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0Deformation behavior of metallic glass composites reinforced with shape memory nanowires studied via molecular dynamics simulations
D. Sopu,1 M. Stoica,1,2 and J. Eckert1,3
1IFW Dresden, Institutfur Komplexe Materialien, Helmholtzstr. 20, D-01069 Dresden, Germany 2Politehnica University ofTimisoara, P-ta Victoriei 2, RO-300006 Timisoara, Romania 3TU Dresden, Institutfur Werkstoffwissenschaft, D-01062 Dresden, Germany
(Received 27 March 2015; accepted 19 May 2015; published online 28 May 2015)
Molecular dynamics simulations indicate that the deformation behavior and mechanism of Cu64Zr36 composite structures reinforced with B2 CuZr nanowires are strongly influenced by the martensitic phase transformation and distribution of these crystalline precipitates. When nanowires are distributed in the glassy matrix along the deformation direction, a two-steps stress-induced martensitic phase transformation is observed. Since the martensitic transformation is driven by the elastic energy release, the strain localization behavior in the glassy matrix is strongly affected. Therefore, the composite materials reinforced with a crystalline phase, which shows stress-induced martensitic transformation, represent a route for controlling the properties of glassy materials. © 2015 AIP Publishing LLC. [http://dx.doi.org/10.106371.4921857]
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One of the most popular ways to improve the plasticity of bulk metallic glasses (BMGs) is to synthesize BMG matrix composites.1-4 The composite materials are heterogeneous microstructures combining a glassy matrix with crystalline secondary phases.5 The interactions between the reinforcing second phase and shear bands (SBs) significantly retard fracture. Moreover, in the presence of nanoscale precipitates multiple SBs form, uniformly distributed through the BMG composite, increasing in this way the resistance against catastrophic crack propagation along one dominant SB.6 A detailed atomistic understanding of the underlying mechanism has been provided by molecular dynamics (MD) simulations,7-11 showing that multiple SBs are nucleated at the amorphous-crystalline interface and are blocked by crystalline particles.
One promising alloy group to form BMG matrix composites are CuZr-based BMGs.5 In this case, ductile B2 CuZr crystalline precipitates form upon quenching from the melt.12 More interestingly, the B2 CuZr precipitates exhibit a martensitic transformation from a B2 to a B19' structure,12-14 which is reversible and renders it a shape-memory alloy.15 Moreover, MD simulations have also revealed a stress-induced martensitic transformation in case of B2 CuZr nanowires.16-18 In line with these preliminary MD results, it is interesting to analyze how the stress-induced martensitic transformation affects the mechanical properties of the composite material reinforced with shape memory crystals.
In this study, we investigate the mechanical properties of Cu64Zr36 BMG composite reinforced with B2 CuZr nanowires by means of MD simulations using the program package Lammps.19 In the first step, the metallic glass block containing 8000 atoms was produced by quenching from the melt: after relaxation at 2000 K for 2 ns to ensure chemical homogeneity, the melt was quenched to 50 K using a cooling rate of 0.01 K/ ps. The atomic structure of the synthesized Cu64Zr36 glass shows good agreement with what has been reported in litera-ture.21,22 After, a slab-shaped Cu64Zr36 glass sample with dimensions of Lx x Ly x Lz = 36 x 7.5 x 84 nm3 and a total number of 1 296 000 atoms is constructed by replicating the
initial BMG block. Two 3D-periodic BMG composites were constructed by inserting 15 B2 CuZr nanowires in the monolithic BMG. [001] nanowires of cross-sectional dimensions of 3.22 x 3.22nm2 and an initial length of 19.4nm are considered. The volume fraction of the crystalline phase related to the total composite volume is 14.1%. The interatomic interaction is described by the modified Finnis-Sinclair type potential for Cu-Zr proposed by Mendelev et al.20 The deformation mechanisms of BMG composites have been studied by deforming under uniaxial tension parallel to the z-direction. All structures were deformed at 50 K with a constant strain rate of 4 x 107 1/s in z-direction. Periodic boundary conditions were applied in all three dimensions and the pressure in x- and y-direction was kept to 0 kbar allowing for lateral contraction. The atomic scale deformation mechanisms were analyzed by visualizing the local atomic shear strain gMises,21-23 calculated with the Open Visualization Tool (OVITO) analysis and visualization software.24 The stress-induced martensitic transformation was investigated during the tensile deformation using Common Neighbor Analysis (CNA).25
In Fig. 1(a), the local atomic shear strain together with the CNA are presented for the case of the BMG composite with nanowires arranged along the deformation direction (z-direction), and we will call this throughout the paper as Clongitudinal. For better visualization, just half of the sample and only the nanowires and those atoms of the glassy matrix with an atomic strain higher than 30% are shown. At a strain of 10%, shear transformation zones (STZs) start forming around the amorphous-crystalline interface. Also part of the nanowires shows a stress-induced martensitic transformation from the B2 phase to an intermediated R-phase. Increasing the strain up to 14%, small embryonic SBs nucleate at the interface and propagate through the glass but, they are immediately blocked by the next nanowires. Moreover, the strain is distributed mostly around those nanowires which suffer severe martensitic transformation (red atoms in Fig. 1(a)). Once the B2 nanowires undergo transformation to the R-phase, the volume increase associated with this transformation will perturb the strain field around the nanowires, so that the glassy phase
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FIG. 1. (a) Local atomic shear strain and CNA for a Cu64Zr36 BMG composite containing 15 CuZr B2 nanowires distributed along the deformation direction. In order to capture the stress-induced martensitic transformation in the B2 crystalline phase, only half of the structure and those atoms with an atomic strain higher than 0.3 are shown. (b) The atomic representation of the three crystalline structures. Cu atoms are colored in red and Zr atoms in blue.
will display a compressive strain field next to the R-phase region (gray atoms) and, in return, a tensile strain filed along the undeformed B2 nanowire. The tensile residual strain assists local dilatation and creation of free volume. As a result, the STZ are readily activated in these soft regions characterized by an increased free volume, as can be seen in the area marked with a circle in Fig. 1(a). However, even at a strain of 20%, none of these embryonic SBs becomes critical being confined between the crystalline nanowires, ensuring a homogeneous deformation of the BMG composite. In addition, all nanowires show martensitic transformation under uniaxial tension. In Fig. 1(a), bottom panel, it can be seen that the all nanowires partially transform from the B2 phase (blue atoms) to an intermediate R-phase (gray atoms) and finally, from the R-phase to the body-centered-tetragonal phase (BCT) colored in green. A detailed atomistic representation of the three structures is shown in Fig. 1(b). Similar two-step phase transformation in B2 CuZr nanowires under tensile
Based on these results, an interesting question arises: how strong the stress-induced phase transformation affects the plasticity of BMG composite? In order to answer the question, we have constructed another composite with the same number and type of nanowires but with a different spatial distribution. Basically, the nanowires are now distributed normal to the loading direction (named Ctransversal) as can be seen in Fig. 2. Although the Ctransversal composite was deformed following the same procedure as in the first case of the Clongitudinal composite, the plastic behavior suffers great modifications. Now, at a strain of 10%, STZ not only nucleates around the amorphous-crystalline interface but also starts precipitating and forming embryonic SBs. Fig. 2 reveals that SBs propagate through the glassy matrix following a free path between the nanowires. However, increasing the strain up to 14% reveals that none of these embryonic SBs goes critical since they block each other or are hindered by the nanowires. Even at a strain of 20%, the local energy release is not sufficient to accelerate one of the shear bands, and therefore, the Ctransversal composite deforms by pattern of multiple SBs. More interestingly, by analyzing in comparison with the case of the Clongitudinal composite, an increased number of atoms with an atomic strain higher than 0.3 can be observed. Moreover, the B2 nanowires show no stress-induced marten-sitic phase transformation even at a strain of 20%. Apparently, the structure of the nanowires is affected by the interaction with the SBs. In cases, where the shear band is only hitting the
loading was reported in the literature.
FIG. 2. Local atomic shear strain and CNA for a Cu64Zr36 BMG composite containing 15 CuZr B2 nanowires distributed normal to the deformation direction. In order to capture the stress-induced martensitic transformation in the B2 crystalline phase, only half of the structure and those atoms with an atomic strain higher than 0.3 are shown.
corners of the B2 precipitates it becomes obvious that the outer layer of the nanowires is amorphized and is starting to attach to the SB, which is indicative for a melting-like behavior.10
At this point, we have found that nanowires distribution affects the strain distribution in the glassy matrix but still not explain how stress-induced martensitic phase transformation modifies the plasticity of composite materials. Therefore, we have realized a quantitative interpretation of strain localization by using the strain localization parameter defined by
Cheng et al.,26 W NEf=i (gfses - C?es)2, where gfvfs is the average von Mises strain over all atoms in the simulation cell. W evaluates the deviation of strain distribution from the homogeneous behavior: a larger W value indicates larger fluctuations in the atomic strain and a more localized deformation mode. In Fig. 3 (upper panel), the W parameter is plotted along the deformation process for the two types of BMG composites in comparison to the monolithic BMG. First, it can be seen that up to a strain of «8% (point A), both BMG composites show similar but much higher W values than the monolithic glass. The different elastic constants of the glass and crystalline phases lead to a stress-induced interfaces reconstruction. Moreover, the weakly bonded atoms at the amorphous-crystalline interfaces result in a lower activation barrier for STZ which, consequently, become mostly activated at the soft interfaces. For the case
FIG. 3. The W values during tensile deformation for a monolithic BMG in comparison with two BMG composites with nanowires distributed longitudinal and transversal to the loading direction, respectively (upper panel). The relative number of atoms with gMises > 0.3 with respect to the total number of glassy atoms in the system (bottom panel).
of monolithic glass, the increase in W value is much lower and mostly due to thermal vibrations and the local atomic rearrangement. However, once the point A is overcome, the monolithic BMG W parameter increases exponentially upon continued loading and at a strain of about 11% intersects the W lines of the two composite structures (see Fig. 3, upper panel). Basically, at this level of strain, the monolithic BMG starts deforming by one major shear band, and, therefore, the W parameter increases drastically indicating a localized deformation mode.
After the point A occurs a split between the W lines of the two composites (see Fig. 3), indicating that the Ctransversal composite shows a higher degree of strain localization compared to the Clongitudinal structure. As already observed by visualizing in comparison the local atomic shear strain in Figs. 1 and 2, in the Ctransversal composite, a higher amount of STZ activate and condensate forming SB nuclei, which mature into extended defects and deformation becomes more localized. On the other hand, the Clongitudinal shows a lower amount of STZ and the resulting embryonic SBs are uniformly distributed and confined between the nanowires. Nevertheless, the W values of the Ctransversal composite did not increase drastically as found for the case of the monolithic BMG since the SB propagation is compromised by the intersection of shear bands with different orientations and by the intersection with nanowires. The different strain distribution behaviors of the two composites are due to the stress-induced martensitic phase transformation, which starts around a strain of 8%. After this strain level, the plasticity of the Clongitudinal composite is mediated besides the SBs nuclea-tion and propagation also by the phase transformation of the nanowires from B2 into R phase. The difference in the W value becomes more pronounced after a strain of 17% (point B), when also the intermediate R phase starts transforming to BCT giving a total difference in the W value equivalent to AW. Since also the martensitic transformation of the B2 phase into R and BCT phases is driven by the elastic energy, the amount of local energy release in the glassy matrix is even lower resulting to a low fraction of percolated STZ and consequently the probability for the formation of mature SBs is decreased. Fig. 3, bottom panel, shows the relative number of atoms with > 0.3 with respect to the total number of glassy atoms along the deformation process for the two composites. It can be easily seen that upon loading the line of Clongitudinal goes below the one of Ctransversal after a strain level of 8% when the crystalline nanowires start showing mar-tensitic transformation. Hence, we can predict that a BMG composite exhibiting stress-induced martensitic transformation will retard strain localization and thus lead to improved plasticity.
In summary, the deformation mechanisms of BMG composite materials reinforced with B2 nanowires have been investigated in comparison to a monolithic BMG. It has been shown how the distribution and the stress-induced martensitic transformation of nanowires drastically affect the strain localization in BMG composites. When deforming in tensile initially SBs form at the amorphous-crystalline interface and propagate through the glassy matrix. However, the SB propagation is compromised by the intersection of shear bands with different orientations or by the intersection with nanowires. If
the crystalline nanowires are distributed along the deformation direction, a two-step stress-induced martensitic phase transformation takes place. Since the martensitic transformation is driven by the elastic energy release, similar to STZ nucleation and precipitation, the formation of a critical SB is retarded. The plasticity of CuZr BMG composite materials can, therefore, be tailored by carefully choosing the density and spatial distribution of B2 crystalline nanowires. Altogether, simulations are encouraging for the future investigations of BMG composite materials exhibiting stress-induced martensitic transformation under tensile deformation and provide an atomistic understanding of the deformation mechanisms.
The authors acknowledge the financial support of the European Research Council under the ERC Advanced Grant INTELHYB (Grant No. ERC-2013-ADG-340025) and the German Science Foundation (DFG) under the Leibniz Program (Grant No. EC 111/26-1). A DAAD-PPP travel grant is also acknowledged. Computing time was made available at ZIH TU Dresden and IFW Dresden as well as by CSC Julich. The authors acknowledge Dr. Simon Pauly and Sergio Scudino for fruitful discussions.
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