Journal of Materials Science & Technology  2019 , 35 (9): 2079-2085 https://doi.org/10.1016/j.jmst.2019.04.014

Orginal Article

Serration and shear avalanches in a ZrCu based bulk metallic glass composite in different loading methods

Haichao Suna, Zhiliang Ninga, Jingli Renb, Weizhong Liangc, Yongjiang Huanga, Jianfei Suna, Xiang Xuea*, Gang Wangd*

a chool of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China
b School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
c School of Materials Science and Engineering, Heilongjiang University of Science and Technology, Harbin 150027, China
d Laboratory for Microstructures, Institute of Materials, Shanghai University, Shanghai 200444, China

Corresponding authors:   ∗Corresponding authors.E-mail addresses: xxue@hit.edu.cn (X. Xue), g.wang@shu.edu.cn (G. Wang).∗Corresponding authors.E-mail addresses: xxue@hit.edu.cn (X. Xue), g.wang@shu.edu.cn (G. Wang).

Received: 2018-11-14

Revised:  2018-12-24

Accepted:  2019-01-26

Online:  2019-09-20

Copyright:  2019 Editorial board of Journal of Materials Science & Technology Copyright reserved, Editorial board of Journal of Materials Science & Technology

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Abstract

In the current research, serrated flow is investigated under tensile and compressive loading in a ZrCu-based bulk metallic glass composite (BMGC) that is well known for its plastic deformability, which is higher than that of metallic glasses. Statistical analysis on serrations shows a complex, scale free process, in which shear bands are highly correlated. The distribution of the elastic-energy density stored in each serration event follows a power-law relationship, showing a randomly generated serrated event under both tension and compression tests. The plastic deformation in the temporal space is explored by a time-series analysis, which is consistent with the trajectory convergent evolution in critical dynamic behavior even in the low strain rate regime in both tests. The results demonstrate that the secondary phase in the BMGC can stabilize the shear band extension and facilitate the critical behavior in the low strain rate regime. This study provides a strong evidence of serrated flow phenomenon in BMGC under tension test, and offers a deep understanding of the correlation between serrations and shear banding in temporal space.

Keywords: Metallic glass ; Bulk metallic glass composites ; Serrated flow ; Shear avalanches ; Statistical analysis ; Critical behavior

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Haichao Sun, Zhiliang Ning, Jingli Ren, Weizhong Liang, Yongjiang Huang, Jianfei Sun, Xiang Xue, Gang Wang. Serration and shear avalanches in a ZrCu based bulk metallic glass composite in different loading methods[J]. Journal of Materials Science & Technology, 2019, 35(9): 2079-2085 https://doi.org/10.1016/j.jmst.2019.04.014

1. Introduction

Plastic deformation of crystals is a complex inhomogeneous process owing to the nucleation and motion of crystallographic defects [1,2]. Bulk metallic glasses (BMGs), without obvious crystalline defects, such as grain boundaries and dislocations, exhibit a quite different deformation mechanism from their crystalline counterparts [3]. Instead of dislocation mediated plasticity, the plasticity of BMGs always confines in thin shear bands with an inhomogeneous manner [4,5]. Because of this confined plastic processing region, a serrated-flow behavior is only manifested in the compressively plastic deformation of BMGs [6,7]. In-situ formed bulk metallic glassy composites show a high plastic-deformation ability [[8], [9], [10], [11]], which provides a good model material to investigate the serrated flow of BMGCs, especially under tension test. Although tremendous theories have been proposed to elucidate the deformation mechanism of BMGs, such as the free volume [12], the shear transformation zone [13], the potential energy landscape [14] theories, the inhomogeneous flow behavior of BMGs could not be well elucidated yet. Especially, these theories could hardly be used in bulk metallic glass composites (BMGCs) owing to the precipitation of crystalline phases. Recently, based on a correlation between the serration events and shear avalanches, the plastic deformation of BMGs in compression has been well described and connected with the concept of deformation dynamics, such as chaotic behavior or critical behavior [6,[15], [16], [17]], which is a promising method to explore and describe the deformation mechanism of BMGCs. Since that, a statistical analysis was used to investigate the serrated-flow behavior of BMGCs containing nanocrystalline phases [18,19] under compression. Nevertheless, so far, the deformation behavior and serrated flow of BMGCs under tension is still not clear because the tension plasticity is difficult to be approached, which leads the links between structural evolution and dynamic behavior of serrated flow of BMGCs be still absent.

In the present study, a ZrCu based BMGC is chosen as the model material for the tension and compression tests because of its high strength and superior ductility, which is a potentially structural material [20]. The serrated-flow behavior in the BMGC under tension test was characterized, and comparatively investigated with that under compression test. The purpose of the present study is not only to understand how the BMGCs deform under tension but also to better understand the dynamics evolution of shear avalanches in spatial and temporal interaction.

2. Experimental methods

Master alloy ingots with a nominal composition Zr49Cu45Al6 (at.%) were prepared by arc melting the mixture of the constitute elements with purity of 99.99% in a Ti-getted argon atmosphere. Each ingot was re-melted four times with the current of 250 A to guarantee the chemical homogeneity. Then, the ingots were suction cast into a copper mold to form a rod-like sample with a diameter of 4 mm and length of 45 mm. The structures of the composite before and after deformation were checked by an X-ray diffractometer with Cu-Kα target (D/max-2500 V + diffractometer). The microstructure of deformed sample was examined by field emission transmission electron microscopy (FETEM, Talos f200x). The fracture morphology and lateral surface of deformed samples were observed in an HITACHI SU-1500 scanning electron microscope (SEM).

The specimens for tensile and compressive tests were taken from the middle and lower part of the as-cast rods. Regarding to the geometric size of the clamped parts in tensile test machine, the deformation part with 2.5 mm × 1 mm × 1 mm (length × width × thickness) of tensile sample was prepared by electric discharge machining and electro-chemical polishing. The compressive specimens with a length/diameter ratio of 2 were carefully ground. Before testing, the microstructures of each specimens were checked by an optical microscope to ensure that the secondary phase with the size of 10-100 μm homogeneously distributed in the specimen. Both tests were conducted in an Instron CMT 5205 machine at room temperature with an initial strain rate of 5 × 10-4 s-1.

3. Results

The tensile and compressive true stress‒strain curves of the Zr49Cu45Al6 BMGC exhibit an elasto-plastic deformation behavior as shown in Fig. 1. Their mechanical parameters are listed in Table 1. The stress fluctuation, i.e., the serration events, in the plastic deformation is hardly seen in BMGs, especially under tension test owing to their ignorable ductility. In the present study, due to the precipitation of crystalline phase, the ZrCu based BMGC exhibits an obviously tensile ductility, in which the serrated flow can be evidently observed. The enlarged plastic strain regimes of the stress‒strain curves are shown in the insets of Fig. 1. These serration events under the tension and compression tests show an irregularity, i.e., the distribution of the amplitude of serration events does not show any periodic change. Comparing with the compression test, the serration events in tension test show smaller amplitude in average.

Fig. 1.   True stress‒strain curves of Zr49Cu45Al6 BMGC (a) in tension and (b) in compression. Both of them exhibit the serration events in plastic deformation region.

Table 1   Mechanical properties of Zr49Cu45Al6 BMGC.

Elastic modulus (GPa)Yielding strength (MPa)Maximum strength (MPa)Maximum strain
Tension85.9970.01696.00.0561
Compression90.2980.61875.60.0658

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Fig. 2(a) shows the XRD patterns of the samples before and after deformation. The pattern of as-cast sample indicates several crystalline peaks and a broad diffuse peak. The crystalline peak can be easily identified to be the B2 CuZr phase, and a B19’ martensitic phase with two crystalline peaks at 44.5° and 65°, respectively. The bright-field TEM image of the as-cast sample shown in Fig. 2(b) indicates that the crystalline phase has a dendrite structure in [011] zone axis, which corresponds to the B2 phase. Fig. 2(c) shows a nanocrystalline phase with several twinning stripes, which verifies that the residual stress can induce a martensitic transformation of the B2 phases during the solidification [21]. After the deformation, the distinct crystalline peaks of the B19’ martensitic phase emerge prominently (Fig. 1(a)). Fig. 2(d) exhibits the microstructure of the deformed sample, which shows the lath-like structure in a crystalline phase. Based on the selected area electron diffraction (SAED) pattern shown in the inset of Fig. 2(d), it can be inferred that twinning and martensitic transformation occur during the deformation.

Fig. 2.   XRD patterns and microstructures of the Zr49Cu45Al6 BMGC. (a) Presents the XRD patterns before and after the deformation, (b) and (c) show the crystalline phases corresponding to the XRD pattern in the as cast sample, (d) shows the deformed sample with twinning structures inside the crystalline phase.

After the deformation, the lateral surfaces and fracture morphology are shown in Fig. 3. The fracture angles, i.e., the angle between the fracture surface and the loading direction, of tensile and compressive samples are 45° and 41°, respectively. Numerous visible shear bands, indicated by the arrows, emerge from the tensile (Fig. 3(a)) and compressive (Fig. 3(b)) specimens’ surface after the deformation. The observed shear bands can be classified into three types according to their directions. Firstly, many fine and wavy shear bands surround the crystalline phases, which are pointed out by the blue arrows in Fig. 3(a). Secondly, many shear bands pointed by the white arrows are parallel to the fracture surface, which cannot shear across the whole cross-section because the effect of the distortion and blocking of the crystalline phases (marked by circles in Fig. 3(a)). For the compression, shear banding behaves along two major directions, as shown in Fig. 3(b). One direction is oriented along the shear-fracture angle of 41°, pointed by the white arrows, which conforms the direction of the maximum shear stress [22]. Another one is perpendicular to the loading direction, which is different from the tension case, and pointed by the green arrows, namely is the third type of shear bands. Moreover, a few fine wavy shear bands are also observed around the crystalline phases, marked by the blue arrows. Fig. 3(c) presents fractographies of the tensile fractured BMGC, which shows some vein-like patterns that is similar to the patterns in MGs. This implies that shear softening and the instability of highly-localized shear banding are still the main reasons dominating the failure process of the BMGC in tension [23]. Furthermore, there are many round cores, owing to the adiabatic heating [24], distributing on the fracture surface. However, on the compressive fracture surface, a mixed morphology consisting of the vein-like patterns and slurry-like patterns indicates the significant difference in fracture features induced by the loading mode. Therefore, it is clear that the formation and propagation of shear bands are affected by the loading mode.

Fig. 3.   Lateral surfaces and fracture morphologies (a), (c) in tension and (b), (d) in compression.

To further characterize the plastic deformation behaviors at different loading modes, the stress‒time curves in the plastic regimes are magnified, which show the serrated-flow behavior (the inset Fig. 1) [6]. The stress‒time curve and corresponding |/dt| plot in the plastic regime are shown in Fig. 4, which indicates that the time intervals between any two neighboring serrations are different in both loading modes. The differential stress‒time curves in the plastic regime suggest that the serration events lack any typical time scale [6]. The time series characteristic parameters are listed in Table 2.

Fig. 4.   Enlarged stress‒time curves and corresponding plots of |dσ/dt| for a part of the serrations (a) in tension and (b) in compression.

Table 2   Characteristic parameters of serration events.

ParametersTensionCompression
Serrations∼60∼150
tl, $\bar{t}_{l}$0.11‒3.51, 0.850.56‒9.94, 2.48
tr, $\bar{t}_{r}$0.06‒0.86, 0.210.06‒1.70, 0.29
tl/tr,$\bar{{t}_{l}/{t}_{r}}$0.71‒37.34,5.71.12‒106.86,16.0
Elastic-energy density (J/m3)7.93‒3604.7557.36‒16851.84
Average elastic-energy density (J/m3)514.2219.6
Stress drop value (MPa)0.74‒28.651.80‒26.23
Average stress drop value (MPa)3.15.74
κ1.18/2.031.18/2.03
Δδc811/19841230/10628
R297.7%/94.3%97.8%/97.8%
Time delay, τ7263
Embedding dimension, m56
Largest Lyapunov exponent, λ-1.42 × 10-4-1.51 × 10-4
Fractal dimension1.0211.053

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In the plastic deformation, each serration event includes two stages. The first one is the stress increase stage, in which the elastic energy accumulates in the deformed BMGC (the inset of Fig. 1). The second one is the stress drop stage, in which the elastic energy is released in a very short time (Fig. 4) but with a large strain (the inset of Fig. 1). The elastic energy accumulated in each serration event is believed to be consumed by shear-banding process. Therefore, the elastic energy accumulated in one serration event can be used to reflect the shear-avalanche size of shear bands. The distribution of shear-avalanche sizes can reflect the shear avalanches in metallic materials [2]. The elastic-energy density covered by one serration event, Δδ, can be express as [6,16,18],

Δδ=Δσ'Δε'/2 (1)

where Δσ’ and Δε’ are the elastic stress and strain in one serration event. Fig. 5 shows the distribution of the elastic-energy density as a function of the true strain. Their ranges and average value are also listed in Table 2. From Fig. 5, it can be seen that the distribution of the elastic-energy density is stochastic. Thus, to further explore the elastic-energy density distribution, a cumulative distribution of the elastic-energy density, namely the percentage of the number of the elastic-energy density larger than a given value is plotted. It can be seen (Fig. 6) that the low elastic-energy densities are more probable and follow a power-law relationship. The high elastic-energy densities decrease exponentially in probability. The probability distributions of the BMGC under tension and compression have an universal scaling function, which can be well approximated by a power-law distribution function accompanied with an exponential decay function [25]:

C(Δδ)∼Δδ-(κ-1)F(Δδ/Δδc) (2)

Fig. 5.   Elastic energy densities in the serration events of Zr49Cu45Al6 BMGC as a function of plastic strain.

Fig. 6.   Cumulative probability distributions for the elastic energy densities of the composites.

where Fδδc) (=exp[-(Δδδc)2]) is a quickly decaying scaling function [26], κ is a scaling exponent, and Δδc is the size of the large critical avalanche that acts as a cut-off in Fδδc). To obtain the κ and Δδc values, Eq. (2) is used to fit the experimental plot in Fig. 6. The parameters of κ and Δδc reflect the profile of the shear-avalanche size distribution, which can characterize the deformation mechanism and the characteristic shear avalanche in metallic glasses. The Δδc value is a characteristic parameter that can be linked to a microstructural characteristic scale, such as the dislocation propagation characteristic length confined by the grain boundary in crystalline solids [27]. For the BMGC, because the strain burst during plastic deformation of the BMGC is associated with the geometric distribution of secondary phase and the shear banding behavior of glassy phase matrix [18,19], the Δδc value should correspond to the characteristic shear size of BMGCs. Larger ductility indicates that the interaction between the secondary phase and shear banding behavior will be enhanced to influence the shear deformation, which results in an increase in the characteristic shear size. As shown in Fig. 6, the elastic-energy densities follow a power-low distribution with over 97% R2 in both loading modes, which is acceptable fitting results. However, the distribution of larger elastic-energy densities dissociates from the fitting curves obviously. According to the serrated-flow behavior in BMGs [[5], [6], [7],18], the distribution of the elastic-energy densities can be well fitted by Eq. (2). But, secondary phase in BMG could interrupt the glassy matrix and influence the elastic-strain field, which makes the scaling exponent change [18]. Due to the martensitic transformation of B2 phase during the plastic deformation, the high elastic-energy densities distributions deviate from the linear relationship in Fig. 6, which can be fitted by a new scaling exponent. So, the dissociated elastic-energy density, i.e., the high elastic-energy density, is fitted again by using the Eq. (2). The parameters of each curves are listed in Table 2.

4. Discussion

4.1. Different stress states leading to different serrated flow behaviors

The serrated-flow phenomenon of BMGs occurs in the compressive deformation has been reported for many years [5,6,18,28]. However, the tensile deformation of BMGs does not show any plasticity. Fig. 7 is a sketch to distinguish and to simplify the different stress state in the BMG and the ZrCu based BMGC in different loading modes. For the BMG, the load could be resolved into two tensors, i.e., the normal stress, σθ, that is perpendicular to the shear plane and the shear stress, τθ, that is parallel to the shear plane. Based on the Mohr-Coulomb criterion, during the tensile deformation (Fig. 7(a)), the normal stress dominates the yielding behavior, which causes that the maximum shear-stress plane [29], and the fracture angle is larger than 45° [23]. In this case, once the shear band or cavitation is formed, adiabatic heating and the shear dilatation generate a viscous layer on the shear plane. Then, the dominantly normal stress can separate the sample along the main shear plane, and the effect of the shear stress is insignificant. The stick-slip dynamics of interacting between shear bands is lack of qualification, and that is the main reason why BMGs can hardly show the serrated flow in tension. For the BMG in compressive deformation (Fig. 7(b)), the fracture angle is usually smaller than 45° [23]. Based on the Mohr-Coulomb criterion, the shear stress dominates the yielding behavior. In the plastic deformation, shear banding is seriously influenced by the shear stress. Furthermore, the normal stress provides a frictional resistance to the stick slip. Therefore, the shear avalanche during the shear-banding process exhibits a discontinuous flow behavior, i.e., the serrated flow. The formation of the serrated flow behavior in the compression is much easier than that in the tension deformation.

Fig. 7.   Sketch for the concepts of the serration event formation (a) in BMG and (b) in BMGC.

Once the crystalline phases precipitate in the glass matrix, the crystalline phase in BMGCs can break the continuity of the glass matrix. These crystalline phases can enhance the formation of multiple shear bands, as shown in Fig. 3(a) and (b), and then prohibit the propagation of shear bands [30]. The interaction between shear bandings and crystalline phase can also disturb the stress field around their interfaces [22]. Owing to the discontinuously serrated flow evidently occurring under compression and tension deformation in the inset of Fig. 1, the illustrations of Fig. 7(c) and (d) simplify the stress state of the BMGC to analyze the serrated-flow behaviors. For the tensile load, as shown in Fig. 7(c), the main shear plane is disturbed by the crystalline phase. The dominant normal stress can also separate the matrix. The shear dilatation can be hindered by the discontinuously viscous layer. Besides, the difference in Young’s modulus and bonding between the glassy matrix and the crystalline phase also provide the extra stresses [22,31], which makes the stick slips possible. For the compression (Fig. 7(d)), the participation of crystalline phase into the plastic deformation provides a more complex frictional resistance for the stick slip as compared with that in BMGs. On the other hand, the shear-bands interaction also contributes the serrated-flow behavior in the plastic deformation of the BMGC. Fig. 3(a) and (b) clearly indicates the interaction between the neighboring shear bands both in the tension and compression deformations, which is the same as that in the ductile BMG in compression deformation [5].

4.2. Serrations in different loading methods

According to the serrated-flow behavior shown in Fig. 4 and Table 2, the elastic-energy accumulation time, tl, is much longer than the relaxation time, tr (both in tension and in compression deformations). The average release time of elastic-energy in the tension deformation is 0.21 s, which is close to the value of 0.29 s in the compression deformation. However, the average accumulation time of elastic-energy in the compression deformation (2.48 s) is much larger than that in the tension deformation (0.85 s). It implies that activating the compressive stick slips needs more energy than that in tension deformation, and the elastic-energy relaxation times in both compression and tension tests are roughly equal. The ratio between the elastic-energy accumulation time and the relaxation time distributes in a wide range in both the tension case and the compression case, which suggests that the shear avalanches are a random occurrence in temporal scale.

According to Fig. 5, the elastic-energy densities in the serration events in the tension deformation are smaller than those in the compression deformation. However, the average elastic-energy density in the tension deformation is larger than that in the compression deformation. Coincidentally, the sums of the elastic-energy density in the serrated flows for both the compression and tension deformations are roughly equal, which may imply the ultimate storage ability of elastic-energy in this BMGC is a constant. Furthermore, the maximum stress drop in the tension case is roughly equal to that in the compression case. It may suggest that there is a threshold value of the stress amplitude during the serrated flow.

Based on the distribution of elastic-energy density, shown in Fig. 6, a critical behavior of the shear avalanche during the plastic deformation in the BMGC can be speculated. The scaling exponents, κ, are almost same in the tension and in compression when the elastic-energy density is small, which suggests that the loading mode has an insignificant effect on the scaling exponent of plastic deformation process. In the large elastic-energy density part, the scaling exponent (κ ≈ 2.0) is larger than the value in the small elastic-energy density part (κ ≈ 1.8), which indicates a different deformation mechanism (might be phases transformation) for the crystalline phase with large elastic-energy densities. The κ value in whole elastic-energy density distribution is close to that of other Zr based BMGs ranged from 1.34 to 1.60 [5,6,15,18,32,33], which implies that the plastic flow of the BMGC is similar, but not identical, to the cases in BMGs. The size of the large critical avalanche, Δδc, namely the cut-off in F(Δδδc) in compression deformation is larger than that in tension deformation. The cut-off values of fitting curves for all elastic-energy densities are on the same order of the magnitude in both loading methods, which implies a comparable critical avalanche size in the tension and the compression deformations. For the crystalline phases with the large elastic-energy densities, the critical avalanche size in the compression deformation is much larger than that in the tension deformation. For the crystalline phases with the high elastic-energy densities, the critical avalanche size in the compression deformation is much larger than that in the tension deformation.

4.3. Critical behavior

To further characterize the critical behavior of the BMGC, the dynamics of shear avalanche during the plastic deformation is investigated. The elastic-energy density signals in the tensile and compressive deformations in the plastic regime are taken as time series. A phase space is reconstructed by a time delay [16,34]. Before reconstructing the phase space from the signal, the time delay, τ, and an embedding dimension, m, are calculated by using a mutual information method [35] and a Cao-method [36]. Based on the elastic-energy density signal, {Δδ(k), (k = 1,2,…,N)}, where N is the number of serrations, a m-dimensional vector is defined by Y(ti) = {Δδ(ti), Δδ(ti+τ),…, Δδ(ti+(m-1)τ), ti = 1, …, [N-(m-1)τ]}, where ti is the i-th evolution time. The set of {Y(ti)= ti = 1, …, [N-(m-1)τ]} constitutes the reconstructed attractor. The largest Lyapunov exponent is calculated by a Wolf’s method [37]. Starting from the initial point, Y(t0), and its nearest neighbor point, Y0(t0), with a distance of L0. The evolution of these two points until a time of t1 is tracked namely by a L0 = | Y(t1) - Y0 (t1)|>ω, where ω is a given constant that is slightly larger than the minimum distance of any neighboring points. Then, another point, Y(t1), and its nearest neighboring point, Y1(t1), can be found. The angular separation between the evolved and the replacement elements is as small as possible. The distance between two points is L1. Tracking the evolution to get L'1 and recycling above process until the m-dimensional vector, Y(ti), reaches the end of the time series, the number of the iterations, M, during tacking the evolution can be obtained. The largest Lyapunov exponent is

The time delay, embedding dimension and the largest Lyapunov exponents for the tension and compression deformations are listed in Table 2. The negative Lyapunov exponent means a stable plastic dynamic, which indicates the trajectories originated from different initial conditions will be convergent under both the tension and the compression tests.

5. Conclusion

In this study, the deformation behavior of the BMGC has been investigated based on the mechanical tests, microstructure observations. The tension plastic deformation was achieved in the ZrCu-based BMGC, which exhibits the serrated-flow behavior that is similar to the plastic deformation in BMG during compression deforming. The serrated flow in the BMGC can be attributed to the interaction between the crystalline phase and the multiple shear bands, which means that both shear banding and the deformation in the secondary phase influence the serrated flow. The statistical analysis of the serration events finds that the elastic-energy density stored in each serration event follows a power-law distribution, which suggests that the dynamic behavior during the plastic deformation of the BMGC is in the critical state. The time-series analysis further confirms that the trajectory convergent evolution of the dynamics of the plastic deformation is in the critical dynamic behavior even in the low strain rate regime. The findings offer a strong evidence for understanding the correlation between serrations and multiple shear bands in the temporal space, which may help to better understand the deformation mechanism of BMGCs.

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Nos. 51671067, 51761135125 and 11771407), the Plan for Scientific Innovation Talent of Henan Province (No. 164200510011), and the Innovative Research Team of Science and Technology in Henan Province (No. 17IRTSTHN007).

The authors have declared that no competing interests exist.


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