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Serrationbehavioursinmetallicglasseswithdifferentplasticity

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Serration behaviours in metallic glasses withdifferent plasticity

G. N. Yang, S. Q. Chen, J. L. Gu, S. F. Zhao, J. F. Li, Y. Shao, H. Wang & K. F. Yao

To cite this article: G. N. Yang, S. Q. Chen, J. L. Gu, S. F. Zhao, J. F. Li, Y. Shao, H. Wang & K. F.Yao (2016): Serration behaviours in metallic glasses with different plasticity, PhilosophicalMagazine, DOI: 10.1080/14786435.2016.1197434

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PhilosoPhical Magazine, 2016http://dx.doi.org/10.1080/14786435.2016.1197434

© 2016 informa UK limited, trading as Taylor & Francis group

Serration behaviours in metallic glasses with different plasticity

G. N. Yanga,b  , S. Q. Chena,b, J. L. Gua,b, S. F. Zhaoa,b, J. F. Lia,b, Y. Shaoa,b, H. Wangc and K. F. Yaoa,b

aschool of Materials science and engineering, Tsinghua University, Beijing, P.R. china; bKey laboratory for advanced Materials Processing Technology, Ministry of education, Beijing, P.R. china; cinstitute of nanosurface science and engineering, shenzhen University, shenzhen, P.R. china

ABSTRACTWe present a statistical study of serration behaviours in Pd77.5Cu6Si16.5, Ti41Zr25Be26Ag8, Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 and Fe50Ni30P13C7 metallic glasses with different plasticity. The four samples show similar serration patterns in the beginning of yielding, and different patterns during later loading. These results indicate that the shear band initiation process in metallic glasses follow some similar dynamics. And the later serration process follows different dynamics and will lead to different plasticity. Here we interpret these serration behaviours from a perspective of inhomogeneity. The different serration patterns and shear band dynamics could be reasonably understood. The serration pattern of the Fe-based sample suggests that the brittleness of metallic glasses might result from a lower degree of inhomogeneity, and a less tendency of forming shear band intersections. This study might provide new experimental evidences for different micro-structures (or inhomogeneity) and dynamic behaviours in metallic glasses with different plasticity.

1. Introduction

Metallic glasses (MGs) have been highly concerned for their excellent physical, chemical and magnetic properties [1,2]. However, the plasticity in many MGs is poor, which limits their further applications. The mechanical studies of MGs have revealed that the deformation of MGs follows a manner of localised flow in shear bands at room temperature [3]. For those brittle MGs, the shear bands could easily fracture once nucleated, and the materials show poor plasticity with few shear band formation [4,5]. For those ductile MGs under some loading conditions, the shear bands could remain stable and be arrested, and the materials could achieve plasticity with multiple shear bands [6–8]. During the multiple shear banding, the materials experience many load–unload cycles, representing the shear bands activation and arrest. Such phenomenon is understood as the serration behaviour and is concerned as a key to reveal the underlying dynamics of shear banding in MGs [9–14]. Some statistics studies reveal that the shear bands follow a self-organised critical (SOC) behaviour or chaotic

KEYWORDMetallic glass; shear band; plasticity; serration

ARTICLE HISTORYReceived 4 February 2016 accepted 30 May 2016

CONTACT Y. shao shaoyang@tsinghua.edu.cn; h. Wang whao@szu.edu.cn; K. F. Yao kfyao@tsinghua.edu.cn

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behaviour in MGs with different plasticity, where the serration pattern falls in a power law distribution or peak distribution [10,11,15]. However, there are also contradictory reports showing different serration patterns and shear band dynamics in plastic MGs [16–18]. Then, it is important to reveal the origin of the different plasticity in MGs, and the relationship among serration pattern, shear band dynamics and plasticity of MGs.

In this work, we studied the plastic dynamics in four typical MG systems (Pd, Ti, Zr and Fe-based MGs) with different plasticity by uniaxial compression. The statistics results showed similar serration patterns in the beginning of yielding, and different patterns during later loading of these MGs. Based on that, some underlying links between the serration pattern and shear band dynamics were discussed, which might shed light on understanding the different plasticity in MGs.

2. Experimental

MGs samples with compositions of Pd77.5Cu6Si16.5, Ti41Zr25Be26Ag8, Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 and Fe50Ni30P13C7 were prepared and tested by uniaxial compression. The ingots of Ti41Zr25Be26Ag8 and Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 were prepared by arc melting the mixtures of high-purity elements of the nominal composition in a Ti-gettered pure argon atmosphere. The ingots were flipped and re-melted by four times to ensure the composition homogeneity. Finally, glassy rod samples of the two compositions were prepared by copper mould casting method. The Fe50Ni30P13C7 and Pd77.5Cu6Si16.5 ingots were prepared by melting the mixture of high purity elements of the desired composition under high purity argon gas protection. The ingots were then purified by fluxing treatment. B2O3 was melted at a temperature of 1400 K for more than 2 h under a vacuum of 10−2 Pa. Then the ingots were immersed into the B2O3 melt and hold at a temperature of 1400 K for more than 10 h. During this process, the ingots were intermittently cooled down by several hundreds of Kelvins and heated up again, and thereby promote the purification process. Finally, rod samples of the Pd77.5Cu6Si16.5 alloy were prepared by water quenching. Rod samples of the Fe50Ni30P13C7 alloy were prepared by copper mould casting method. The as-prepared samples were proved to be in glassy state by conventional X-ray diffraction. The samples of the four MGs were machined into a rod shape of φ2 × 4 mm for uniaxial compression tests. The tests were performed by a WDW-50 testing machine under a constant engineering strain rate of 1 × 10−4 s−1 at room temperature. The strain was measured by an extensometer attached to the testing machine. During loading, the data of engineering stress, engineering strain and time were recorded by the testing machine. Details of the later data processing would be described in the related parts of the Results section.

3. Results

To correct the increasing sample’s cross-sectional area during compression, the recorded data of engineering stress and engineering strain were converted into true stress σ and true strain ε according to the expressions of:

(1)� = �e

(

1 + �e

)

(2)� = ln(

1 + �e

)

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where σe stands for engineering stress and εe stands for engineering strain.The true stress–strain (σ  −  ε) loading curves of the Pd77.5Cu6Si16.5, Ti41Zr25Be26Ag8,

Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 and Fe50Ni30P13C7 MG samples are shown in Figure 1. The Pd77.5Cu6Si16.5 sample showed a yielding stress of ~1320 MPa and did not fracture with up to 40% plastic strain. The Ti41Zr25Be26Ag8 MG showed a yielding stress of ~1850 MPa and a relatively smaller plastic strain up to ~5%. The Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 MG showed a yielding stress of ~1900 MPa and a plastic strain up to ~2%. And the Fe50Ni30P13C7 MG showed a yielding stress of ~3000 MPa and a plastic strain up to ~3%.

Jerky stress-drops (serrations) were observed on the loading curves of the four samples, which represented the activation and arrest of shear bands. A statistic result of these ser-rations is shown in Figure 2, where each stress-drop on the loading curves is represented by a point. The horizontal axis represents the strain ε when the stress-drop occurs, and the vertical axis represents the magnitude of the stress-drop Δσ. The vibration of the machine also could induce small serrations on the loading curves [10,11]. In this study, the magnitude of the machine vibration would be less than 1 MPa. Therefore, in the statistical analysis, those serrations with a size less than 1 MPa are not counted. The results in Figure 2 show that these serrations have very different sizes, and there is an upper limit for the serration size in each sample.

In addition, the serration patterns in the beginning of yielding of the four samples are similar. The serration size is small at first, and would increase with strain during further loading, as shown by the red lines in Figure 2. The increasing rate of serration size after yielding (Δσmax/Δε) is different in the four samples. To determine the slope of the increasing

Figure 1.  (colour online) The true stress–strain (σ–ε) loading curves of the (a) Pd77.5cu6si16.5, (b) Ti41zr25Be26ag8, (c) zr41.2Ti13.8cu12.5ni10.0Be22.5 and (d) Fe50ni30P13c7 Mg samples.

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serration size, the points near the left boundary of the stress-drop maps (as marked by red points in Figure 2) were analysed by linear fitting. The results showed that the increasing serration size with strain in the beginning of yielding was almost linear. In the Pd-based sample, the serration size reaches a maximum Δσmax ≈ 30 MPa when the strain increases by Δε ≈ 2% after yielding (Δσmax/Δε ≈ 13 MPa/%). In the Ti-based sample, the serration size reaches a maximum of Δσmax ≈ 40 MPa when the strain increases by Δε ≈ 3% after yielding (Δσmax/Δε ≈ 12 MPa/%). In the Zr-based sample, the serration size reaches a maximum Δσmax ≈ 24 MPa when the strain increases by Δε ≈ 1.5% after yielding (Δσmax/Δε ≈ 15 MPa/%). In the Fe-based sample, the serration size reaches a maximum of Δσmax ≈ 45 MPa when the strain increases by Δε ≈ 1% after yielding (Δσmax/Δε ≈ 40 MPa/%). Finally, the serration process in the Ti, Zr and Fe-based MG samples ended by fracture (Figure 2(b)–(d)), and the serration process in the Pd-based MG sample could sustain (Figure 2(a)).

From the loading curves (Figure 1) and statistics of serrations (Figure 2), different ser-ration patterns (distribution of serration density at different sizes) could be observed in the four MGs with different plasticity. In the Pd-based MG sample, many large serrations with a size near 20–30 MPa and many small serrations with a size less than 5 MPa could be observed. In the Ti and Zr-based MG samples, fewer large serrations with a size of a few 10 MPa and many small serrations with a size less than 5 MPa could be observed. In the Fe-based MG sample, most serrations have a large size of about 45 MPa, and no serration with a size less than 30 MPa could be observed when the strain increases beyond 3.5%.

To further understand the serration patterns, the distribution of the serration number at different serration sizes of the four MG samples are shown in Figure 3. To exclude the affection of increasing serration size in the beginning of yielding and make comparison with

Figure 2. (colour online) a statistic result of the serrations in the (a) Pd77.5cu6si16.5, (b) Ti41zr25Be26ag8, (c) zr41.2Ti13.8cu12.5ni10.0Be22.5 and (d) Fe50ni30P13c7 Mg samples. each point represents a stress-drop on the loading curves. The horizontal axis represents the strain ε when the stress-drop occurs, and the vertical axis represents the magnitude of the stress-drop Δσ.

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some previous studies [10], only the serrations in stable plastic regime were counted (the serrations at strains larger than 5%, 4%, 3%, 3% in the Pd, Ti, Zr, Fe-based samples were counted). In the Pd-based MG sample, the serration density is high when the size is below 5 MPa, and also forms a peak near the size of ~15 MPa. The serration density of the Ti and Zr-based MG samples is also high at small size, and some large-sized serrations could also be observed. The serrations of the Fe-based MG sample form a peak at a large size near 45 MPa, with a much less density at small size.

4. Discussion

The above results clearly show different plasticity and serration behaviours in the four MG systems. Based on the serration patterns, the shear band dynamics in these MGs could be further discussed.

4.1. Serration size and number

In the previous studies of serration behaviours in MGs, it has been revealed that the ser-rations are related to the multiple shear band movement. By activating and sliding of a

Figure 3. (colour online) Distribution of the overall serration number at different serration sizes in the (a) Pd77.5cu6si16.5, (b) Ti41zr25Be26ag8, (c) zr41.2Ti13.8cu12.5ni10.0Be22.5 and (d) Fe50ni30P13c7 Mg samples.

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shear band, the stress in the material could be partly released, manifested as a stress-drop on the loading curve [9]. Therefore, the size and number of serrations observed from the loading curve could represent the sliding distance and number of shear bands activated in the sample. Both these two parameters are important for the plasticity. As the shear bands carry the deformation of MGs at ambient temperature, better plasticity are always accompanied by more shear bands formation. On the other hand, a large stress-drop or a longer shear band sliding distance usually relate to a higher possibility of fracture. Due to the shear softening effect induced by shear dilatation [19,20], the formation of cavities [21], and the heat induced by elastic energy release [22], the shear bands would become weaker during shearing. Therefore, large serration size might adversely affect the plasticity of MGs.

For the MG samples measured in this study, the Fe-based sample shows the largest serra-tion size of ~50 MPa, and a high proportion of serrations at large size (Figure 3(d)). The other three Ti, Zr, Pd-based samples show much smaller serration sizes, and a high proportion of serrations at small size (Figure 3(a)–(c)). In Figure 2 (right tick label) and Figure 3 (top tick label), the serration size is normalised by the yielding strength (Δσ/σy), which show that the serration density in the as-measured samples could form a peak near the serration size of 0.01–0.02σy. It indicates that the large serration size in a MG might be related to a large modulus and yielding strength. With a higher yielding stress, more elastic energy will be released during the shear band sliding by the same distance, which could lead to higher temperature rise, easier shear band fracture and poorer plasticity. This might be a reason that the Fe-based MGs usually show poorer plasticity than the other three MG systems. (The Pd, Ti, Zr-based MGs are typical ductile MG systems [7,23–26], and the Fe50Ni30P13C7 MG used in this study is one of the few Fe-based MGs that could show plasticity [4,5,27].)

4.2. Serration pattern and shear band dynamics

Different serration patterns could be observed in the four MG samples in this study (Figures 2 and 3). It has been revealed that the serration pattern of MGs is closely related to the plasticity [10,11,15]. Some studies indicate that if the serrations follow a power law distribution with more serrations at smaller size, the shear bands in the sample will follow a SOC behaviour, where the shear bands has strong interaction and could form networks to accommodate plasticity [11]. If the serration density shows a peak shape distribution at a large size, a chaotic shear band behaviour could be expected [28], where the material deforms by individual primary shear band movements and will show poor plasticity. Such understanding has been used to explain the different plasticity achieved in different MG systems [11] or under different strain rates [15].

As revealed before, the cumulative distribution of serration vs. serration size in SOC dynamics would follow the power law [11]:

where P stands for the probability of finding a serration with a size larger than s, A stands for a normalised constant, β stands for a scaling exponent, and s stands for the serration size.

The studies of avalanche dynamics also indicate that if the avalanche events correlated, the incubation time of the events also would follow a power law distribution [10], with an expression of

(3)P(>s) = As−𝛽

(4)P(>te) ∼ t

−De

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where P stands for the probability of finding a serration with an incubation time larger than te, D stands for a scaling exponent.

Conversely, if the events are uncorrelated and randomly generated, the incubation time of the events might follow a Poisson distribution [10], with an expression of

where P stands for the probability of finding a serration with an incubation time larger than te, τ stands for a rate parameter.

According to this understanding, the cumulative distribution of serration size and incu-bation time of the serrations in the stable plastic regime of the four MG samples were ana-lysed. Figure 4 shows the results of cumulative distribution of serration size. If the serration size follows the power law distribution, they would form a straight line on the logarithmic plot (the insets in the figure). It could be found that in the Pd, Ti and Zr-based samples, the small stress-drops approximately follow the power law distribution. However, when the serration size increases, the distribution would largely deviate from the power law. It results from the relatively large number of serrations at large size (Figure 3(a)–(c)). The serrations of the Fe-based sample showed a peak distribution (Figure 3(d)). Accordingly, the cumulative distribution of serrations deviates from the power law distribution.

Figure 5 shows the result of cumulative distribution of incubation time, with a log-arithmic vertical coordinate and linear horizontal coordinate. If the incubation time of serrations follows the Poisson distribution, they would form a straight line on the plot. If the incubation time of serrations follows the power law distribution, they would form a concave line on the plot. The results show that the incubation time distributions of the serrations in the as-measured four MG samples approximately follow the Poisson distribution but not power law distribution.

The above results of serration size distribution indicate that only the small serrations might follow the SOC behaviour, and the incubation time distribution indicates that the serration might be actually individual events instead of correlated events suggested by the SOC dynamics. Although the four measured MGs show considerable plasticity, their serra-tion patterns differ from the previous studies of SOC behaviour. The serrations in the Pd, Ti and Zr-based MG samples consist of accompanied large and small shear band movements (Figure 3(a)–(c)), but did not follow a monotone decreasing power law distribution. Such results indicate that a pure SOC behaviour might not be the only option for MGs plas-ticity. Some other studies also have shown that the plasticity could also be achieved with a serration pattern in peak distribution [17,18]. Some studies suggest that the shear band dynamics in plastic MGs could also be understood by a tuned criticality behaviour instead of the SOC behaviour [16].

The serration size could reflect the sliding distance of the shear bands [29,30]. The ser-ration size distribution (Figure 4) of the Pd, Ti and Zr-based MG samples indicates that the materials deform by shear bands with different sliding distance. The largely varied serration size might hint a tendency of shear band multiplication and branching [11], which might be the reason that the materials could form secondary shear bands outside the primary shear plane and achieve plasticity. In the Fe-based MG sample, however, the serrations show a peak distribution near 45 MPa (Figure 3(d)), and almost no small-sized serrations could be observed at a strain beyond 3.5% (Figure 2(d)). This serration pattern is similar to that

(5)P(>te) ∼ exp(−t

e∕𝜏)

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Figure 5. (colour online) cumulative distribution of incubation time of serrations in the four as-measured Mg samples.

Figure 4. (colour online) cumulative distribution of serration size in the four as-measured Mg samples.

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in the chaotic dynamics [11,28], which indicates that the material deforms by unrelated shear bands sliding on some primary shear planes, with less shear band number and poor plasticity. With this understanding, it could be reasonable to explain that the Pd, Ti and Zr-based MG usually show considerable plasticity, and the Fe-based MGs usually show brittleness. The plasticity can also be achieved by mixed large and small serrations, where the serrations of different sizes might follow different dynamics.

4.3. Serration pattern in the beginning of yielding

We also notice the similar serration patterns in the beginning of yielding of the four sam-ples. The serration size is small at first, and would increase with strain during later loading (Figures 1 and 2). This phenomenon occurs commonly in the four measured samples, and could also be noticed in some other MG systems for mechanical testing, such as Zr–Cu–Ni–Al MG [10,16,31,32], Pd–Ni–P MG [33] and Cu–Zr–Al MG [34]. It indicates that the yielding or shear band initiation process in MGs might follow some similar dynamics. The physical origin of this phenomenon is still debatable. In this study, we suggest that this question could be understood from a perspective of inhomogeneity.

It has been noticed that the structure and stress distribution in MGs are not homogene-ous. At atomic scale, due to the structure and composition fluctuation, the material might form some loosely-packed regions. The study of molecular dynamics simulation suggested that the MG structure might consist of both solid-like and liquid-like sites [35]. Based on the simulated atomic strain distribution, it suggested that there might exist flow regions and stable regions in MG, with different energy barriers [36]. The relative weak positions have also been termed as soft spots [37]. Besides these studies of atomic scale inhomo-geneity, there are also studies indicating that there could be some flaws and heterogenei-ties at micro scale, such as surface imperfections and secondary phase. Considering these heterogeneities, it is suggested that MGs could show a noticeable size effect of decreasing strength with increasing size in a size range of sub-micron to a few microns [38]. There might also be inhomogeneity at larger scale, such as cavities and the stress concentration near the press-head. From these sites with inhomogeneous structure and stress, the shear bands could nucleate more easily.

To consider these inhomogeneous regions in the sample, we suppose that the stress for shear band viscous sliding could be expressed as σflow, and the yielding stress for shear band nucleation could be expressed as σy, which is higher than σflow. As illustrated in Figure 6a, during loading in the elastic regime, the stress of the sample would increase approximately linearly. After the shear band nucleation at σy, it will slide to release the stress, and the global stress-drops by Δσ = σy − σflow. Since there could be many inhomogeneous regions in the sample, the yielding stress for shear band nucleation σy at these inhomogeneous regions would be different. For those inhomogeneous regions with relative low local yielding stress σy, the value of σy might be just slightly larger than σflow. Due to the low yielding stress, these places could form shear bands firstly during loading, and lead to small stress-drops. After these shear bands being arrested, the stress could continue to increase, and new shear bands might be nucleated from those inhomogeneous regions with higher local yielding stress σy, and form larger stress-drops. By this process, an increasing stress-drop amplitude with strain could be observed during the yielding process (Figures 2 and 6).

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According to this understanding, the slope of stress-drop (Δσmax/Δε, marked by the red lines in Figure 2) might reflect the frequency of shear band nucleation and the degree of inhomogeneity in the sample. As illustrated in Figure 6(b), considering the sample could form different numbers of shear bands during loading. If there are many inhomogeneous regions in the sample, many shear bands could nucleate during the yielding process. Since the shear bands sliding could release the stress, the increase of stress-drop could be delayed, manifested as a small slope of stress-drop Δσmax/Δε (curve B). If there are fewer inhomoge-neous regions in the sample, fewer shear bands could nucleate during the yielding process, and the stress could increase faster and form high stress-drop earlier, manifested as a steep slope of stress-drop Δσmax/Δε (curve A).

During the later serration process, some inhomogeneous regions in the sample could develop into shear band, and some places of the sample also might become new inhomo-geneous positions. If the later shear bands could propagate along a direction different from the former shear bands, they could pass through the former shear bands and form shear band intersections. Due to the stress concentration at the intersections, these intersections could become new potential sites for shear band nucleation. Therefore, the serration and shear band multiplication process could sustain. With different degrees of stress concen-tration at the shear band intersections, the yielding stress for shear band nucleation from these intersections could be different, and could lead to different stress-drops during fur-ther multiple shear banding. With this understanding, the as-observed serration patterns of mixed serration size in Figure 2 could be explained. Conversely, if the material deform along a primary shear plane with fewer intersections, fewer small-sized stress-drops could be observed. Based on the serration pattern in Figure 2, we could expect that the Fe-based MG sample with a large slope of Δσmax/Δε would have fewer inhomogeneous regions for shear bands nucleation. Since the Fe-based sample showed only large serrations at the strain beyond 3.5%, the sample might deform only by primary shear band movements during this process. Therefore, the brittleness of Fe-based MGs might result from a less inhomogeneous structure and lower tendency of forming shear band interactions. The plasticity of Pd, Ti and Zr-based MGs might result from an inhomogeneous structure and strong shear band interaction. Such understanding might provide new insight into the shear band dynamics and micro-structure in MGs with different plasticity.

Figure 6. (colour online) (a) illustration of the increasing stress-drop amplitude with strain during the yielding process. (b) illustration of different stress increasing rate in samples with different numbers of shear bands during loading.

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5. Conclusion

The serration behaviour of the Pd77.5Cu6Si16.5, Ti41Zr25Be26Ag8, Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 and Fe50Ni30P13C7 MGs with different plasticity is statistically analysed and compared. Different serration patterns are observed in the four MGs, which provide new experimen-tal evidences for different shear band dynamics and micro-structure (inhomogeneity) in MGs with different plasticity. Some conclusions are drawn as followed:

(1) Small serration size and large serration number are beneficial to plasticity. A small serration size could represent a shorter sliding distance and better shear band stability. A large serration number could represent the avalanches of mul-tiple shear bands. The result shows that the serration size of the Fe-based MG sample is relatively larger than the other three MGs, which might result from the large modulus and yielding strength of Fe-based MG.

(2) A pure SOC behaviour might not be the only option for MGs plasticity. The plas-ticity can also be achieved by mixed large and small serrations. In the Pd, Ti and Zr-based MG samples, the serrations consist of both small and large sizes. The mixed serration size indicates that the materials deform by shear banding with different sliding distance. It hints that the as-formed shear bands could intersect and induce more shear band nucleation sites, which could lead to multiple shear banding and plasticity. In the Fe-based MG sample, most serrations are large, which indicate that the sample deforms by primary shear band movements, with less secondary shear bands formation and poor plasticity.

(3) Similar serration patterns have been observed in the yielding process of the four samples, which imply a similar yielding dynamics in MGs. The serration size in the beginning of yielding is small, and will increase during further loading. From a perspective of inhomogeneity, the slope of maximum stress-drop Δσmax/Δε could reflect the degree of inhomogeneity and density of shear band nucleation sites in the material. A larger slope indicates less inhomogeneous structure and fewer shear bands formation. The Fe-based sample suggests that the brittleness of metallic glasses might result from a lower degree of inhomogeneity, and a less tendency of forming shear band intersections.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by National Natural Science Foundation of China [grant numbers 51571127, 51271095 and 51101090]. H. Wang is grateful for the supports provided by the Guangdong Provincial Natural Science Foundation of China [grant number 2015A030313543] and the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars (SRF for ROCS), State Education Ministry, China.

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12 G. N. YANG eT AL.

ORCID

G. N. Yang   http://orcid.org/0000-0003-4872-2443

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