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A strategy for improving mechanical properties of metallic glass by tailoring interface structure
Journal of Non-Crystalline Solids xxx (xxxx) xxx
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A strategy for improving mechanical properties of metallic glass by tailoring interface structure J.L. Ma , H.Y. Song *, M.R. An , W.W. Li , R.Q. Han School of Material Science and Engineering, Xi’an Shiyou University, Xi’an 710065, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Metallic glass Interface Mechanical property Molecular dynamics simulation
The strength-plasticity trade-off of the metallic glass (MG) is a topical issue that researchers are constantly pursuing. Controlling the glass/glass interface (GGI) structure has become a key avenue for advancing MG performance. Here, the effect of the Cu composition in the boundary region (BR) (i.e., GGI structure) on the mechanical properties of the Cu85Zr15/CuxZr100-x dual-phase nanoglass (DPNG) under tensile loading is inves tigated by molecular dynamics simulation method. The results indicate that the strength of the DPNG can be significantly improved while its excellent plasticity is maintained by adjusting the Cu composition in the BR. The results also show that the mechanical properties of the DPNGs are not only related to the strength of the BR and the grain region (GR), but also to the GGI structure. The optimal matching relationship between the GR and the BR is obtained. The results will present a theoretical basis for developing the high-performance DPNG.
1. Introduction Since the discovery of metallic glass (MG), it has become an ideal candidate for a variety of applications due to their distinguished me chanical properties, a great deal of effort has been made in recent years to study the MG [1-4]. However, it is still a challenge to achieve considerable macro plasticity in the MG at room temperature, which is a science problem to be resolved urgently. Fortunately, as early as 1989, Gleiter [5] had tried to extend the material design concept of nano structured metals to the MG, and proposed that it can be possible to introduce plenty of glass/glass interfaces (GGIs) into the monolithic glass and this new form of glass has been termed as nanoglass (NG). Compared with the bulk MG, the GGIs in the NG belongs to the area with lower density or higher free volume fraction, which is easy to flow and is favorable to stable plastic deformation “homogeneously”. This unique microstructure is capable to sustain high-density shear bands (SBs) and consequently to enhance the global plasticity of the NG. Feng et al. [6] have shown that the GGI, as soft regions, can be a critical defect to promote uniform deformation. Besides, some studies have found that the NG exhibits a super-plasticity behavior due to the presence of the GGIs, where shear transformation zones (STZs) are easily activated nearby to promote global deformation [7,8]. Despite many advances have been made, the widespread application of these alloys remains elusive, largely limited by the irreconcilable conflict between strength and
ductility [9,10]. For instance, Wang et al. [11] have shown that under the uniaxial tension test, more than 15% plastic strain can be obtained for the Sc75Fe25 NG, but at the same time, the strength decreases about 0.4 GPa. Qiao et al. [12] also have indicated that compared with the bulk MG, super ductile behavior emerges in the NG, while the strength is much lower than that in the MG. The reason for these cases is that the internal GGIs inherent of the NGs have been characterized as a “soft” phase promoting the nucleation of the STZs to improve tensile plasticity. In turn, the GGIs with high free volume reduce the activation barrier for the STZs, which makes the yield strength of the NG greatly lower than that of the MG [9,13]. Therefore, the strength-plasticity trade-off of the NG is still a topical issue that researchers are constantly pursuing. Controlling the interface structure has become a key avenue for advancing materials performance. For nanocrystalline materials, improving the interface stability can prevent the dislocation from moving and enhance the interaction between dislocation and interface, thus improving their mechanical properties [14-16]. Hu et al. [17] have discovered that the hardness of nano-grained metals can continue to increase with the decrease of grain size by adjusting the grain boundary stability, which provides a new mechanism for strengthening the strength of extremely fine nano-grained metals. Inspired by the design of high-performance nanocrystalline materials, the effect of the GGI on the mechanical properties of the MGs has attracted the attention of re searchers. Kalcher et al. [18] have manipulated the pristine NG by
* Corresponding author. E-mail addresses: [email protected], [email protected] (H.Y. Song). https://doi.org/10.1016/j.jnoncrysol.2020.120464 Received 29 August 2020; Received in revised form 28 September 2020; Accepted 4 October 2020 0022-3093/© 2020 Elsevier B.V. All rights reserved.
Please cite this article as: J.L. Ma, Journal of Non-Crystalline Solids, https://doi.org/10.1016/j.jnoncrysol.2020.120464
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replacing the GGI with crystalline interphases with higher yield strength. They found that when the soft-phase GGI of the NG is replaced by a stronger crystal structure, the yield strength is significantly increased, which makes it possible to strengthen and toughen the single-phase NG (SPNG). Similarly, Cheng et al. [19] have also revealed a mechanism of strengthening the NG by controlling the short-range ordered structure and free volume of the GGI, and find that its strength is comparable to that of the bulk MG. In 2018, Li et al. [20] uncover a strengthening mechanism for the dual-phase structure, in which the presence of micro-sized secondary phases usually leads to strengthening via the blocking or branching of the SB. The CuZr MG has been regarded as a relatively stable structure due to its excellent glass formation ability [21]. But so far, the strengthening of the second amorphous phase on the boundary region (BR) has been barely mentioned in the CuZr NG. In addition, the trade-off between strength and plasticity of the CuZr NG has not been effectively overcome. Due to the sufficient theoretical research of predecessors and the urgent de mand of the material market for the CuZr amorphous alloy with high mechanical properties, searching for a new method that is more controllable is necessary for designing and fabricating high-performance nanostructured the CuZr amorphous alloy. Recently, molecular dy namics (MD) simulation method has been widely used to study various fundamental physical problems in materials science and has greatly improved our understanding of the nature of the NGs [22-24]. Here, the deformation behavior and mechanical properties of the Cu85Zr15/ CuxZr100-x dual-phase nanoglass (DPNG) under tensile loading are studied using MD simulation method. The results indicate that the DPNG can obtain a superior combination of strength and plasticity by opti mizing the microstructure of the dual-phase nanostructured amorphous alloy. This study will provide initial guidance and theoretical basis for designing and preparing of high-performance NGs. The paper comprises of the following parts. Section 2 presents the simulation model and method of atomistic simulation. The results and discussion are shown in Section 3. Ultimately, the conclusion is sum marized in Section 4.
Fig. 1. (a) Schematic of the Cu85Zr15/CuxZr100-x DPNGs. (b) Enlarged view of dual-phase structure and interface information. (c) High-resolution trans mission electron microscopy images of the DPNG prepared by multi-phase pulsed electrodeposition technique [20]. The BR and the GR are colored by green and purple, respectively.
different Cu composition in the BRs means that the different GGI structures are introduced. For convenience, the Cu85Zr15/CuxZr100-x DPNGs are labeled 85/x DPNGs. Here, the 85/20 DPNG, 85/25 DPNG, 85/36 DPNG, 85/50 DPNG, 85/64 DPNG, 85/75 DPNG, and 85/80 DPNG are considered. As shown in Fig. 1(a), the dimensions of the Cu85Zr15 SPNG and all the 85/x DPNGs in the X-direction, Y-direction, and Z-direction are 20.0 nm, 54.5 nm, and 3.1 nm, respectively. The size (d) of the GR is 11.6 nm and the thickness (t) of the BR is 2.0 nm for all the 85/x DPNGs. Here it is needed to point out that the GGI in the 85/x DPNGs is taken as 1.0 nm in Fig. 1(b) [26]. During uniaxial tensile loading, a maximum strain of 20% is applied to the samples along the Y-direction with a strain rate of 2.5 × 108 /s at 50 K. The PBCs are applied to the Y- and Z-directions, while the free surface condition is used along the X-direction. In the MD simula tion, the embedded atom model (EAM) potential is exploited to describe the interatomic interactions in the Cu-Zr system [27]. This potential has been proved to be consistent with experimental measured structure factors [28] and has been extensively used to investigate the deforma tion behavior of the Cu-Zr amorphous alloys [29,30]. To intuitively analyze the atomic configurations during plastic deformation, all microstructural analysis and visualization of atomic configurations are performed using the Open Visualization Tool (OVITO) [31].
2. Simulation model and method To explore the better mechanical properties of the DPNG, the deformation behaviors of the Cu85Zr15/CuxZr100-x DPNGs and the Cu85Zr15 SPNG under tensile loading are systematically investigated by the MD simulation method. Fig. 1 shows the schematic and atomic-scale model of the DPNG. Here, the Cu85Zr15/CuxZr100-x DPNG is composed of grain region (GR), namely the Cu85Zr15 amorphous phase, surrounding by the BR shell (i.e., the CuxZr100-x amorphous phase). In other words, the GGIs in the Cu85Zr15 SPNG are replaced by the BR shells, which produce two GGI different from the previous GGI structure. The pro duction process of the model is as follows, for the first step, a small MG containing 5850 atoms is produced by quenching from the melt with a cooling rate of 1012 K/s to 50 K at zero pressure, during which periodic boundary conditions (PBC) are applied to all three dimensions. By multiplication of the quenched MG, the specimens of sizes up to 245,700 atoms are generated. To obtain the Cu85Zr15 SPNG and the Cu85Zr15/ CuxZr100-x DPNGs samples, combination modes of single phase and dual phases are created by using Voronoi tessellation method [25]. Subse quently, the Cu85Zr15 SPNG and the Cu85Zr15/CuxZr100-x DPNGs are annealed from 600 K to 50 K at a cooling rate of 1012 K/s to release the stress and eliminate voids [26]. In the preparation of the experiment, some researchers have successfully prepared the DPNGs by multiple pulse deposition method by carefully controlling the deposition voltage, current density, and time duration at different deposition stages [20], as shown in Fig. 1(c). In order to study the mechanical behavior of the DPNGs during deformation, we manipulate the model of the Cu85Zr15 SPNG by replacing the GGI with different second amorphous phases (i. e., the BRs), which are Cu20Zr80, Cu25Zr75, Cu36Zr64, Cu50Zr50, Cu64Zr36, Cu75Zr25, and Cu80Zr20, respectively. It should be noted that the
3. Results and discussion 3.1. Deformation behavior of SPNG and DPNG In previous work, it is known that the mechanical properties of the NG can be effectively adjusted by controlling the Cu composition of the amorphous phase [32]. And the results indicated that the strength of the Cu85Zr15 SPNG is the highest, but the plasticity is poor. The purpose of this paper is to improve the mechanical properties of the Cu85Zr15 SPNG at the same time by tailoring the GGI structure. To study the effect of the GGI structure on the mechanical property of the NG, Fig. 2 gives the stress-strain curves of the Cu85Zr15 SPNG and the 85/50 DPNG under 2
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Fig. 3. Stress-strain curves of the 85/x DPNGs and the Cu85Zr15 SPNG.
Fig. 2. Stress-strain curves of the Cu85Zr15 SPNG and the 85/50 DPNG.
the stress-strain curves of all the samples is similar, but the peak stress is obviously different. The results indicate that the curve of the Cu85Zr15 SPNG clearly separates those of the 85/x DPNGs into two cases in Fig. 3. When the x is less than 50%, the Young’s modulus and peak stress of the 85/x DPNGs are weakened compared with the Cu85Zr15 SPNG. How ever, the 85/x DPNGs with x greater than 50% show stronger Young’s modulus and peak stress. That is to say, not all the BRs can effectively enhance the strength of the Cu85Zr15 SPNG, and there may be a certain kind deformation mechanism which weakens the strength of the Cu85Zr15 SPNG matrix. Here it also can be found that with the increase of strain, the values Δτ/τy of SPNG and DPNGs are different. The Δτ/τy of the Cu85Zr15 SPNG, 85/20 DPNG, 85/25 DPNG, 85/36 DPNG, 85/50 DPNG, 85/64 DPNG, 85/75 DPNG, and 85/80 DPNG are 0.179, 0.183, 0.188, 0.171, 0.141, 0.268, 0.274, and 0.289, respectively. Thus, to systematically understand the mechanical properties of the 85/x DPNGs during the tensile deformation process, it is very necessary to investigate the characteristics of the 85/x DPNGs with different Cu composition in the BR. Fig. 4 shows a clearer relationship between the peak stress and the normalized difference Δτ/τy of all the 85/x DPNGs, and the red star presented the Cu85Zr15 SPNG. Compared with the Cu85Zr15 SPNG and the 85/50 DPNG (also shown in Fig. 2), other samples are mainly
tensile loading. It can be seen from Fig. 2 that after the stress reaches peak stress (τy), both materials show tardy decrease in the stress, and the stress then approaches a relatively steady-state value. The average flow stress (τs) is obtained by calculating the average stress in the plastic flow process. The τy is the stress from which the plastic deformation begins and it can be regarded as the global yield strength of the undeformed glass, while the τs can be considered as the flow strength of the glass or the strength of the material inside a propagating SB [33-35]. Recent theoretical studies and simulations have shown that the normalized difference Δτ (Δτ =τy -τs) between flow strength and yield strength corresponds to the tendency toward strain localization, which influences the tensile plasticity [36,37]. Subsequently, the normalized difference (∆τ/τy) between flow strength and yield strength is proposed to indicate the tendency towards strain localization more precisely [38,39]. The smaller the ∆τ/τy is, the better the plasticity is. It can be seen from Fig. 2 that the ∆τ/τy of the 85/50 DPNG is smaller than that of the Cu85Zr15 SPNG, which indicates that if the Cu50Zr50 amorphous phase is intro duced into the Cu85Zr15 SPNG, the plasticity of the NG can be improved. However, it is observed that neither the τy nor the τs in the 85/50 DPNG is higher than those of the Cu85Zr15 SPNG. In other words, the addition of second amorphous phase (i.e., the Cu50Zr50 amorphous phase) can improve the tensile ductility of the Cu85Zr15 SPNG and lead to a brittle-to-ductile transition of the deformation mode, although at the expense of some strength. According to previous research result, the strength and plasticity are heavily dependent on the Cu composition of the amorphous phase [40]. The interface structure of the GGI has sig nificant influence on the mechanical properties of the NG. Therefore, we consider changing the Cu composition in the BR to change the GGI structure of the NG, and try to further optimize the mechanical prop erties of the DPNG. 3.2. Effect of GGI structure on the deformation behavior of DPNG In order to search for a wonderful combination of superior strength and high plasticity of DPNG, the GGI of the Cu85Zr15 SPNG is replaced by the second amorphous phase (i.e., the BR) with different Cu composi tions. Here, seven kinds of the BRs (namely, the amorphous phase Cu20Zr80, Cu25Zr75, Cu36Zr64, Cu50Zr50, Cu64Zr36, Cu75Zr25, and Cu80Zr20, respectively) are considered, and the percentage of Cu varies is between 20% and 80%. It is pointed out again that the different Cu compositions in the BRs mean that the different GGI structures are introduced. Fig. 3 shows the stress-strain curves of all the DPNGs under uniaxial tensile loading. For comparison purpose, the curve of the Cu85Zr15 SPNG is also given. It is clearly seen that the change trend of
Fig. 4. Relationship between peak stress and Δτ/τy of the 85/x DPNGs and the Cu85Zr15 SPNG. 3
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concentrated in A and B regions marked in Fig. 4. In other words, the effects of the GGI structure on the peak stress and the normalized dif ference Δτ/τy of the 85/x DPNGs are obvious. It can be clearly seen from Fig. 4 that the peak stress of the DPNGs in region A is enhanced about 0.2–0.3 GPa compared with the Cu85Zr15 SPNG, and simultaneously ensured the plasticity of the Cu85Zr15 amorphous matrix (i.e., the Cu85Zr15 SPNG). On the contrary, the strength and plasticity of the DPNGs in region B are all obviously smaller than those of the Cu85Zr15 SPNG. The normalized differences Δτ/τy of the DPNGs have increased about 0.09–0.11, and the consumption of peak stress is about 0.2–0.4 GPa comparing with that of the Cu85Zr15 SPNG. That is to say, the losses of Δτ/τy and peak stress are approximately 55% and 9% in the DPNGs when the Cu composition increases from 20% to 36%. Accordingly, the DPNGs with the Cu composition in the BR from 64% to 80% have a more attractive integration of outstanding mechanical properties, which makes it possible to obtain the DPNG with perfect combination of strength and plasticity. It is a though-provoking problem that why the DPNGs with different Cu compositions in the BR present different me chanical properties. This probably means that the DPNGs with different GGI structures can exhibit different plastic deformation mechanisms. To investigate the potential deformation behavior of the DPNGs, we choose three representative models (i.e., the 85/20 DPNG, the 85/50 DPNG and the 85/80 DPNG, respectively) in each region and they will be analyzed and compared in Figs. 5-7, which gives the evolution of the local atomic shear strain of the DPNGs at different strains. In order to better reveal the deformation details of the samples in region B (as shown in Fig. 4) during the tensile loading, Fig. 5 illustrates the atomic deformation images of the 85/20 DPNGs at different strains, in which the presence of regions with relatively large atomic strain implies that they have undergone large localized plastic deformation. As shown in Fig. 5(a), the priority activation positions are located at the free surface of the BR (marked by the arrows), hence, free volume begins to evolve in the interfaces at early stage owing to lower cohesion. In other words, the STZs start to accumulate causing softening in these regions. From that point until it fails, the plastic deformation is mainly confined to the BR. Notably, the plasticity occurs by the generation of a high density of the STZs which are primarily activated in the BR due to the abundant free volume. The 85/20 DPNG then fails in the form of propagation of cross-SBs across, as shown in Fig. 5(c). Along with this, four larger steps are generated at the surface position, with the size of 2.1 nm, 3.9 nm, 2.8 nm, and 2.2 nm, respectively. In order to see more intuitively the expansion process of SBs of the BR, Fig. 5(e) gives the atomic displacement vector maps of the 85/20 DPNG, which are the enlarged regions of Fig. 5(d). The trajectories of the cross-SBs and the nearby atoms show certain regularity as shown in Fig. 5(e). In order to
obtain more details of Figs. 5(e) and (f) gives the zoomed up section of the black square. It is found from Fig. 5(f) that the atomic displacement is deflected and the atom moves is confined to the BR region, which may be due to the existence of high-strength GGI. Similar results have been reported by Hua et al. [41] It can be concluded that the strain locali zation is mainly concentrated at the BR due to the softening of the BR caused by a large amount of free volume and the atomic motion in the BR is blocked by the GGI. This phenomenon greatly weakens the overall strength and plasticity of the 85/20 DPNG, which can be shown in Fig. 4. The snapshots of the deformation behavior of the 85/50 DPNG at different strains are displayed in Fig. 6. As shown in Fig. 6(a), at the strain of 14.1%, the high shear strains are primarily concentrated where the STZs atomic aggregation occur on the GGIs and the BRs, especially on the free surfaces of the BR (marked by the arrows), leading to the cross-SBs have been formed near the BR as shown in Fig. 6(c). The von Mises strain of the 85/50 DPNG in Fig. 6(c) is about 0.5, which is obviously lower than that of the 85/20 DPNG in Fig. 5(c), and the wider STZs are formed in the 85/50 DPNG. Besides, there are no large steps on the free surface. Fig. 6(e) and (f) show the details of the expansion process of the SBs by displaying the atomic displacement. The final orientation of the atomic displacement of the 85/50 DPNG is almost the same as that of the loading direction, while the atomic displacement of the 85/20 DPNG is obviously deflected in the X direction, which is due to the severe shear effect of the soft BR phase (i.e., the Cu20Zr80 amorphous phase) during deformation by comparing Figs. 5(e) and 6(e). Fig. 6(f) shows the zoomed up a section of the black square (i.e., the detailed atomic displacement diagram at the cross-SBs) shown in Fig. 6(e). The simulation indicates that unlike the 85/20 DPNG, the atomic displace ment is not hindered by the GGI of the 85/50 DPNG instead of the GR in the 85/50 DPNG, in other words, the trajectories of atoms severely de flects after passing through the soft GGI, which may be due to the blocking effect of the high-strength GR on atomic motion. It is known that the strain localization is mainly concentrated at the soft phase, which contains a large number of free volumes leading to higher atomic mobility and the atomic deflection is easy to occur. Hence, the strain softening occurs due to the soft GGIs in the 85/50 DPNG, resulting in lower strength than the original matrix phase (i.e., the Cu85Zr15 SPNG). By changing the Cu composition in the BR into 80%, the deformation behavior shows a completely different trend (see Fig. 7). Here, the 85/80 DPNG with great combination of strength and plasticity is chosen as a representative of region A as shown in Fig. 4. In order to explain the reason why the strength of the DPNG is the highest when the Cu composition in the BR is 80%, the mechanical properties of the bulk CuZr MGs with different Cu composition are calculated. The result shows that the peak stresses of the Cu20Zr80 MG, Cu25Zr75 MG, Cu36Zr64
Fig. 5. (a-d) Atomic configurations of the 85/20 DPNG at strains of 9.4% and 20%, colored with von Mises strain and chemical heterogeneity. The zoomed up section of the dashed box of (e) is shown in (f). 4
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Fig. 6. (a-d) Atomic configurations of 85/50 DPNG at strains of 14.1% and 20%, colored with von Mises strain and chemical heterogeneity. The zoomed up section of the dashed box of (e) is shown in (f).
Fig. 7. (a-d) Atomic configurations of the 85/80 DPNG at strains of 14.1% and 20%, colored with von Mises strain and chemical. The zoomed up section of the dashed box of (e) is shown in (f).
MG, Cu50Zr50 MG, Cu64Zr36 MG, Cu75Zr25 MG, Cu80Zr20 MG, and Cu85Zr15 MG are 2.813 GPa, 2.879 GPa, 3.099 GPa, 3.491 GPa, 4.330 GPa, 4.381 GPa, 4.741 GPa, and 4.342 GPa, respectively. The results indicate that the peak stress of the Cu80Zr20 MG is the highest. From the point of view of mixing rule of composite, this result can explain the relationship between the strength of the 85/x DPNGs and the Cu composition of the BR, as shown in Fig. 4. Of course, the mechanical properties of the DPNGs cannot be explained simply from the point of view of mixing rule of composites, and the mechanical properties of the DPNGs depend on the synergistic effect of the two amorphous phases to a certain extent. It can be seen from Fig. 7 that a relatively homogeneous local plastic deformation commences in the 85/80 DPNG instead of deformation localization like the 85/20 DPNG and the 85/50 DPNG in Figs. 5 and 6. And an interesting phenomenon is found in Fig. 7(a), most of the high strain region is concentrated in the interior of the GR rather than in the BR or the GGI as the formers (indicated by ellipses and ar rows in Figs. 7(a) and (b)). For the 85/80 DPNG, many STZs homoge neously nucleate in the soft phase (i.e., the GR) and a series of immature embryo SBs intersect each other and block by hard phase (i.e., the BR) without forming a dominant SB as shown in Fig. 7(c). So the BR as a hard phase can effectively block the propagation of the SB and promote the branching of the SB, this is the key to the equilibrium strength and
plasticity of the DPNG [20]. Just as shown in Fig. 4, the 85/x DPNGs in region A have exhibited excellent mechanical properties. Figs. 7(e) and (f) give the atomic displacement in the high strain region and the enlarged view of the local area. Compared with the 85/20 DPNG and the 85/50 DPNG, there is no obvious phenomenon of atomic trajectory deflection, which is mainly due to the synergistic interaction between two amorphous phases with similar strength. In other words, the STZs are activated almost at the same time in the process of deformation of the BR and the GR with similar strength, so as to realize the coordinated movement (like the 85/80 DPNG). When the strength difference be tween the two phases is large, the softer phase will preferentially deform, and the deformation of the harder phase is smaller, so the local deformation dominated by the soft phase occurs like the 85/20 DPNG and the 85/50 DPNG. The mechanical properties of the DPNGs are not only related to the strength of the BR and the GR, but also to the GGI structure. In order to verify the above inference, a more detailed structural description will be shown in the following. In order to study the internal deformation mechanism of the 85/x DPNGs mentioned above, the voronoi polyhedron (VP) is used to analyze the mechanical properties of the BR, the GGI, and the GR. The advantage of the VP on the structural analysis of the DPNG is that it can 5
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reflect atomic clusters directly so that it is capable of distinguishing the local atomic environment and microstructure by forming a contrast in the GR, the BR, and the GGI [42]. To characterize the topological structure of short range order, the VP denoted by 〈n3 n4 n5 n6〉 is employed. The VP with n5 = 6 possesses low five-fold symmetry, while the VP with n5 = 8, 10 and 12 possess high five-fold symmetry [6]. It is indicated that the full icosahedron (FI) 〈0 0 12 0〉, and the icosahedral-like polyhedra 〈0 2 8 1〉 and 〈0 2 8 2〉 here are the most prominent local structures impacting elasticity stage in the CuZr amor phous alloy [43]. Especially the FI clusters have a great effect on sta bilizing the glassy structure and increasing its resistance against deformation [44,45]. At the same time, the flow defects accompanied by the increase of the VPs with index 〈0 3 6 3〉 and 〈0 3 6 4〉, which could affect plasticity [35]. The previous results indicated that the high five-fold symmetry region tends to undergo elastic deformation, while the low five-fold symmetry region is easily deformed plastically [40]. In other words, the FI clusters play a strengthening role because of their shear deformation resistance and high stability, while the VPs with index 〈0 3 6 3〉 and 〈0 3 6 4〉 act as a softener for increasing plasticity during tensile loading. Fig. 8 gives the six most populous polyhedral types of the BR, the GR, and the GGI in the 85/20 DPNG, the 85/50 DPNG, and the 85/80 DPNG, respectively. For the 85/20 DPNG, the GR shows strong deformation resistance due to its high fraction of FI clusters, in turn, the BR only has few FI clusters, which lead to lower of the deformation resistance, strain softening, and thereby strong shear localization. It should be noted that the GGI with more FI clusters is stable relative to the BR, the deforma tion is only confined in the BR, and the atomic motion of the BR will be hindered by the GGI, which will show a narrow cross-SBs as shown in Fig. 5(c) and (f). For the 85/50 DPNG, the number of FI clusters in the BR is still much lower than that in the GR, so it shows a deformation mode similar to that of the 85/20 DPNG, i.e. a pair of cross-SBs through the specimen. It can be noticed that the proportion of the VPs with low fivefold symmetry (i.e., 〈0 3 6 3〉 and 〈0 3 6 4〉) in the GGI is slightly higher than those of the BR and the GR, while the FI clusters in the GGI is lower than those of the BR and the GR. So, the GGI shows excellent plastic flow ability, and it shows a wider cross-SBs dominated by the BR deforma tion, as shown in Fig. 6(c). In the 85/50 DPNG, the GR with more FI clusters has higher shear deformation resistance. The atoms in the BR pass through the GGI and deflect due to the strong GR, which further confirms the results of Fig. 6(f). It can be seen from Fig. 8 that for the 85/ 80 DPNG, the FI clusters in the BR, the GR, and the GGI are all plentiful, and the FI cluster in the BR is the largest, followed by the GR and the GGI. Hence, the shear deformation resistance of the BR, the GR, and the GGI in the 85/80 DPNG shows stronger, and the elastic modulus and
strength convey a higher value, which is consistent with the result given in Fig. 4. The STZs are preferentially activated in the GGI because it has the least FI clusters (see Fig. 7(a)). Subsequently, the stress concentra tion in the GGI further activates the STZs in the softer phase GR, which is because the FI cluster in the GR is slightly lower than that of the BR. At the same time, the free surface of the GR (i.e., the soft phase) is also the key area to induce STZs. With the increase of strain, these two activation sites activate more STZs in the GR and the BR, which is attributed to the little difference in the FI clusters proportion between the two phases, thus promoting the local uniform plastic deformation of the 85/80 DPNG, as shown in Fig. 7(c). In other words, the little fraction difference of FI clusters between the BR and the GR is also more conducive to the coordinated movement of each other in the plastic deformation process. Therefore, there is no obvious deviation of the atomic trajectory, as shown in Fig. 7(f). In addition, the three models in Fig. 8 reveal a certain relationship between FI clusters and the peak stress. When the difference of the fraction of the FI clusters is larger among the BR, the GR, and the GGI, the amorphous phase with less FI clusters will become the soft phase weaken the overall strength of the 85/x DPNGs, just as shown in the region B of Fig. 4. On the contrary, the number of FI clusters in the BR, the GR, and the GGI is abundant, and the FI clusters fraction difference between the three is tiny, so all of them will show high shear defor mation resistance, and the 85/x DPNGs will have higher peak stress as shown in the region A of Fig. 4. In order to further explore the deformation behavior of the BR and the GR in the 85/x DPNGs during deformation, the plastic strain parti tioning between the GR and the BR is quantified as a function of participation rate of locally deformed atoms. It needs to be explained as follows: the local atomic shear strain (or atomic von Mises strain) is defined as [46]: √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ( )2 )2 ( ηyy − ηzz + (ηxx − ηzz )2 + ηxx − ηyy Mises η = η2yz + η2xz + η2xy + 6 The ηMises is an excellent standard of measurement for evaluating the plastic stage of material. Atoms with a larger magnitude of ηMises contribute more to the plasticity. Atoms with ηMises ≥ 0.2 are normally utilized to visualize the plastic deformation within the specimen [47, 48]. To visualize the deformation mechanisms in the DPNGs, only the atoms with ηMises ≥ 0.2 are considered, which indicate the STZs during the tension process [29,48]. In order to quantify the degree of locali zation we quote a quantity called the deformation participation ratio [49]. The ψ is used to represent the deformation participation ratio, which is equal to the percentage of the number of atoms with the ηMises greater than 0.2 divided by the total number of atoms in the whole sample. That ψ local is equal to the percentage that the number of atoms with the ηMises greater than 0.2 in the BR (or the GR) divides by the total number of atoms in the BR (or the GR). For all of the 85/x DPNGs, the BR and the GR of the DPNGs play different roles during the tension process, and their respective ψ local are shown in Figs. 9(a) and (b). As shown in Fig. 9, when the strain is<6%, the DPNGs all display near-zero (local) shear strain, which is because there is no deformation localization in the elastic deformation stage. After the strain of 6%, the large atomic strain clusters begin to accumulate at stress concentrations. The strain about 6% is just around the yield point, in which a large number of the STZs are activated and distorted along with favorable orientation after pass ing the yield point. Meanwhile, it can be noticed from Fig. 9(a) that the ψ local of the BRs increase speed is higher than that of the GRs. That is to say, the local deformation in the plastic stage is mainly concentrated on the BR for the DPNGs with the Cu composition in the BR from 20% to 50%, as shown in Fig. 9(a). For example, this phenomenon can be observed in the 85/20 DPNG and the 85/50 DPNG in Figs. 5 and 6. It is worth noting that for the 85/50 DPNG, the ψ local of the GR is obviously higher than those of the GRs in the other DPNG, as shown in Fig. 9(a), more atoms in the GRs participate in the local deformation processes,
Fig. 8. Fraction of populous voronoi polyhedrons of the BR, the GGI, and the GR for the 85/20 DPNG, the 85/50 DPNG, and the 85/80 DPNG. 6
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softening, and thereby strong shear localization. Therefore, the plastic deformation of the 85/20 DPNG is dominated by the local deformation (i.e., a pair of cross-SBs). And the GGI with more FI clusters is stable relative to the BR, the deformation is only confined in the BR, and the atomic motion of the BR will be hindered by the GGI. However, for the 85/80 DPNG, the FI clusters in the BR, the GR, and the GGI are all plentiful, and the FI cluster in the BR is the largest, followed by the GR and the GGI. Hence, the shear deformation resistance of the BR, the GR, and the GGI in the 85/80 DPNG shows stronger, and the elastic modulus and strength convey a higher value. The results also indicate that for the 85/80 DPNG, the little fraction difference of FI clusters between the BR and the GR is also more conducive to the coordinated movement of each other in the plastic deformation process, showing uniform plastic deformation. The results provide not only an in-depth atomic under standing of the deformation mechanism of the DPNG, but also optimize the heterostructure to achieve the desired mechanical properties in nanostructured amorphous alloys. Data availability statement The data used to support the findings of this study are available from the corresponding author upon request. CRediT authorship contribution statement J.L. Ma: Investigation, Data curation, Formal analysis, Methodology, Writing - original draft. H.Y. Song: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Writing - review & editing. M.R. An: Data curation, Formal analysis, Methodology, Writing - original draft. W.W. Li: Formal analysis, Methodology, Writing - original draft. R.Q. Han: Formal analysis, Methodology, Writing - original draft. Fig. 9. Participation rate of locally deformed atoms of the 85/x DPNGs.
Declaration of Competing Interest
and then a pair of wider cross-SBs can be formed as shown in Fig. 6. Compared with the DPNGs in Fig. 9(a), the ψ local of the BR and the GR in the 85/64 DPNG, the 85/75 DPNG and the 85/80 DPNG has no signif icant difference, but the ψ local of the GR is slightly larger at the strain between 17% to 20% (marked in insert map in Fig. 9(b)), which in dicates that the GR is the main carrier of plastic deformation of the DPNG. This situation is consistent with the research results reported in Fig. 7. In addition, the ψ local with a similar value in the BR and the GR is also beneficial to local uniform plastic deformation of the DPNG. The existing results indicate that a strong correlation exists between me chanical properties of DPNGs and Cu composition, which is useful for the synthesis of the DPNGs with predominant ductility and high strength.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 11572259), Natural Science Foundation of Shaanxi Province (No. 2019JQ-827), Scientific Research Program Funded by Shanxi Provincial Education Department (No. 19JK0672), and Program for Graduate Innovation Fund of Xi’an Shiyou University (No. YCS18211005). References
4. Conclusion
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The deformation behavior and mechanical properties of the 85/x DPNGs under tensile loading are investigated by MD simulation method. The results indicate that the mechanical properties of the DPNG can be significantly improved by adjusting the Cu composition in the BR. The strength of the DPNGs in region A (i.e., the Cu composition in the BR is more than 50%) is enhanced about 0.2–0.3 GPa compared with the Cu85Zr15 SPNG, and simultaneously ensured the plasticity of the Cu85Zr15 amorphous matrix. On the contrary, the strength and plasticity of the DPNGs in region B (i.e., the Cu composition in the BR is less than 50%) are all obviously smaller than those of the Cu85Zr15 SPNG. The results also show that the mechanical properties of the DPNGs are not only related to the strength of the BR and the GR, but also to the GGI structure. For the 85/20 DPNG, the GR shows strong deformation resistance due to its high fraction of FI clusters, in turn, the BR only has few FI clusters, which lead to lower of the deformation resistance, strain 7
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A strategy for improving mechanical properties of metallic glass by tailoring interface structure J.L. Ma , H.Y. Song *, M.R. An , W.W. Li , R.Q. Han School of Material Science and Engineering, Xi’an Shiyou University, Xi’an 710065, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Metallic glass Interface Mechanical property Molecular dynamics simulation
The strength-plasticity trade-off of the metallic glass (MG) is a topical issue that researchers are constantly pursuing. Controlling the glass/glass interface (GGI) structure has become a key avenue for advancing MG performance. Here, the effect of the Cu composition in the boundary region (BR) (i.e., GGI structure) on the mechanical properties of the Cu85Zr15/CuxZr100-x dual-phase nanoglass (DPNG) under tensile loading is inves tigated by molecular dynamics simulation method. The results indicate that the strength of the DPNG can be significantly improved while its excellent plasticity is maintained by adjusting the Cu composition in the BR. The results also show that the mechanical properties of the DPNGs are not only related to the strength of the BR and the grain region (GR), but also to the GGI structure. The optimal matching relationship between the GR and the BR is obtained. The results will present a theoretical basis for developing the high-performance DPNG.
1. Introduction Since the discovery of metallic glass (MG), it has become an ideal candidate for a variety of applications due to their distinguished me chanical properties, a great deal of effort has been made in recent years to study the MG [1-4]. However, it is still a challenge to achieve considerable macro plasticity in the MG at room temperature, which is a science problem to be resolved urgently. Fortunately, as early as 1989, Gleiter [5] had tried to extend the material design concept of nano structured metals to the MG, and proposed that it can be possible to introduce plenty of glass/glass interfaces (GGIs) into the monolithic glass and this new form of glass has been termed as nanoglass (NG). Compared with the bulk MG, the GGIs in the NG belongs to the area with lower density or higher free volume fraction, which is easy to flow and is favorable to stable plastic deformation “homogeneously”. This unique microstructure is capable to sustain high-density shear bands (SBs) and consequently to enhance the global plasticity of the NG. Feng et al. [6] have shown that the GGI, as soft regions, can be a critical defect to promote uniform deformation. Besides, some studies have found that the NG exhibits a super-plasticity behavior due to the presence of the GGIs, where shear transformation zones (STZs) are easily activated nearby to promote global deformation [7,8]. Despite many advances have been made, the widespread application of these alloys remains elusive, largely limited by the irreconcilable conflict between strength and
ductility [9,10]. For instance, Wang et al. [11] have shown that under the uniaxial tension test, more than 15% plastic strain can be obtained for the Sc75Fe25 NG, but at the same time, the strength decreases about 0.4 GPa. Qiao et al. [12] also have indicated that compared with the bulk MG, super ductile behavior emerges in the NG, while the strength is much lower than that in the MG. The reason for these cases is that the internal GGIs inherent of the NGs have been characterized as a “soft” phase promoting the nucleation of the STZs to improve tensile plasticity. In turn, the GGIs with high free volume reduce the activation barrier for the STZs, which makes the yield strength of the NG greatly lower than that of the MG [9,13]. Therefore, the strength-plasticity trade-off of the NG is still a topical issue that researchers are constantly pursuing. Controlling the interface structure has become a key avenue for advancing materials performance. For nanocrystalline materials, improving the interface stability can prevent the dislocation from moving and enhance the interaction between dislocation and interface, thus improving their mechanical properties [14-16]. Hu et al. [17] have discovered that the hardness of nano-grained metals can continue to increase with the decrease of grain size by adjusting the grain boundary stability, which provides a new mechanism for strengthening the strength of extremely fine nano-grained metals. Inspired by the design of high-performance nanocrystalline materials, the effect of the GGI on the mechanical properties of the MGs has attracted the attention of re searchers. Kalcher et al. [18] have manipulated the pristine NG by
* Corresponding author. E-mail addresses: [email protected], [email protected] (H.Y. Song). https://doi.org/10.1016/j.jnoncrysol.2020.120464 Received 29 August 2020; Received in revised form 28 September 2020; Accepted 4 October 2020 0022-3093/© 2020 Elsevier B.V. All rights reserved.
Please cite this article as: J.L. Ma, Journal of Non-Crystalline Solids, https://doi.org/10.1016/j.jnoncrysol.2020.120464
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replacing the GGI with crystalline interphases with higher yield strength. They found that when the soft-phase GGI of the NG is replaced by a stronger crystal structure, the yield strength is significantly increased, which makes it possible to strengthen and toughen the single-phase NG (SPNG). Similarly, Cheng et al. [19] have also revealed a mechanism of strengthening the NG by controlling the short-range ordered structure and free volume of the GGI, and find that its strength is comparable to that of the bulk MG. In 2018, Li et al. [20] uncover a strengthening mechanism for the dual-phase structure, in which the presence of micro-sized secondary phases usually leads to strengthening via the blocking or branching of the SB. The CuZr MG has been regarded as a relatively stable structure due to its excellent glass formation ability [21]. But so far, the strengthening of the second amorphous phase on the boundary region (BR) has been barely mentioned in the CuZr NG. In addition, the trade-off between strength and plasticity of the CuZr NG has not been effectively overcome. Due to the sufficient theoretical research of predecessors and the urgent de mand of the material market for the CuZr amorphous alloy with high mechanical properties, searching for a new method that is more controllable is necessary for designing and fabricating high-performance nanostructured the CuZr amorphous alloy. Recently, molecular dy namics (MD) simulation method has been widely used to study various fundamental physical problems in materials science and has greatly improved our understanding of the nature of the NGs [22-24]. Here, the deformation behavior and mechanical properties of the Cu85Zr15/ CuxZr100-x dual-phase nanoglass (DPNG) under tensile loading are studied using MD simulation method. The results indicate that the DPNG can obtain a superior combination of strength and plasticity by opti mizing the microstructure of the dual-phase nanostructured amorphous alloy. This study will provide initial guidance and theoretical basis for designing and preparing of high-performance NGs. The paper comprises of the following parts. Section 2 presents the simulation model and method of atomistic simulation. The results and discussion are shown in Section 3. Ultimately, the conclusion is sum marized in Section 4.
Fig. 1. (a) Schematic of the Cu85Zr15/CuxZr100-x DPNGs. (b) Enlarged view of dual-phase structure and interface information. (c) High-resolution trans mission electron microscopy images of the DPNG prepared by multi-phase pulsed electrodeposition technique [20]. The BR and the GR are colored by green and purple, respectively.
different Cu composition in the BRs means that the different GGI structures are introduced. For convenience, the Cu85Zr15/CuxZr100-x DPNGs are labeled 85/x DPNGs. Here, the 85/20 DPNG, 85/25 DPNG, 85/36 DPNG, 85/50 DPNG, 85/64 DPNG, 85/75 DPNG, and 85/80 DPNG are considered. As shown in Fig. 1(a), the dimensions of the Cu85Zr15 SPNG and all the 85/x DPNGs in the X-direction, Y-direction, and Z-direction are 20.0 nm, 54.5 nm, and 3.1 nm, respectively. The size (d) of the GR is 11.6 nm and the thickness (t) of the BR is 2.0 nm for all the 85/x DPNGs. Here it is needed to point out that the GGI in the 85/x DPNGs is taken as 1.0 nm in Fig. 1(b) [26]. During uniaxial tensile loading, a maximum strain of 20% is applied to the samples along the Y-direction with a strain rate of 2.5 × 108 /s at 50 K. The PBCs are applied to the Y- and Z-directions, while the free surface condition is used along the X-direction. In the MD simula tion, the embedded atom model (EAM) potential is exploited to describe the interatomic interactions in the Cu-Zr system [27]. This potential has been proved to be consistent with experimental measured structure factors [28] and has been extensively used to investigate the deforma tion behavior of the Cu-Zr amorphous alloys [29,30]. To intuitively analyze the atomic configurations during plastic deformation, all microstructural analysis and visualization of atomic configurations are performed using the Open Visualization Tool (OVITO) [31].
2. Simulation model and method To explore the better mechanical properties of the DPNG, the deformation behaviors of the Cu85Zr15/CuxZr100-x DPNGs and the Cu85Zr15 SPNG under tensile loading are systematically investigated by the MD simulation method. Fig. 1 shows the schematic and atomic-scale model of the DPNG. Here, the Cu85Zr15/CuxZr100-x DPNG is composed of grain region (GR), namely the Cu85Zr15 amorphous phase, surrounding by the BR shell (i.e., the CuxZr100-x amorphous phase). In other words, the GGIs in the Cu85Zr15 SPNG are replaced by the BR shells, which produce two GGI different from the previous GGI structure. The pro duction process of the model is as follows, for the first step, a small MG containing 5850 atoms is produced by quenching from the melt with a cooling rate of 1012 K/s to 50 K at zero pressure, during which periodic boundary conditions (PBC) are applied to all three dimensions. By multiplication of the quenched MG, the specimens of sizes up to 245,700 atoms are generated. To obtain the Cu85Zr15 SPNG and the Cu85Zr15/ CuxZr100-x DPNGs samples, combination modes of single phase and dual phases are created by using Voronoi tessellation method [25]. Subse quently, the Cu85Zr15 SPNG and the Cu85Zr15/CuxZr100-x DPNGs are annealed from 600 K to 50 K at a cooling rate of 1012 K/s to release the stress and eliminate voids [26]. In the preparation of the experiment, some researchers have successfully prepared the DPNGs by multiple pulse deposition method by carefully controlling the deposition voltage, current density, and time duration at different deposition stages [20], as shown in Fig. 1(c). In order to study the mechanical behavior of the DPNGs during deformation, we manipulate the model of the Cu85Zr15 SPNG by replacing the GGI with different second amorphous phases (i. e., the BRs), which are Cu20Zr80, Cu25Zr75, Cu36Zr64, Cu50Zr50, Cu64Zr36, Cu75Zr25, and Cu80Zr20, respectively. It should be noted that the
3. Results and discussion 3.1. Deformation behavior of SPNG and DPNG In previous work, it is known that the mechanical properties of the NG can be effectively adjusted by controlling the Cu composition of the amorphous phase [32]. And the results indicated that the strength of the Cu85Zr15 SPNG is the highest, but the plasticity is poor. The purpose of this paper is to improve the mechanical properties of the Cu85Zr15 SPNG at the same time by tailoring the GGI structure. To study the effect of the GGI structure on the mechanical property of the NG, Fig. 2 gives the stress-strain curves of the Cu85Zr15 SPNG and the 85/50 DPNG under 2
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Fig. 3. Stress-strain curves of the 85/x DPNGs and the Cu85Zr15 SPNG.
Fig. 2. Stress-strain curves of the Cu85Zr15 SPNG and the 85/50 DPNG.
the stress-strain curves of all the samples is similar, but the peak stress is obviously different. The results indicate that the curve of the Cu85Zr15 SPNG clearly separates those of the 85/x DPNGs into two cases in Fig. 3. When the x is less than 50%, the Young’s modulus and peak stress of the 85/x DPNGs are weakened compared with the Cu85Zr15 SPNG. How ever, the 85/x DPNGs with x greater than 50% show stronger Young’s modulus and peak stress. That is to say, not all the BRs can effectively enhance the strength of the Cu85Zr15 SPNG, and there may be a certain kind deformation mechanism which weakens the strength of the Cu85Zr15 SPNG matrix. Here it also can be found that with the increase of strain, the values Δτ/τy of SPNG and DPNGs are different. The Δτ/τy of the Cu85Zr15 SPNG, 85/20 DPNG, 85/25 DPNG, 85/36 DPNG, 85/50 DPNG, 85/64 DPNG, 85/75 DPNG, and 85/80 DPNG are 0.179, 0.183, 0.188, 0.171, 0.141, 0.268, 0.274, and 0.289, respectively. Thus, to systematically understand the mechanical properties of the 85/x DPNGs during the tensile deformation process, it is very necessary to investigate the characteristics of the 85/x DPNGs with different Cu composition in the BR. Fig. 4 shows a clearer relationship between the peak stress and the normalized difference Δτ/τy of all the 85/x DPNGs, and the red star presented the Cu85Zr15 SPNG. Compared with the Cu85Zr15 SPNG and the 85/50 DPNG (also shown in Fig. 2), other samples are mainly
tensile loading. It can be seen from Fig. 2 that after the stress reaches peak stress (τy), both materials show tardy decrease in the stress, and the stress then approaches a relatively steady-state value. The average flow stress (τs) is obtained by calculating the average stress in the plastic flow process. The τy is the stress from which the plastic deformation begins and it can be regarded as the global yield strength of the undeformed glass, while the τs can be considered as the flow strength of the glass or the strength of the material inside a propagating SB [33-35]. Recent theoretical studies and simulations have shown that the normalized difference Δτ (Δτ =τy -τs) between flow strength and yield strength corresponds to the tendency toward strain localization, which influences the tensile plasticity [36,37]. Subsequently, the normalized difference (∆τ/τy) between flow strength and yield strength is proposed to indicate the tendency towards strain localization more precisely [38,39]. The smaller the ∆τ/τy is, the better the plasticity is. It can be seen from Fig. 2 that the ∆τ/τy of the 85/50 DPNG is smaller than that of the Cu85Zr15 SPNG, which indicates that if the Cu50Zr50 amorphous phase is intro duced into the Cu85Zr15 SPNG, the plasticity of the NG can be improved. However, it is observed that neither the τy nor the τs in the 85/50 DPNG is higher than those of the Cu85Zr15 SPNG. In other words, the addition of second amorphous phase (i.e., the Cu50Zr50 amorphous phase) can improve the tensile ductility of the Cu85Zr15 SPNG and lead to a brittle-to-ductile transition of the deformation mode, although at the expense of some strength. According to previous research result, the strength and plasticity are heavily dependent on the Cu composition of the amorphous phase [40]. The interface structure of the GGI has sig nificant influence on the mechanical properties of the NG. Therefore, we consider changing the Cu composition in the BR to change the GGI structure of the NG, and try to further optimize the mechanical prop erties of the DPNG. 3.2. Effect of GGI structure on the deformation behavior of DPNG In order to search for a wonderful combination of superior strength and high plasticity of DPNG, the GGI of the Cu85Zr15 SPNG is replaced by the second amorphous phase (i.e., the BR) with different Cu composi tions. Here, seven kinds of the BRs (namely, the amorphous phase Cu20Zr80, Cu25Zr75, Cu36Zr64, Cu50Zr50, Cu64Zr36, Cu75Zr25, and Cu80Zr20, respectively) are considered, and the percentage of Cu varies is between 20% and 80%. It is pointed out again that the different Cu compositions in the BRs mean that the different GGI structures are introduced. Fig. 3 shows the stress-strain curves of all the DPNGs under uniaxial tensile loading. For comparison purpose, the curve of the Cu85Zr15 SPNG is also given. It is clearly seen that the change trend of
Fig. 4. Relationship between peak stress and Δτ/τy of the 85/x DPNGs and the Cu85Zr15 SPNG. 3
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concentrated in A and B regions marked in Fig. 4. In other words, the effects of the GGI structure on the peak stress and the normalized dif ference Δτ/τy of the 85/x DPNGs are obvious. It can be clearly seen from Fig. 4 that the peak stress of the DPNGs in region A is enhanced about 0.2–0.3 GPa compared with the Cu85Zr15 SPNG, and simultaneously ensured the plasticity of the Cu85Zr15 amorphous matrix (i.e., the Cu85Zr15 SPNG). On the contrary, the strength and plasticity of the DPNGs in region B are all obviously smaller than those of the Cu85Zr15 SPNG. The normalized differences Δτ/τy of the DPNGs have increased about 0.09–0.11, and the consumption of peak stress is about 0.2–0.4 GPa comparing with that of the Cu85Zr15 SPNG. That is to say, the losses of Δτ/τy and peak stress are approximately 55% and 9% in the DPNGs when the Cu composition increases from 20% to 36%. Accordingly, the DPNGs with the Cu composition in the BR from 64% to 80% have a more attractive integration of outstanding mechanical properties, which makes it possible to obtain the DPNG with perfect combination of strength and plasticity. It is a though-provoking problem that why the DPNGs with different Cu compositions in the BR present different me chanical properties. This probably means that the DPNGs with different GGI structures can exhibit different plastic deformation mechanisms. To investigate the potential deformation behavior of the DPNGs, we choose three representative models (i.e., the 85/20 DPNG, the 85/50 DPNG and the 85/80 DPNG, respectively) in each region and they will be analyzed and compared in Figs. 5-7, which gives the evolution of the local atomic shear strain of the DPNGs at different strains. In order to better reveal the deformation details of the samples in region B (as shown in Fig. 4) during the tensile loading, Fig. 5 illustrates the atomic deformation images of the 85/20 DPNGs at different strains, in which the presence of regions with relatively large atomic strain implies that they have undergone large localized plastic deformation. As shown in Fig. 5(a), the priority activation positions are located at the free surface of the BR (marked by the arrows), hence, free volume begins to evolve in the interfaces at early stage owing to lower cohesion. In other words, the STZs start to accumulate causing softening in these regions. From that point until it fails, the plastic deformation is mainly confined to the BR. Notably, the plasticity occurs by the generation of a high density of the STZs which are primarily activated in the BR due to the abundant free volume. The 85/20 DPNG then fails in the form of propagation of cross-SBs across, as shown in Fig. 5(c). Along with this, four larger steps are generated at the surface position, with the size of 2.1 nm, 3.9 nm, 2.8 nm, and 2.2 nm, respectively. In order to see more intuitively the expansion process of SBs of the BR, Fig. 5(e) gives the atomic displacement vector maps of the 85/20 DPNG, which are the enlarged regions of Fig. 5(d). The trajectories of the cross-SBs and the nearby atoms show certain regularity as shown in Fig. 5(e). In order to
obtain more details of Figs. 5(e) and (f) gives the zoomed up section of the black square. It is found from Fig. 5(f) that the atomic displacement is deflected and the atom moves is confined to the BR region, which may be due to the existence of high-strength GGI. Similar results have been reported by Hua et al. [41] It can be concluded that the strain locali zation is mainly concentrated at the BR due to the softening of the BR caused by a large amount of free volume and the atomic motion in the BR is blocked by the GGI. This phenomenon greatly weakens the overall strength and plasticity of the 85/20 DPNG, which can be shown in Fig. 4. The snapshots of the deformation behavior of the 85/50 DPNG at different strains are displayed in Fig. 6. As shown in Fig. 6(a), at the strain of 14.1%, the high shear strains are primarily concentrated where the STZs atomic aggregation occur on the GGIs and the BRs, especially on the free surfaces of the BR (marked by the arrows), leading to the cross-SBs have been formed near the BR as shown in Fig. 6(c). The von Mises strain of the 85/50 DPNG in Fig. 6(c) is about 0.5, which is obviously lower than that of the 85/20 DPNG in Fig. 5(c), and the wider STZs are formed in the 85/50 DPNG. Besides, there are no large steps on the free surface. Fig. 6(e) and (f) show the details of the expansion process of the SBs by displaying the atomic displacement. The final orientation of the atomic displacement of the 85/50 DPNG is almost the same as that of the loading direction, while the atomic displacement of the 85/20 DPNG is obviously deflected in the X direction, which is due to the severe shear effect of the soft BR phase (i.e., the Cu20Zr80 amorphous phase) during deformation by comparing Figs. 5(e) and 6(e). Fig. 6(f) shows the zoomed up a section of the black square (i.e., the detailed atomic displacement diagram at the cross-SBs) shown in Fig. 6(e). The simulation indicates that unlike the 85/20 DPNG, the atomic displace ment is not hindered by the GGI of the 85/50 DPNG instead of the GR in the 85/50 DPNG, in other words, the trajectories of atoms severely de flects after passing through the soft GGI, which may be due to the blocking effect of the high-strength GR on atomic motion. It is known that the strain localization is mainly concentrated at the soft phase, which contains a large number of free volumes leading to higher atomic mobility and the atomic deflection is easy to occur. Hence, the strain softening occurs due to the soft GGIs in the 85/50 DPNG, resulting in lower strength than the original matrix phase (i.e., the Cu85Zr15 SPNG). By changing the Cu composition in the BR into 80%, the deformation behavior shows a completely different trend (see Fig. 7). Here, the 85/80 DPNG with great combination of strength and plasticity is chosen as a representative of region A as shown in Fig. 4. In order to explain the reason why the strength of the DPNG is the highest when the Cu composition in the BR is 80%, the mechanical properties of the bulk CuZr MGs with different Cu composition are calculated. The result shows that the peak stresses of the Cu20Zr80 MG, Cu25Zr75 MG, Cu36Zr64
Fig. 5. (a-d) Atomic configurations of the 85/20 DPNG at strains of 9.4% and 20%, colored with von Mises strain and chemical heterogeneity. The zoomed up section of the dashed box of (e) is shown in (f). 4
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Fig. 6. (a-d) Atomic configurations of 85/50 DPNG at strains of 14.1% and 20%, colored with von Mises strain and chemical heterogeneity. The zoomed up section of the dashed box of (e) is shown in (f).
Fig. 7. (a-d) Atomic configurations of the 85/80 DPNG at strains of 14.1% and 20%, colored with von Mises strain and chemical. The zoomed up section of the dashed box of (e) is shown in (f).
MG, Cu50Zr50 MG, Cu64Zr36 MG, Cu75Zr25 MG, Cu80Zr20 MG, and Cu85Zr15 MG are 2.813 GPa, 2.879 GPa, 3.099 GPa, 3.491 GPa, 4.330 GPa, 4.381 GPa, 4.741 GPa, and 4.342 GPa, respectively. The results indicate that the peak stress of the Cu80Zr20 MG is the highest. From the point of view of mixing rule of composite, this result can explain the relationship between the strength of the 85/x DPNGs and the Cu composition of the BR, as shown in Fig. 4. Of course, the mechanical properties of the DPNGs cannot be explained simply from the point of view of mixing rule of composites, and the mechanical properties of the DPNGs depend on the synergistic effect of the two amorphous phases to a certain extent. It can be seen from Fig. 7 that a relatively homogeneous local plastic deformation commences in the 85/80 DPNG instead of deformation localization like the 85/20 DPNG and the 85/50 DPNG in Figs. 5 and 6. And an interesting phenomenon is found in Fig. 7(a), most of the high strain region is concentrated in the interior of the GR rather than in the BR or the GGI as the formers (indicated by ellipses and ar rows in Figs. 7(a) and (b)). For the 85/80 DPNG, many STZs homoge neously nucleate in the soft phase (i.e., the GR) and a series of immature embryo SBs intersect each other and block by hard phase (i.e., the BR) without forming a dominant SB as shown in Fig. 7(c). So the BR as a hard phase can effectively block the propagation of the SB and promote the branching of the SB, this is the key to the equilibrium strength and
plasticity of the DPNG [20]. Just as shown in Fig. 4, the 85/x DPNGs in region A have exhibited excellent mechanical properties. Figs. 7(e) and (f) give the atomic displacement in the high strain region and the enlarged view of the local area. Compared with the 85/20 DPNG and the 85/50 DPNG, there is no obvious phenomenon of atomic trajectory deflection, which is mainly due to the synergistic interaction between two amorphous phases with similar strength. In other words, the STZs are activated almost at the same time in the process of deformation of the BR and the GR with similar strength, so as to realize the coordinated movement (like the 85/80 DPNG). When the strength difference be tween the two phases is large, the softer phase will preferentially deform, and the deformation of the harder phase is smaller, so the local deformation dominated by the soft phase occurs like the 85/20 DPNG and the 85/50 DPNG. The mechanical properties of the DPNGs are not only related to the strength of the BR and the GR, but also to the GGI structure. In order to verify the above inference, a more detailed structural description will be shown in the following. In order to study the internal deformation mechanism of the 85/x DPNGs mentioned above, the voronoi polyhedron (VP) is used to analyze the mechanical properties of the BR, the GGI, and the GR. The advantage of the VP on the structural analysis of the DPNG is that it can 5
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reflect atomic clusters directly so that it is capable of distinguishing the local atomic environment and microstructure by forming a contrast in the GR, the BR, and the GGI [42]. To characterize the topological structure of short range order, the VP denoted by 〈n3 n4 n5 n6〉 is employed. The VP with n5 = 6 possesses low five-fold symmetry, while the VP with n5 = 8, 10 and 12 possess high five-fold symmetry [6]. It is indicated that the full icosahedron (FI) 〈0 0 12 0〉, and the icosahedral-like polyhedra 〈0 2 8 1〉 and 〈0 2 8 2〉 here are the most prominent local structures impacting elasticity stage in the CuZr amor phous alloy [43]. Especially the FI clusters have a great effect on sta bilizing the glassy structure and increasing its resistance against deformation [44,45]. At the same time, the flow defects accompanied by the increase of the VPs with index 〈0 3 6 3〉 and 〈0 3 6 4〉, which could affect plasticity [35]. The previous results indicated that the high five-fold symmetry region tends to undergo elastic deformation, while the low five-fold symmetry region is easily deformed plastically [40]. In other words, the FI clusters play a strengthening role because of their shear deformation resistance and high stability, while the VPs with index 〈0 3 6 3〉 and 〈0 3 6 4〉 act as a softener for increasing plasticity during tensile loading. Fig. 8 gives the six most populous polyhedral types of the BR, the GR, and the GGI in the 85/20 DPNG, the 85/50 DPNG, and the 85/80 DPNG, respectively. For the 85/20 DPNG, the GR shows strong deformation resistance due to its high fraction of FI clusters, in turn, the BR only has few FI clusters, which lead to lower of the deformation resistance, strain softening, and thereby strong shear localization. It should be noted that the GGI with more FI clusters is stable relative to the BR, the deforma tion is only confined in the BR, and the atomic motion of the BR will be hindered by the GGI, which will show a narrow cross-SBs as shown in Fig. 5(c) and (f). For the 85/50 DPNG, the number of FI clusters in the BR is still much lower than that in the GR, so it shows a deformation mode similar to that of the 85/20 DPNG, i.e. a pair of cross-SBs through the specimen. It can be noticed that the proportion of the VPs with low fivefold symmetry (i.e., 〈0 3 6 3〉 and 〈0 3 6 4〉) in the GGI is slightly higher than those of the BR and the GR, while the FI clusters in the GGI is lower than those of the BR and the GR. So, the GGI shows excellent plastic flow ability, and it shows a wider cross-SBs dominated by the BR deforma tion, as shown in Fig. 6(c). In the 85/50 DPNG, the GR with more FI clusters has higher shear deformation resistance. The atoms in the BR pass through the GGI and deflect due to the strong GR, which further confirms the results of Fig. 6(f). It can be seen from Fig. 8 that for the 85/ 80 DPNG, the FI clusters in the BR, the GR, and the GGI are all plentiful, and the FI cluster in the BR is the largest, followed by the GR and the GGI. Hence, the shear deformation resistance of the BR, the GR, and the GGI in the 85/80 DPNG shows stronger, and the elastic modulus and
strength convey a higher value, which is consistent with the result given in Fig. 4. The STZs are preferentially activated in the GGI because it has the least FI clusters (see Fig. 7(a)). Subsequently, the stress concentra tion in the GGI further activates the STZs in the softer phase GR, which is because the FI cluster in the GR is slightly lower than that of the BR. At the same time, the free surface of the GR (i.e., the soft phase) is also the key area to induce STZs. With the increase of strain, these two activation sites activate more STZs in the GR and the BR, which is attributed to the little difference in the FI clusters proportion between the two phases, thus promoting the local uniform plastic deformation of the 85/80 DPNG, as shown in Fig. 7(c). In other words, the little fraction difference of FI clusters between the BR and the GR is also more conducive to the coordinated movement of each other in the plastic deformation process. Therefore, there is no obvious deviation of the atomic trajectory, as shown in Fig. 7(f). In addition, the three models in Fig. 8 reveal a certain relationship between FI clusters and the peak stress. When the difference of the fraction of the FI clusters is larger among the BR, the GR, and the GGI, the amorphous phase with less FI clusters will become the soft phase weaken the overall strength of the 85/x DPNGs, just as shown in the region B of Fig. 4. On the contrary, the number of FI clusters in the BR, the GR, and the GGI is abundant, and the FI clusters fraction difference between the three is tiny, so all of them will show high shear defor mation resistance, and the 85/x DPNGs will have higher peak stress as shown in the region A of Fig. 4. In order to further explore the deformation behavior of the BR and the GR in the 85/x DPNGs during deformation, the plastic strain parti tioning between the GR and the BR is quantified as a function of participation rate of locally deformed atoms. It needs to be explained as follows: the local atomic shear strain (or atomic von Mises strain) is defined as [46]: √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ( )2 )2 ( ηyy − ηzz + (ηxx − ηzz )2 + ηxx − ηyy Mises η = η2yz + η2xz + η2xy + 6 The ηMises is an excellent standard of measurement for evaluating the plastic stage of material. Atoms with a larger magnitude of ηMises contribute more to the plasticity. Atoms with ηMises ≥ 0.2 are normally utilized to visualize the plastic deformation within the specimen [47, 48]. To visualize the deformation mechanisms in the DPNGs, only the atoms with ηMises ≥ 0.2 are considered, which indicate the STZs during the tension process [29,48]. In order to quantify the degree of locali zation we quote a quantity called the deformation participation ratio [49]. The ψ is used to represent the deformation participation ratio, which is equal to the percentage of the number of atoms with the ηMises greater than 0.2 divided by the total number of atoms in the whole sample. That ψ local is equal to the percentage that the number of atoms with the ηMises greater than 0.2 in the BR (or the GR) divides by the total number of atoms in the BR (or the GR). For all of the 85/x DPNGs, the BR and the GR of the DPNGs play different roles during the tension process, and their respective ψ local are shown in Figs. 9(a) and (b). As shown in Fig. 9, when the strain is<6%, the DPNGs all display near-zero (local) shear strain, which is because there is no deformation localization in the elastic deformation stage. After the strain of 6%, the large atomic strain clusters begin to accumulate at stress concentrations. The strain about 6% is just around the yield point, in which a large number of the STZs are activated and distorted along with favorable orientation after pass ing the yield point. Meanwhile, it can be noticed from Fig. 9(a) that the ψ local of the BRs increase speed is higher than that of the GRs. That is to say, the local deformation in the plastic stage is mainly concentrated on the BR for the DPNGs with the Cu composition in the BR from 20% to 50%, as shown in Fig. 9(a). For example, this phenomenon can be observed in the 85/20 DPNG and the 85/50 DPNG in Figs. 5 and 6. It is worth noting that for the 85/50 DPNG, the ψ local of the GR is obviously higher than those of the GRs in the other DPNG, as shown in Fig. 9(a), more atoms in the GRs participate in the local deformation processes,
Fig. 8. Fraction of populous voronoi polyhedrons of the BR, the GGI, and the GR for the 85/20 DPNG, the 85/50 DPNG, and the 85/80 DPNG. 6
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softening, and thereby strong shear localization. Therefore, the plastic deformation of the 85/20 DPNG is dominated by the local deformation (i.e., a pair of cross-SBs). And the GGI with more FI clusters is stable relative to the BR, the deformation is only confined in the BR, and the atomic motion of the BR will be hindered by the GGI. However, for the 85/80 DPNG, the FI clusters in the BR, the GR, and the GGI are all plentiful, and the FI cluster in the BR is the largest, followed by the GR and the GGI. Hence, the shear deformation resistance of the BR, the GR, and the GGI in the 85/80 DPNG shows stronger, and the elastic modulus and strength convey a higher value. The results also indicate that for the 85/80 DPNG, the little fraction difference of FI clusters between the BR and the GR is also more conducive to the coordinated movement of each other in the plastic deformation process, showing uniform plastic deformation. The results provide not only an in-depth atomic under standing of the deformation mechanism of the DPNG, but also optimize the heterostructure to achieve the desired mechanical properties in nanostructured amorphous alloys. Data availability statement The data used to support the findings of this study are available from the corresponding author upon request. CRediT authorship contribution statement J.L. Ma: Investigation, Data curation, Formal analysis, Methodology, Writing - original draft. H.Y. Song: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Writing - review & editing. M.R. An: Data curation, Formal analysis, Methodology, Writing - original draft. W.W. Li: Formal analysis, Methodology, Writing - original draft. R.Q. Han: Formal analysis, Methodology, Writing - original draft. Fig. 9. Participation rate of locally deformed atoms of the 85/x DPNGs.
Declaration of Competing Interest
and then a pair of wider cross-SBs can be formed as shown in Fig. 6. Compared with the DPNGs in Fig. 9(a), the ψ local of the BR and the GR in the 85/64 DPNG, the 85/75 DPNG and the 85/80 DPNG has no signif icant difference, but the ψ local of the GR is slightly larger at the strain between 17% to 20% (marked in insert map in Fig. 9(b)), which in dicates that the GR is the main carrier of plastic deformation of the DPNG. This situation is consistent with the research results reported in Fig. 7. In addition, the ψ local with a similar value in the BR and the GR is also beneficial to local uniform plastic deformation of the DPNG. The existing results indicate that a strong correlation exists between me chanical properties of DPNGs and Cu composition, which is useful for the synthesis of the DPNGs with predominant ductility and high strength.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 11572259), Natural Science Foundation of Shaanxi Province (No. 2019JQ-827), Scientific Research Program Funded by Shanxi Provincial Education Department (No. 19JK0672), and Program for Graduate Innovation Fund of Xi’an Shiyou University (No. YCS18211005). References
4. Conclusion
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The deformation behavior and mechanical properties of the 85/x DPNGs under tensile loading are investigated by MD simulation method. The results indicate that the mechanical properties of the DPNG can be significantly improved by adjusting the Cu composition in the BR. The strength of the DPNGs in region A (i.e., the Cu composition in the BR is more than 50%) is enhanced about 0.2–0.3 GPa compared with the Cu85Zr15 SPNG, and simultaneously ensured the plasticity of the Cu85Zr15 amorphous matrix. On the contrary, the strength and plasticity of the DPNGs in region B (i.e., the Cu composition in the BR is less than 50%) are all obviously smaller than those of the Cu85Zr15 SPNG. The results also show that the mechanical properties of the DPNGs are not only related to the strength of the BR and the GR, but also to the GGI structure. For the 85/20 DPNG, the GR shows strong deformation resistance due to its high fraction of FI clusters, in turn, the BR only has few FI clusters, which lead to lower of the deformation resistance, strain 7
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