al bi-crystals can be
divided into three stages. At the first stage, the residual strain slightly increases or even does not change. At the second stage, a sharp increase of the strain during two loading-unloading cycles is observed. At the third stage, before sample failure, a continuous but not rapid increase in its size occurs. Quite different behavior for the Al-Co and Al-Ti bi-crystals is revealed: almost no increase in the residual strain for the Al-Co and only insignificant elongation after ten loading-unloading cycles for the Al-Ti bi-crystal.
Fig. 4. Residual strain along the y axis vs. cycle number after unloading of the bi-crystals.
3.2. Effect of grain boundary segregation on crack growth Recall that in order to speed up the bi-crystal failure during its cycling, the microcrack is introduced at GB in the middle of the computational cell (Fig. 1 (a) and (b)). Therefore it would be interesting to study the effect of GB segregation on the crack growth during the cyclic loading. In Fig. 5, the dependence of crack length and its maximal opening as a function of the cycle number, N, is given for the considered bi-crystals. Slopes of the crack length curves and the maximal crack opening curves are different for the bi-crystals. Overall, it is clearly seen that in the pure Al, the crack growth rate is higher than that in the Al-Co and Al-Ti bi-crystals. During the cycling, before the last full cycle, the crack length for the “Al_Al-Co base” and “Al_Al-Ti base” bi-crystals increases
from ~ 27 and 30 Å to ~ 40 and 45 Å demonstrating an abrupt change in the size at N = 10 and N = 4, respectively. With further cycling, up to the samples’ failure, the crack grows gradually undergoes some oscillations but without any sufficient changes. At the same time, the crack growth rate during the cycling of the bi-crystals with GB segregation is lower. Thus, for the Al-Ti bi-crystal, with the exception of the last full cycle, the crack propagates gradually from ~ 27 to 35 Å. It is interesting that in the case of the Al-Co bi-crystal, its value almost does not change upon the cycling. Another important difference is that, unlike the pure Al, the bi-crystals with GB segregation do not demonstrate any abrupt changes of the crack size during the cycling. The maximal crack opening curves behave in a similar way (Fig. 5 (b)). With the increase in cycle number, the cracks for the “Al_Al-Co base” and “Al_Al-Ti base” bi-crystals open up to ~18 and 17 Å at N = 25 and N = 13, respectively. Like for the crack length curves, the bi-crystals demonstrate an abrupt increase in the crack opening value at N = 4 and N = 10. In the case of the Al-Co bi-crystal, similar to the crack length, the sample does not show any significant changes in its opening. As for the Al-Ti bi-crystal, the maximal crack opening value gradually increases (up to ~ 13 Å), but the slope of the curve is much lower than for the corresponding pure Al bi-crystal.
Fig. 5. Crack length (a) and maximal crack opening (b) vs. cycle number, N.
4. Discussion In order to understand the effect of Co and Ti addition to GBs on the deformation behavior of Al bi-crystals, the analysis of structure evolution in the pure Al, Al-Co and Al-Ti bi-crystals during their cyclic loading is carried out. In Figs. 6 to 9, the common neighbor analysis results are presented for the “Al_Al-Co base”, “Al_Al-Ti base”, Al-Co and Al-Ti bi-crystals, respectively. Here, single and double rows of hexagonal close-packed (hcp) crystal atoms refer to twin boundaries and stacking faults, respectively. Atoms of bcc and disordered structures are mostly located along microcrack surfaces, GBs and near point defects. For all the samples, the presence of multiple atomic-scale disordered regions can be observed, especially in the loaded state. Some of such regions are encircled in Fig. 6 for the first cycle. These areas represent localized large-amplitude thermal fluctuations of atoms and point defects. It is seen that the pure Al samples deform by twinning during the cycling loading (Figs. 6 and 7). The formation of first twins in the “Al_Al-Co base” bi-crystal can be observed at N = 11, while in the “Al_Al-Ti base” bi-crystal this process takes place earlier at N = 5. The appearance of twin plates is preceded by the formation of stacking faults crossing the grains from one GB to another that can be seen at an early stage of the cycling. The Shockley partials, which are precursors to the formation of stacking faults, are emitted from the internal free surface of the microcrack or nearby. Similar observation was made in Ref. [61], where the authors found that free surface facilitates the nucleation of dislocations from GBs. As a consequence of such dislocation emission, an appearance of atomic steps on the microcrack surface and its growth are observed (Figs. 6 and 7). The latter finding is consistent with the models suggesting void growth by an emission of dislocations [62-65].
Fig. 6. Structure evolution of the “Al_Al-Co base” bi-crystal during cyclic loading (N is cycle number). The common neighbour analysis is given: red color represents hcp atoms, dark blue – bcc atoms and light blue – atoms of the disordered structure. To avoid cluttering, atoms of the fcc structure are made invisible. Loaded and unloaded structures are indicated on the left by “σmax” and “σmin”, respectively.
The first twin appears in the upper grain of the bi-crystals with the higher Schmid factor. It is worth noting that the distance between the neighbouring twin boundaries increases in the loaded state and decreases after unloading. During unloading, twins can again transform into stacking faults or completely disappear (Fig. 7), i.e. detwinning process takes place. Twin boundary migration occurs via partial dislocation gliding along a twin boundary on the adjacent {111} plane [66-68]. Due to very fast movement of perfect dislocations their cores are not seen in the snapshots presented in Figs. 6 to 9. Normally in conventional coarse-grained metals with high stacking fault energy such as Al, perfect dislocations do not split into partials. In the case of NC Al, the splitting distance is quite small, i.e. emission of trailing Shockley partial follows right after the nucleation of leading partial forming a short stacking fault in between [69-71]. Such perfect dislocations after travelling through the entire grain do not leave stacking faults and therefore cannot be detected by the common neighbour analysis. At the same time, it is known that conventional fcc metals normally deform by dislocation sliding and have a little contribution from twinning. Therefore, in order to evaluate perfect and partial dislocation activity in the bi-crystals’ structure subjected to the cyclic loading, the dislocation extraction algorithm is used [60]. Figure 10 shows the dependence of the number of the 1/2<110> perfect and the 1/6<112> Shockley partial dislocations vs. cycle number in the loaded and unloaded states. The other type of dislocations, such as the 1/3<111> Frank and 1/6<110> stair-rod dislocations, are also present in the bi-crystals’ structure, but their percentage is insignificant from the total number of defects, and therefore they are not taken into consideration.
Fig. 7. Same as in Fig. 6 but for the “Al_Al-Ti base” bi-crystal.
For both the pure Al bi-crystals, at the early stage of the cycling, the number of perfect dislocations detected in the GB regions is higher than the Shockley partials (Figs. 10 (a) and (b)). Their amount decreases with increase in a number of cycles that can be easily seen especially in the case of the “Al_Al-Co base” bi-crystal (Fig. 10 (a)). Given this, in the pure Al bi-crystal at the early stage of the cycling, the main deformation mechanism is the perfect dislocation sliding. Further cycling and consequently higher internal stresses lead to a reduction of perfect dislocation activity and switching-on of the twinning mechanism, i.e. when Shockley partials emitted on adjacent glide plane travel through an entire grain. A similar transition from one deformation mechanism to another in NC materials was revealed earlier [72]. Such tendency to twinning in NC metals can be explained by the fact that their deformation requires considerably higher stresses in comparison with conventional coarse-grained materials [73]. It is noticeable that the cyclic stress-strain curves for the “Al_Al-Co base” and “Al_Al-Ti base” bi-crystals are getting denser with an increase in the number of cycles (Figs. 3 (a) and (b)), wherein the residual strain tends to saturation (Fig. 4). This is presumably related to the change in deformation mechanism from the perfect dislocation sliding to twinning. Such deformation behavior is accompanied by an abrupt increase in the crack length and its opening at N = 4 and N = 10 for the “Al_Al-Co base” and “Al_Al-Ti” bi-crystals, respectively (Fig. 5 (a) and (b)). The “Al_Al-Co base” and “Al_Al-Ti” bi-crystals demonstrate different maximal number of cycles to failure, 25 and 13, respectively (Fig. 3(a) and (b)). This oddity can be explained by the fact that the Al-Ti interatomic potential gives for pure Al approximately 30 % lower surface energy than in the case of the Al-Co potential. The latter means that the formation of free surfaces in the “Al_Al-Ti” bi-crystal occurs easier and, as a consequence, it results in an earlier fracture in comparison with the “Al_Al-Co base” bi-crystal.
Fig. 8. Same as in Fig. 6 but for the Al-Co bi-crystal. The arrows show examples of Shockley partials.
Fig. 9. Same as in Fig. 6 but for the Al-Ti bi-crystal.
The deformation behavior of the Al bi-crystals with GB segregation significantly differs from that of the pure Al. It is revealed that the Al-Co bi-crystal does not undergo any twin formation (Fig. 8). Unlike the pure Al (Figs. 6 and 7), an increase in cycle number does not lead to significant crack growth as well as to rise in the residual strain up to sample failure (Figs. 4 and 5). The dislocation analysis shows only minor perfect dislocation activity, while the number of Shockley partials is higher than in the case of the pure Al in the whole range of cycling that especially evident in the loaded state (Fig. 10 (c)). Partial dislocations, as well as stacking faults, can be observed in the highly defected layer near GBs and mostly in the upper grain having the higher Schmid factor. A few examples of a Shockley dislocation location are indicated by the arrows in Fig. 8 for N = 1. Obviously, an absence of the perfect dislocation sliding and twinning results in merging of cyclic stress-strain curves for the AlCo bi-crystal (Fig. 3 (c)). Apparently, in this case, the plastic deformation of the bi-crystal occurs via sliding of the partial dislocations. Such remarkable difference in deformation behavior of the pure Al and Al-Co bi-crystals is due to highly defected regions formed near GBs that caused by the presence of Co atoms (Fig. 8). This is in agreement with the observation that the formation of GB segregations suppresses a dislocation initiation at GBs due to a solute drag [42]. Apparently, due to the weaker drag force of Ti, compared to Co, its GB segregation cannot stop the GB migration during deformation process that has been also observed earlier in [50]. Thus, it is clearly seen that the position of the crack, which was initially introduced under the GB (Fig. 1 (a)), after equilibration procedure, is located directly in it (Fig. 9) that explained by insignificant migration of the GB down to the microcrack level. For the Al-Ti bi-crystal, similar to the previous case, the twinning process does not take place during the cyclic loading (Fig. 9). Twins can be observed only in the last cycle right before the fracture, while stacking faults appear in the structure already at first cycles. The number of Shockley partials in the structure is noticeably higher than the number of perfect dislocations (Fig. 10). In this case, the main deformation mechanism is the partial dislocation sliding with less pronounced the perfect dislocation slip. The stress-strain loops, even though look
dense, do not merge as in the case of the Al-Co bi-crystal (Fig. 3 (c) and (d)). It can be explained by the contribution of perfect dislocations into the total plastic strain which is also reflected in a slight increase of the residual strain (Fig. 4). This is probably also associated with the weak drag force of Ti and some migration of the GB mentioned earlier. At the last cycle in the upper grain, the switching-on of additional slip systems with the lower Schmid factor can be observed (Fig. 9). All the studied bicrystals undergo failure at the corresponding cycle right after reaching σmax (see Figs. 6-9).
Fig. 10. Dependence of a number of dislocation segments vs. cycle number for the “Al_Al-Co base” (a), “Al_Al-Ti base” (b), Al-Co (c) and Al-Ti (d) bi-crystals. In the remarks, the symbols “l” and “unl” denote the loaded and unloaded states, respectively.
Another interesting effect is that the number of Shockley partials in both the Al-Co and Al-Ti bicrystals practically does not change with the cycle number in contrast to the number of perfect
dislocations in the pure Al structure which drastically decreases (Fig. 10). At first cycles, the release of internal stresses in the pure Al bi-crystals takes place via perfect dislocation sliding and, as a consequence, the wider stress-strain loops are observed (Fig. 2 (a) and (b)). At further cycles, an activity of all dislocations significantly decreases and the loops become denser, i.e. high internal stresses cannot be removed via dislocation slip that finally leads to failure. Unlike the pure Al, the bicrystals of Al-Co and Al-Ti demonstrate high partial dislocation activity during the whole cycling. Nevertheless, such amount of Shockley partials still cannot provide full structure relaxation and accommodation of plastic strain to prevent premature fracture of the samples. Based on the aforesaid, from the atomistic point of view, polycrystalline materials stable to cyclic loading should provide constantly high dislocation activity during cycling. The reduction of dislocation activity must be compensated by increasing the role of accommodation processes, such as GB sliding, GB migration, grain rotation etc., similar to those found in NC materials [72,74,75]. Another way to increase the partial dislocation activity in a material is through lowering stacking fault energy, which can be achieved by alloying.
5. Summary In summary, the stress-strain behavior and deformation mechanisms in the bi-crystals of pure Al and Al with GB segregation of Co or Ti during their cyclic loading were studied by means of the MD simulation. The results showed that during the cycling, the pure Al undergoes plastic deformation trough perfect dislocation sliding followed by twinning. An addition of Co or Ti atoms in GBs inhibits the perfect dislocation slip as well as the twin formation, thus decreasing plastic flow and residual strain after sample unloading. The main contribution to the deformation in the binary systems is from the slip of Shockley partials, while perfect dislocation activity is very low. The difference in the deformation behavior of the pure Al and its counterparts having GB segregation can be explained by the change of GB structure due to the presence of additional elements
that promotes splitting of the perfect dislocations on Shockley partials in the NC material with the high stacking fault energy. It was shown also that the emission of perfect dislocations from GBs and the twin formation promote crack propagation. Therefore, in Al bi-crystals with GB segregation, the crack grows slower in comparison with that in pure Al samples. As a result, an addition of both the considered alloying elements has the positive effect on the fatigue behavior of Al bi-crystals. The results of the present study suggest that GB segregation can improve fatigue properties of UFG and NC metallic materials, and therefore more studies in this direction, theoretical and experimental, are needed.
Acknowledgements R.I. Babicheva acknowledges the Singapore International Graduate Award (SINGA) for providing her PhD scholarship. The work was supported by the SIMTech-NTU Joint Lab on Reliability (Singapore) and the Russian Foundation for Basic Research (RFBR) [16-32-00618 mol_a]. S.V. Dmitriev acknowledges financial support from the Russian Science Foundation [14-13-00982].
References 1. P. Chowdhury, H. Sehitoglu, Mechanisms of fatigue crack growth – a critical digest of theoretical developments. Fatigue Fract. Engng. Mater. Struct. 39 (2016) 652–674. 2. R.Z. Valiev, A.P. Zhilyaev, T.G. Langdon, Bulk Nanostructured Materials: Fundamentals and Applications, (Hoboken, New Jersey: Wiley, 2014) 440 p. 3. A.P. Zhilyaev, T.G. Langdon, Using high-pressure torsion for metal processing: fundamentals and applications. Prog. Mater. Sci. 53 (2008) 893–979. 4. M. Zehetbauer, R. Grössinger, H. Krenn, M. Krystian, R. Pippan, P. Rogl, T. Waitz, R. Würschum, Bulk nanostructured functional materials by severe plastic deformation. Adv. Eng. Mater. 12(8) (2010) 692–700. 5. Y. Estrin, A. Vinogradov, Extreme grain refinement by severe plastic deformation: A wealth of challenging science. Acta Mater. 61 (2013) 782–817. 6. O. Sitdikov, E. Avtokratova, R. Babicheva, T. Sakai, K. Tsuzaki, Y. Watanabe, Influence of processing regimes on fine-grained microstructure development in an AlMgSc alloy by hot equal-channel angular pressing. Mater. Trans. 53(1) (2012) 56–62. 7. O.Sh. Sitdikov, E.V. Avtokratova, R.I. Babicheva, Effect of temperature on the formation of a microstructure upon equal-channel angular pressing of the Al-Mg-Sc 1570 alloy. Phys. Met. Metallogr. 110(2) (2010) 153–161. 8. I.P. Semenova, A.V. Polyakov, V.V. Polyakova, Y. Huang, R.Z. Valiev and T.G. Langdon, High-cycle fatigue behavior of an ultrafine-grained Ti–6Al–4V alloy processed by ECAP and extrusion. Adv. Eng. Mater. 18(12) (2016) 2057–2062. 9. S. Zherebtsov, G. Salishchev, R. Galeyev, K. Maekawa, Mechanical properties of Ti-6Al-4V titanium alloy with submicrocrystalline structure produced by severe plastic deformation. Mater. Trans. 46 (2005) 2020–2025. 10. L.R. Saitova, H.W. Höppel, M. Göken, I.P. Semenova, G.I. Raab, R.Z. Valiev, Fatigue behavior of ultrafine-grained Ti-6Al-4V 'ELI' alloy for medical applications. Mater. Sci. Eng. A 503 (2009) 145–147. 11. I.P. Semenova, E.B. Yakushina, V.V. Nurgaleeva, R.Z. Valiev, Nanostructuring of Ti-alloys by SPD processing to achieve superior fatigue properties. Int. J. Mater. Res. 100 (2009) 1691– 1696. 12. A. V. Polyakov, I. P. Semenova, Y. Huang, R. Z. Valiev, T. G. Langdon, Fatigue life and failure characteristics of an ultrafine-grained Ti-6Al-4V alloy processed by ECAP and extrusion. Adv. Eng. Mater. 16 (2014) 1038-1043.
13. H. W. Höppel, M. Kautz, C. Xu, M. Murashkin, T. G. Langdon, R. Z. Valiev, H. Mughrabi, An overview: Fatigue behaviour of ultrafine-grained metals and alloys. Int. J. Fatigue 28 (2006) 1001-1010. 14. R. Liu, Y. Tian, Z. Zhang, X. An, P. Zhang, Z. Zhang, Exceptional high fatigue strength in Cu15at.%Al alloy with moderate grain size. Sci. Rep. 6 (2016), 27433, DOI: 10.1038/srep27433 15. X. Zhou, X. Li, C. Chen. Atomistic mechanisms of fatigue in nanotwinned metals. Acta Mater. 99 (2015) 77–86. 16. K.S. Kumar, H. Van Swygenhoven, S. Suresh, Mechanical behavior of nanocrystalline metals and alloys. Acta Mater. 51 (2003) 5743. 17. P.B. Chowdhury, H. Sehitoglu, R.G. Rateick, H.J. Maier, Modeling fatigue crack growth resistance of nanocrystalline alloys. Acta Mater. Volume 61, Issue 7, (2013), Pages 2531– 2547. 18. L.L. Li, P. Zhang, Z.J. Zhang, Z.F. Zhang, Effect of crystallographic orientation and grain boundary character on fatigue cracking behaviors of coaxial copper bicrystals. Acta Mater. 61 (2013) 425–438. 19. I.J. Beyerlein, M.J. Demkowicz, A. Misra, B.P. Uberuaga, Defect-interface interactions. Prog. Mater. Sci. 74 (2015) 125–210. 20. R.I. Babicheva, K.Y. Mulyukov, Thermomechanical treatment to achieve stable two-way shape memory strain without training in Ti-49.8 at.% Ni alloy. Appl. Phys. A 116(4) (2014) 1857-1865. 21. R.I. Babicheva, K.Y. Mulyukov, I.Z. Sharipov, I.M. Safarov, Influence of the structure of the Ti-49.8 at % Ni alloy on its thermal expansion during the martensitic phase transformation. Phys. Solid State 54(7) (2012) 1480-1485. 22. K. Nishimura, N. Miyazaki, Molecular dynamics simulation of crack growth under cyclic loading. Comput. Mater. Sci. 31 (2004) 269–278. 23. G.P. Potirniche, M.F. Horstemeyer, P.M. Gullett, B. Jelinek, Atomistic modelling of fatigue crack growth and dislocation structuring in FCC crystals. Proc. R. Soc. A 462 (2006) 3707– 3731. 24. D. Farkas, M. Willemann, B. Hyde, Atomistic Mechanisms of Fatigue in Nanocrystalline Metals. PRL 94 (2005) 165502 (4 pages). 25. M.F. Horstemeyer, D. Farkas, S. Kim, T. Tang, G. Potirniche, Nanostructurally small cracks (NSC): A review on atomistic modeling of fatigue. Int. J. Fatigue 32 (2010) 1473–1502. 26. K.L. Baker, D.H. Warner, An atomistic investigation into the nature of near threshold fatigue crack growth in aluminum alloys. Eng. Fract. Mech. 115 (2014) 111–121.
27. E. Bitzek, J.R. Kermode, P. Gumbsch, Atomistic aspects of fracture. Int. J. Fracture. 191 (2015) 13–30. 28. L. Ma, S. Xiao, H. Deng, W. Hu, Molecular dynamics simulation of fatigue crack propagation in bcc iron under cyclic loading. Int. J. Fatigue 68 (2014) 253–259. 29. K.A. Bukreeva, R.I. Babicheva, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, A.I. Potekaev, Nonuniform elastic deformation of nanofilms formed from NiAl and FeAl alloys. Russian Physics Journal 57(1) (2014) 69-78. 30. R.I. Babicheva, K.A. Bukreeva, S.V. Dmitriev, R.R. Mulyukov, K. Zhou, Strengthening of NiAl nanofilms by introducing internal stresses. Intermetallics 43 (2013) 171-176. 31. R.I. Babicheva, K.A. Bukreeva, S.V. Dmitriev, K. Zhou, Discontinuous elastic strain observed during stretching of NiAl single crystal nanofilms. Comput. Mater. Sci. 79 (2013) 52-55. 32. K.A. Bukreeva, R.I. Babicheva, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, Inhomogeneous elastic deformation of nanofilms and nanowires of NiAl and FeAl alloys. JETP Letters 98 (2) (2013) 91-95. 33. K.A. Bukreeva, R.I. Babicheva, A.B. Sultanguzhina, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, Effect of temperature on inhomogeneous elastic deformation and negative stiffness of NiAl and FeAl alloy nanofilms. Phys. Solid State 56(6) (2014) 1157-1162. 34. K.A. Bukreeva, R.I. Babicheva, S.V. Dmitriev, K. Zhou, R.R. Mulyukov, Negative stiffness of the FeAl intermetallic nanofilm. Phys. Solid State 55(9) (2013) 1963-1967. 35. T.J. Rupert, C.A. Schuh, Mechanically driven grain boundary relaxation: A mechanism for cyclic hardening in nanocrystalline Ni. Phil. Mag. Letters 92(1) (2012) 20-28. 36. A.J. Detor, C.A. Schuh, Grain boundary segregation, chemical ordering and stability of nanocrystalline alloys: Atomistic computer simulations in the Ni-W system. Acta Mater. 55 (2007) 4221–4232. 37. T. Frolov, K.A. Darling, L.J. Kecskes, Y. Mishin, Stabilization and strengthening of nanocrystalline copper by alloying with tantalum. Acta Mater. 60 (2012) 2158–2168. 38. N.Q. Vo, J. Schaefer, R.S. Averback, K. Albe, Y. Ashkenazy, P. Bellon, Reaching theoretical strengths in nanocrystalline Cu by grain boundary doping. Scripta Mater. 65 (2011) 660–663. 39. S. Özerinç, K. Tai, N.Q. Vo, P. Bellon, R.S. Averback, W.P. King, Grain boundary doping strengthens nanocrystalline copper alloys. Scripta Mater. 67 (2012) 720–723. 40. L. Kurmanaeva, Y. Ivanisenko, J. Markmann, K. Yang, H.J. Fecht, J. Weissmuller, Work hardening and inherent plastic instability of nanocrystalline metals. Phys. Status Solidi (RRL) 4 (2010) 130–132.
41. J. Schafer, A. Stukowski, K. Albe, Plastic deformation of nanocrystalline Pd-Au alloys: On the interplay of grain boundary solute segregation, fault energies and grain size. Acta Mater. 59 (2011) 2957–2968. 42. R.Z. Valiev, N.A. Enikeev, M.Yu. Murashkin, V.U. Kazykhanov, X. Sauvage, On the origin of the extremely high strength of ultrafine-grained Al alloys produced by severe plastic deformation. Scripta Mater. 63(9) (2010) 949–952. 43. K. Tugcu, G. Sha, X.Z. Liao, P. Trimby, J.H. Xia, M.Y. Murashkin, Y. Xie, R.Z. Valiev, S.P. Ringer, Enhanced grain refinement of an Al-Mg-Si alloy by high-pressure torsion processing at 100ºC. Mater. Sci. Eng. A552 (2012) 415–418. 44. W.-P. Wu, Y.-L. Li, X.-Y. Sun, Molecular dynamics simulation-based cohesive zone representation of fatigue crack growth in a single crystal nickel. Comput. Mater. Sci. 109 (2015) 66–75. 45. W.P. Wu, N.L. Li, Y.L. Li, Molecular dynamics-based cohesive zone representation of microstructure and stress evolutions of nickel intergranular fracture process: Effects of temperature. Comput. Mater. Sci. 113 (2016) 203–210. 46. P. White, Molecular dynamic modelling of fatigue crack growth in aluminium using LEFM boundary conditions. Int. J. Fatigue 44 (2012) 141–150. 47. T. Tang, S. Kim, M.F. Horstemeyer, Fatigue crack growth in magnesium single crystals under cyclic loading: Molecular dynamics simulation. Comput. Mater. Sci. 48 (2010) 426–439. 48. A. Machová, J. Pokluda, A. Uhnáková, P. Hora, 3D atomistic studies of fatigue behaviour of edge crack (001) in bcc iron loaded in mode I and II. Int. J. Fatigue 66 (2014) 11–19. 49. A. Uhnáková, J. Pokluda, A. Machová, P. Hora, 3D atomistic simulation of fatigue behavior of a ductile crack in bcc iron loaded in mode II. Comput. Mater. Sci. 61 (2012) 12–19. 50. R.I. Babicheva, S.V. Dmitriev, Y. Zhang, S.W. Kok, N. Srikanth, B. Liu, K. Zhou, Effect of grain boundary segregations of Fe, Co, Cu, Ti, Mg and Pb on small plastic deformation of nanocrystalline Al. Comput. Mater. Sci. 98 (2015) 410-416. 51. R.I. Babicheva, S.V. Dmitriev, L. Bai, Y. Zhang, S.W. Kok, G. Kang, K. Zhou, Effect of grain boundary segregation on the deformation mechanisms and mechanical properties of nanocrystalline binary aluminum alloys. Comput. Mater. Sci. 117 (2016) 445-454. 52. R. Babicheva, S. Dmitriev, Y. Zhang, S.W. Kok, K. Zhou, Effect of grain boundary segregation on shear deformation of nanocrystalline binary aluminum alloys at room temperature. Mater. Sci. Forum 838-839 (2016) 89-94.
53. R.I. Babicheva, D.V. Bachurin, S.V. Dmitriev, Y. Zhang, S.W. Kok, L. Bai, K. Zhou, Elastic moduli of nanocrystalline binary Al alloys with Fe, Co, Ti, Mg and Pb alloying elements. Phil. Mag. 96(15) (2016) 1598-1612. 54. R. Babicheva, S. Dmitriev, Y. Zhang, S.W. Kok, K. Zhou, Effect of Co distribution on plastic deformation of nanocrystalline Al-10.2 at.% Co alloy. Journal of Nanomaterials 2015, 2015. 55. S. Plimpton. Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117 (1995) 1–19. 56. M.S. Daw, M.I. Baskes, Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29(12) (1984) 6443–6453. 57. G.P. Purja Pun, V. Yamakov, Y. Mishin, Interatomic potential for the ternary Ni–Al–Co system and application to atomistic modeling of the B2–L10 martensitic transformation. Modelling Simul. Mater. Sci. Eng. 23 (2015) 065006. 58. R.R. Zope and Y. Mishin, Interatomic potentials for atomistic simulations of the Ti-Al system. Phys. Rev. B 68, 024102 (2003). DOI: 10.1103/PhysRevB.68.024102. 59. A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO – the Open Visualization Tool. Modelling Simul. Mater. Sci. Eng. 18 (2010), 015012. 60. A. Stukowski, V. V. Bulatov, A. Arsenlis, Automated identification and indexing of dislocations in crystal interfaces. Modelling Simul. Mater. Sci. Eng. 20 (2012), 085007. 61. D.V. Bachurin, D. Weygand, P. Gumbsch, Dislocation-grain boundary interaction in <111> textured thin metal films. Acta Mater. 58 (2010) 5232–5241. 62. V.A. Lubarda, M.S. Schneider, D.H. Kalantar, B.A. Remington, M.A. Meyers, Void growth by dislocation emission. Acta Mater. 52 (2004) 1397–1408. 63. I.A. Ovid'ko, A.G. Sheinerman, Dislocation emission from nanovoids in single-phase and composite nanocrystalline materials. Rev. Adv. Mater. Sci. 11 (2006) 46–55. 64. D.C. Ahn, P. Sofronis, M. Kumar, J. Belak, R. Minich, Void growth by dislocation-loop emission. J. Appl. Phys. 101 (2007) 063514. 65. L. Wang, J.Q. Zhou, Y.G. Liu, S. Zhang, Y. Wang, W. Xing, Nanovoid growth in nanocrystalline metal by dislocation shear loop emission. Mater. Sci. Eng A 528 (2011) 5428– 5434. 66. J. Wang, N. Li, O. Anderoglu, X. Zhang, A. Misra, J.Y. Huang, J.P. Hirth, Detwinning Mechanisms for Growth Twins in Face Centered Cubic Metals. Acta Mater. 58 (2010) 2262– 2270.
67. H. Mirkhani, S.P. Joshi, Mechanism-Based Crystal Plasticity Modeling of Twin Boundary Migration in Nanotwinned Face-Centered Cubic Metals. J. Mech. Phys. Solids 68 (2014) 107– 133. 68. Y. Wei, The Kinetics and Energetics of Dislocation Mediated De-Twinning in NanoTwinned Face-Centered Cubic Metals. Mater. Sci. Eng. A 528(3) (2011) 1558–1566. 69. A. Froseth, H. Van Swygenhoven, P.M. Derlet, The influence of twins on the mechanical properties of nc-Al. Acta Mater. 52 (2004) 2259–2268. 70. A.G. Froseth, P.M. Derlet, H. Van Swygenhoven, Dislocations emitted from nanocrystalline grain boundaries: nucleation and splitting distance. Acta Mater. 52 (2004) 5863–5870. 71. H. Van Swygenhoven, P.M. Derlet, A.G. Froseth, Nucleation and propagation of dislocations in nanocrystalline fcc metals. Acta Mater. 54 (2006) 1975–1983. 72. D.V. Bachurin, P. Gumbsch, Accommodation processes during deformation of nanocrystalline palladium. Acta Mater. 58 (2010) 5491–5501. 73. Y.T. Zhu, X.Z. Liao, X.L. Wu, Deformation twinning in nanocrystalline materials. Prog. Mater. Sci. 57 (2012) 1–62. 74. H. Van Swygenhoven, P.A. Derlet, Grain-boundary sliding in nanocrystalline fcc metals. Phys. Rev. B 64(22) (2001) 224105. 75. N.Q. Vo, R.S. Averback, P. Bellon, S. Odunuga, A. Caro, Quantitative description of plastic deformation in nanocrystalline Cu: Dislocation glide versus grain boundary sliding. Phys. Rev. B 77(13) (2008) 134108.
Highlights
• Cycling of Al bi-crystal leads to perfect dislocation sliding followed by twinning. • Co and Ti in GBs of Al inhibit formation of perfect dislocations and twins. • Co and Ti in GBs promote partial dislocation slip during cycling of Al bi-crystal. • GB segregation can decrease ductility and cracking rate during nanomaterial cycling.