Brittle-to-Ductile Transition in Metallic Glass Nanowires - Nano Letters

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Brittle-to-ductile transition in metallic glass nanowires Daniel Sopu, Alireza Foroughi, Mihai Stoica, and Jurgen Eckert Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b01636 • Publication Date (Web): 01 Jun 2016 Downloaded from http://pubs.acs.org on June 3, 2016

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Brittle-to-ductile transition in metallic glass nanowires D. S¸opu,∗,† A. Foroughi,† M. Stoica,†,‡ and J. Eckert¶,§ IFW Dresden, Institut f¨ ur Komplexe Materialien, Helmholtzstr. 20, D-01069 Dresden, Germany, Politehnica University of Timisoara, P-ta Victoriei 2, RO-300006 Timisoara, Romania, Erick Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstrasse 12, A-8700 Leoben, Austria, and Department Materials Physics, Mountanuniversit¨at Leoben, Jahnstrasse 12, A-8700 Leoben, Austria E-mail: [email protected]

Abstract When reducing the size of metallic glass samples down the nanoscale regime, experimental studies on the plasticity under uniaxial tension show a wide range of failure modes ranging from brittle to ductile ones. Simulations on the deformation behavior of nanoscaled metallic glasses report an unusual extended strain softening and are not able to reproduce the brittle-like fracture deformation as found in experiments. Using large-scale molecular dynamics simulations we provide an atomistic understanding of the deformation mechanisms of metallic glass nanowires and differentiate the extrinsic size effects and aspect ratio contribution to plasticity. A model for predicting the ∗

To whom correspondence should be addressed IFW Dresden, Institut f¨ ur Komplexe Materialien, Helmholtzstr. 20, D-01069 Dresden, Germany ‡ Politehnica University of Timisoara, P-ta Victoriei 2, RO-300006 Timisoara, Romania ¶ Erick Schmid Institute of Materials Science, Austrian Academy of Sciences, Jahnstrasse 12, A-8700 Leoben, Austria § Department Materials Physics, Mountanuniversit¨at Leoben, Jahnstrasse 12, A-8700 Leoben, Austria †

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critical nanowire aspect ratio for the ductile-to-brittle transition is developed. Furthermore, the structure of brittle nanowires can be tuned to a softer phase characterized by a defective short-range order and an excess free volume upon systematic structural rejuvenation, leading to enhanced tensile ductility. The presented results shed light on the fundamental deformation mechanisms of nanoscaled metallic glasses and demarcate ductile and catastrophic failure.

Keywords: Metallic glasses, molecular dynamics simulations, nanowires, aspect ratio, ductility. Usually, metallic glasses show negligible global plasticity under uniaxial tension. 1 However, when reducing the length scale, a transition from brittle behavior to tensile ductility and homogeneous plastic flow has been observed in nano-sized metallic glasses. 2–4 The sample-size effects have been put forward to explain the suppression of localization and failure of metallic glass wires with dimensions of the order of 100 nm. 2 For such small samples, the change in the plastic deformation from inhomogeneous brittle to homogeneous ductile was explained considering the crossover between competing energy terms, elastic and shear band energy. 3,5 An intrinsic brittle-to-ductile transition is obtained when nanowire diameter approach the estimated length scale of the shear band nucleus size. 6 However, results in disagreement with above hypothesis have been reported, showing that plastic deformation in compression is always size-independent and localized in shear bands. 7,8 Moreover, simulation results support the picture of size-independent shear banding until sample dimensions approach the shear band thickness. 9 It is believed that the different mechanical responses are reflected sensitively in the processing route of how the wires are made. The long exposure to high-energy ions incurred during FIB milling was claimed to affect the structure and properties of nanowires, inducing the unusual room temperature ductility. 10,11 Indeed, metallic glass nanowires fabricated by thermoplastic molding fracture in a brittle manner and exhibit significant plasticity when irradiated by Ga+ ions. 12 Furthermore, heat treatments below transition temperature of the irradiated nanowires elicits structural relaxation 2


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and returns the glass state to its as-molded condition and corresponding mechanical behavior. 13 Additionally, when it comes to mechanical testing of nanoscale specimen, experimental artifacts due to tapering of cylindrical pillars for compression tests, heating induced by the electron beam in in-situ mechanical testing, or confinement effects, can change the operating deformation mechanism. 14,15 As we will see below, two characteristics are important for the deformation behavior under tensile load of nano-sized metallic glasses: the aspect ratio (length to diameter ratio, L:d) and the structure of the nanowire. Hence, a new model is proposed to calculate the critical aspect ratio value at which the brittle-to-ductile transition occurs in metallic glass nanowires. Moreover, we will show that by modifying the atomic structure of a brittle nanowire through systematic structural rejuvenation, in terms of creating free volume and disturbing the short-range order (SRO), enhanced tensile ductility can be attained. To understand this failure mode transition and achieve an atomistic level description of the deformation mechanism, molecular dynamics (MD) simulation proved useful at this stage. MD computer simulations using the software LAMMPS 16 were used to discriminate between the extrinsic size effects and aspect ratio contribution to the plasticity. The Cu64 Zr36 glass was simulated using the Finnis-Sinclair type potential by Mendelev et al. 17 A metallic glass block containing 8000 atoms was produced by quenching it from the melt to 50 K with a cooling rate of 1010 K/s. Cylindrical-shaped metallic glass nanowires were prepared via bulk cutting from a sample obtained by replicating the initial quenched glassy block. Periodic boundary condition was only imposed along the axial direction, while the lateral directions were left free. Uniaxial tensile tests were conducted on the nanowires at 50 K with a constant strain rate of 4×107 1/s. The atomic scale deformation mechanisms were analyzed by visualizing the local atomic shear strain µM ises , 18 calculated with the OVITO analysis and visualization software. 19 Figure 1 shows the stress-strain curves of two nanowires with a diameter of d=20 nm and aspect ratio of 3 and 12.5, respectively, together with a sequence of snapshots of the

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local atomic shear strain evolution during deformation. The selected diameter is equal to the calculated threshold value of 20 nm for this alloy composition necessary to stabilize a dominant shear band. 20 Regardless of the aspect ratio, within the elastic regime, both nanowires behaved in the same manner. Once the maximum stress is overcome, the two nanostructures show radically different plastic regimes. Although in both cases plastic deformation starts at almost the same strain level of 9% and is localized in shear bands, only the nanowire with the high aspect ratio fail catastrophically under tensile load following the sudden initiation and propagation of one shear band. This is consistent with the stress drop to zero in the stress-strain curve, as illustrated in Figure 1. Moreover, despite the fact that three shear bands nucleate, only one of them goes critical mediating the plasticity of the long nanowire. With decreasing the aspect ratio, a shear band sets in, but the slip is arrested and the nanowire undergoes a finite stress drop. The nanowire will continue to deform plastically and the shear band will develop extensively and gradually leading to an extended plastic strain of 28% before failure (see Figure 1). Valuable insights about the interplay of irradiation, 21,22 processing routes, 23 notch, 24,25 size effects 26–28 and plastic behavior of nanoscaled metallic glasses have been recently provided. However, in these studies an extensive plasticity have been reported. Even those glassy nano-sized samples in which plasticity occurs in a highly localized region, i.e. the shear band, 9,29–31 show no brittle-like fracture deformation as found in experiments. 10,13 From the strain level when the shear band forms until the final fracture of the sample an unusual extended strain softening occurs, and closely resembles the deformation behavior observed in the case of the nanowire with a low aspect ratio. The slower shear band propagation is even more questionable while considering that direct measurements and MD simulations of shear band propagation in metallic glasses approaches a velocity close to the speed of sound. 32,33 Previously, the sharp brittle-to-ductile transition was only achieved via reducing the covalency of the bonding and increasing disorder in the atomic structure. 34 The strength of the angular constraint of the covalent bonding explains the fracture behavior observed in Fe-

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P nanowires with a small aspect ratio, L:d=3. 35 Besides, other previous atomistic simulations of the deformation behaviour under tensile loading of different nano-sized metallic glasses were unable to observe brittle failure. Further, we will demonstrate that the inappropriately chosen aspect ratio is the most relevant factor for the unusual extended plastic strain. On the basis of the results discussed above, we propose a simple approach for guiding the design of nano-sized metallic glasses as models for investigating mechanical properties under tensile loading as shown in Figure 2. Let’s consider a nanowire with the initial length, L0 , and diameter, d0 . We assume that all plastic deformation occurs in one single slip plane. The plastic deformation is defined in terms of the total translational displacement along the axial direction, LSB (see Figure 2). The length, LSB , is directly proportional to the nanowire elongation under the applied stress, ∆L. In other words, for a complete slip ∆L ≥ LSB , were ∆L = L0 · ǫel and ǫel is yield strain. Considering the shear band plane oriented in 45◦ -angle towards the tensile axis, the length LSB = d0 . Under these assumptions L0 · ǫel ≥ d0 and from here the aspect ratio must satisfy the condition L0 /d0 ≥ 1/ǫel to ensure a shear slip until the final fracture. For Cu64 Zr36 nanowires ǫel =0.08 is extracted from the stress-strain curve, and for this value a critical L:d = 12.5 is predicted. If this critical condition is not met, the slip is arrested and the nanowire undergoes a finite stress drop equivalent to the axial displacement load Lel SB as shown in Figure 2. From this point until the final fracture, LSB , the shear slip

is related to the further loading, ǫload . This model is based on the assumption that only a single shear band propagates across the nanowire, and therefore may underestimate the actual aspect ratio if the plastic deformation is accommodated by concurrent or sequential nucleation of multiple shear bands. Additionally, since the nanowire shows very little lateral contraction under tensile load, for simplicity, we choose to ignore the Poisson’s ratios from the calculation. It should be mentioned that this model only applies to wires with diameters at the nanoscale. Embrittlement effect due to the maturation of stable shear banding to unstable crack propagation occurs over a typical distance of sub-microns. 36 MD simulations on single FCC Cu nanowires under uniaxial tension also demonstrated

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that the aspect ratio plays a significant role in determining brittle or ductile behavior. 37 The transition in plastic behavior is explained based on discrete bursts of dislocation activities. Only those nanowires with an aspect ratio L:d > 800 show localized shear failure via dislocation activity along a single plane. Nevertheless, our model predicts a much smaller critical aspect ratio for metallic glass nanowires. For an average yield strain ǫel ≈ 2-3% calculated in experiments, we expect the failure mode transition to occur at L:d ≈ 40. Consistent with the theoretical model presented here, previous experimental work on strained small-scale metallic glasses with high aspect ratios have also revealed brittle-like fracture and negligible inelastic deformation 10,12,13 while those nanowires with low aspect ratio displayed enhanced ductility. 3,4,21 Note that this assumption may not apply to nanowires with structures and properties affected by the processing routes such as ion irradiation or FIB milling. Evidence that irradiation strongly influences the mechanical response of metallic glasses through structural changes and manifested as a decrease in yield stress and ductile-like mode deformation have been experimentally disclosed. 12,13 Here, the ion irradiation appears to act as an agent for glass rejuvenation manifested as increase in the free volume. Hence, to emulate the irradiated nanowires and, consequently, to simulate the rejuvenation process we randomly remove 10 % of atoms in the nanowire with high aspect ratio. In this way the rejuvenated volume fraction of the glass can be systematically controlled. To investigate how variation in the irradiated volume fraction changes in mechanical response, two structures were prepared, in one case only an outer shell of 3 nm was diluted while the whole volume was heavily rejuvenated in the second case. After diluting by 10 % both structures relax to a density distribution with 2% density difference to the bulk sample in maximum, which matches the flow strain of the homogeneous sample 38 (see Figure 3). The difference in the density is also related to the strong variation in the degree of SRO. The common topological feature of SRO in amorphous Cu-Zr is the dominance of Cu-centered full-icosahedral (FI) clusters. 39,40 These FI units have a high packing density and shear resistance. 41 Figure 3 displays the evolution of the FIs clusters together with the atomic volume distribution in the

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two rejuvenated nanowires in comparison to the as-cast one. The fraction of Cu-centered FIs is as low as 14% in the diluted glass compared to average FI value of the as-cast glass of about 22% (with respect to the number of Cu atoms in the system). The new phase exhibits similar structural features as glass-glass interfaces in nanoglasses. 42 Indeed, Sc75 Fe25 nanoglass have revealed excellent plastic deformation ability relative to the monolithic metallic glass nanowires. 43 Moreover, the systematic modification of the structure through dilution coupled with the structural softening process observed in the ion-irradiated nanoscaled metallic glasses. Low energy collision cascades have produced distortion of the topological SRO and free volume growth. 22 We explore deformation mechanisms in the both structures following the same procedure as before. The first effect observed with increasing the rejuvenated volume fraction is a reduction in the yield stress as shown in Figure 4. For the nanowire displaying increased structural softening at the outer shell, the yield stress decreases from 3.5 to 2.75 GPa and goes down to only 2 GPa for the case of nanowire with whole volume rejuvenated. As the FI clusters have a high shear resistance, 44 a decrease in the total amount of FI clusters can explain the decrease in yield stress. Accounting for the volume fraction of the softer phase in the outer shell results in value equal to half the volume of the nanowire. Therefore, the change in the yield stress can be seen as an average of the constituent glassy phases in the shell and core counterpart. On the other hand, changing the structural state by rejuvenating the outer shell and leaving unaffected the core of the nanowire, leads to only negligible tensile ductility. The snapshots in Figure 4 reveal a quasi-localized deformation related to a twoglassy-phase composite structure. The plastic strain must be accommodated in both the rejuvenated (soft) outer shell and the unaffected (hard) core. In the first place the soft outer shell is likely to commence yielding before the undamaged core. In Figure 4, only half of the nanowires are displayed for an easier observation of the shell containing atoms with high strain values, which means that these atoms are highly activated. Upon further loading, the applied strain localizes in form of a shear band in the hard core of the nanowire. Once the

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instability develops, it immediately propagates into a catastrophic failure as also revealed by the sudden stress drop in the stress-strain curve. In contrast, the nanowire with the whole volume being rejuvenated shows a transition from brittle to extended plastic behavior. As shown in Figure 4, the sample experienced obvious necking prior to the final fracture. The necked region enlarged and spread out gradually, and the extensive necking led to a total elongation to failure of 15%, a typical characteristic of ductile deformation. Therefore, we believe that a transition in the mechanical responses of metallic glass nanowires can be only attained through structural rejuvenation of a large volume fraction of the sample resulting in a more softer structure that facilitates an entirely distinct mechanism for accommodating plasticity via homogeneous flow at low temperature. The observed transition in the deformation modes are consistent with the experimental prediction, so that, in nanowires that have been subjected to FIB processing or ion irradiation, the plastic behavior is largely controlled by the irradiated volume of the specimen. At low irradiated volume fraction, the deformation mode is characterized as shear band-mediated, similar to the as-cast case 13 while heavily rejuvenated nanowires, approaching a liquid-like state, show significant tensile ductility. 4 In summary, we studied the uniaxial tensile failure of metallic glass nanowires using MD simulations. Our simulations show that the aspect ratio and the structural rejuvenation play the critical role in the plastic behavior of nanoscaled glassy materials. Above a critical aspect ratio, nanowires fail catastrophically under tensile load subsequent to the initiation and propagation of one shear band. Besides, in nanowires with an aspect ratio lower than the critical value the shear slip is arrested and an extended plastic strain is observed. A simple theoretical model, which provides a qualitative interpretation of the transition from brittle to ductile behavior, was developed. Furthermore, we have shown that structural rejuvenation of a large volume fraction of the nanowires lead to enhanced tensile ductility. A sharp brittleto-ductile transition was achieved when changing the structural state in terms of creating free volume and disturbing the short-range order. We believe this letter will motivate future

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theoretical studies on the deformation behavior of metallic glass nano-sized structures and shed light on the understanding of how to differentiate the extrinsic size effects and aspect ratio contribution to plasticity. Notes: The authors declare no competing financial interests. Supporting Information: MD simulation movies of samples deformed in tension. This material is available free of charge via the Internet at http://pubs.acs.org. The authors acknowledge financial support of the European Research Council under the ERC Advanced Grant INTELHYB (grant ERC-2013-ADG-340025) and the German Science Foundation (DFG) under the Leibniz Program (grant EC 111/26-1). A DAAD-PPP travel grant is also acknowledged. The authors gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on the supercomputer JUROPA at the J¨ ulich Supercomputing Centre (JSC). Additional computing time was made available by the Center for Information Services and High Performance Computing (ZIH) at TU Dresden. The authors also thank U. Nitzsche for technical assistance concerning the computer simulations. The authors acknowledge Dr. S. Pauly for insightful discussions.

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ε [%] Figure 1: Uniaxial tensile stress-strain curves together the most representative snapshots of the local atomic shear strain along the deformation of two Cu64 Zr36 glass nanowires with aspect ratio of 3 (panels A to F, up) and 12.5 (panels A to C, at right), respectively. The color scale indicates the atomic local shear strain.

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Figure 2: Schematic illustration of the deformation mechanism. Nanowire has a cylindrical cross section. Only a nanowire with high aspect ratio, so that ∆L ≥ LSB , shows brittle-like fracture under uniaxial tension.

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Figure 3: Contour maps showing the atomic volume distribution relative to the bulk value in the nanowires with the shell (a) and whole volume (b) rejuvenated, respectively, in comparison to the as-cast sample (c). The white circles mark the locations of the FI local motifs within a thin slab of a thickness of 5 nm cut out of the cylindrical nanowires. It may be seen that the structural rejuvenation of metallic glasses manifested as increased free volume (low density) and decreased in the total amount of FI clusters (low degree of SRO).

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ε [%]

Figure 4: Uniaxial tensile stress-strain curves together with representative snapshots of the local atomic shear strain along the deformation of two structural rejuvenated nanowires in comparison with the as-cast nanowire and having an aspect ratio of 12.5. Left hand side panels (A to C) show the localized plastic behavior in the nanowire with a soft outer shell and hard inner core while the right side panels (A to D) display the transition from brittle to extended plastic behavior when the entire volume fraction of the nanowires is subjected to structural rejuvenation.

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Brittle-to-Ductile Transition in Metallic Glass Nanowires - Nano Letters

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