- Email: [email protected]
Stochastic deformation and shear transformation zones of the glassy matrix in CuZr-based metallic-glass composites
International Journal of Plasticity xxx (xxxx) xxx
Contents lists available at ScienceDirect
International Journal of Plasticity journal homepage: http://www.elsevier.com/locate/ijplas
Stochastic deformation and shear transformation zones of the glassy matrix in CuZr-based metallic-glass composites S.S. Jiang a, b, c, K.F. Gan d, Y.J. Huang a, b, c, *, P. Xue a, b, c, Z.L. Ning b, J.F. Sun a, b, A.H. W. Ngan d a
State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China c Key Laboratory of Micro-systems and Micro-structures Manufacturing (Harbin Institute of Technology), Ministry of Education, Harbin, China d Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Metallic glass Cooling rate Incipient plasticity Stochastic deformation Free volume Shear transformation zone
The incipient plasticity of an amorphous solid represents the onset of shear deformation, which is a stochastic progress closely related to microstructure evolution. It is well known that the cooling rate plays a crucial role in the microstructure evolution of a glass. Nevertheless, how the cooling rate affects the incipient plasticity is still unclear. In this work, the incipient plastic deformation of the amorphous phase in Cu47.5Zr48Al4Nb0.5 bulk metallic glass composites (BMGCs) cast with different cooling rates is systematically studied. The incipient plasticity of the glassy matrix of the BMGCs is found to occur via a first displacement burst, the occurrence of which is more stochastic as the cooling rate decreases. According to the auto-correlation functions and cooperative shear model, the stochastic behavior is attributed to the effects of the cooling rate on the initial free volume and subsequent activated shear transformation zones (STZs). A higher content of free volume is present in the glassy matrix of the studied samples cooled at a faster rate, which fa cilitates the operation of STZs. Moreover, the larger incipient burst size is correlated with the higher content of free volume and larger STZs in the glassy matrix. The larger STZs result in more preferable propagation of multiple shear bands, leading to less stochastic deformation and more obvious plastic deformation. This study provides further understanding on the incipient plasticity of glassy matrix in BMGCs.
1. Introduction Owing to the unique structure free of crystalline defects, bulk metallic glasses (BMGs) often offer high strength and elastic limit compared with traditional crystalline materials (Huang et al., 2009; Johnson, 1999; Pan et al., 2017; Qiao and Pelletier, 2014; Wang et al., 2004). However, the room-temperature brittleness and work softening largely restrict their wide applications in engineering (Greer et al., 2013; Huang et al., 2014a). BMGs usually experience shear localization within nano-scaled narrow shear bands, resulting in catastrophic fracture under tensile loading. To overcome this limitation, numerous strategies have been proposed (Dong et al., 2017; Huang et al., 2014b; Jiang et al., 2018; Narayan et al., 2018; Pauly et al., 2010; Qiao et al., 2016). Among them, developing BMG composites (BMGCs) comprising crystalline phases of different length scales distributed in the amorphous matrix has been proven to be
* Corresponding author. State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, China. E-mail address: [email protected] (Y.J. Huang). https://doi.org/10.1016/j.ijplas.2019.09.005 Received 4 January 2019; Received in revised form 15 June 2019; Accepted 4 September 2019 Available online 7 September 2019 0749-6419/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: S.S. Jiang, International Journal of Plasticity, https://doi.org/10.1016/j.ijplas.2019.09.005
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 1. (a) XRD patterns of Cu47.5Zr48Al4Nb0.5 (at. %) alloy samples with different diameters (The sample with 2 mm, 3 mm, 4 mm, or 5 mm in diameter is labeled as S2, S3, S4, and S5, respectively), and optical micrograph images of (b) S2, (c) S3, (d)S4 and (e) S5 samples.
effective in improving toughness and plasticity, because the ductile secondary phases can effectively distribute the plastic strain over a larger volume of materials (Bian et al., 2005; Chen et al., 2015; Lee et al., 2004; Liu et al., 2018; Narayan et al., 2012; Qiao et al., 2011; Sha et al., 2017; Wang et al., 2012). Nevertheless, such BMGCs exhibit a disappointing strain softening behavior in tension, resulting in unstable deformation. Recently, this shortcoming has been successfully circumvented by adopting the concept of transformation-induced plasticity (TRIP) in BMG composites (Wu et al., 2010b). Pronounced tensile properties have been achieved through introducing an in situ B2 phase into the glassy matrix (Liu et al., 2012; Song et al., 2012; Wang et al., 2018; Wu et al., 2014, 2017). B2 phase reinforced BMGCs consist of a crystalline phase and an amorphous phase. Considerable attention has been put in the crystalline B2 phase in relation to the deformation mechanism of the entire composite. While the work-hardening ability originates mainly from the deformation-induced martensitic transformation of cubic B2 CuZr into monoclinic B190 phase (Song et al., 2012; Wu et al., 2014, 2017) and the high elastic limit and ductility are attributable to the interaction of the B2 phase with the glassy matrix (Sun et al., 2016; Wu et al., 2011, 2014), numerous studies have shown that the high yield strength of BMGCs is mainly attributed to the amorphous phase (Jiang et al., 2018; Wu et al., 2013, 2017). However, the plastic deformation behavior of the amorphous phase in BMGCs has remained unclear, although this is essential for the further understanding of the intrinsic deformation mechanism of BMGCs. The plastic deformation of the amorphous phase is dominated by the evolution of shear bands (Perepezko et al., 2014), the nucleation of which is intricately related to the initial free volumes and subsequently activated shear transformation zones (STZs) (Greer et al., 2013; Huang et al., 2007; Wang et al., 2004). Although monolithic BMGs have been widely studied (Cheng and Ma, 2011), there is little scientific basis to assume that the structural features and deformation behavior of the glassy matrix in a BMGC are identical in every aspect to those of monolithic BMG alloys. In particular, as the atomic-scale structural features in terms of free volume and STZs in a glassy phase depend sensitively on the preparation method especially the solidification condition, it would be practically impossible to produce a monolithic BMG alloy that could duplicate exactly a composite’s glassy matrix. As such, testing the local properties using a local probe such as nanoindentation is the only reliable way to know the properties of the glassy matrix of a BMGC. Therefore, in the present study, the amorphous matrix of CuZrAlNb B2-reinforced BMGCs prepared by different cooling rates is characterized by nanoindentation. We focus on the onset of plasticity in the amorphous phase as this marks the nucleation of shear banding and the first yielding condition of the glassy matrix (Perepezko et al., 2014). By systematically analyzing the effects of cooling rate on the local mechanical behavior of the glassy matrix, the role of the initial free volumes and the subsequently activated STZs on the incipient plastic deformation behaviors at nano-scale of the glassy matrix in BMGCs will be elucidated. The results will help us further understand the plastic deformation mechanism of the amorphous phase, and the relationship between the fabrication, microstructure and mechanical properties of BMGCs. 2. Experimental details The ingots of Cu47.5Zr48Al4Nb0.5 (at. %) alloy samples were fabricated through arc melting mixtures of Cu, Zr, Nb, and Al metals (purity > 99.99 wt %) in a Ti-gettered Ar atmosphere. To avoid compositional inhomogeneity and segregation, the ingots were remelted at least five times with electromagnetic stirring. Cylindrical alloy samples with diameters of 2 mm, 3 mm, 4 mm and 5 mm, hereafter labeled as S2, S3, S4 and S5, respectively, were fabricated using drop casting the alloy melt into a copper mold under the argon atmosphere. Due to the difference in their dimensions, these samples correspond to different cooling rates from the melt, i.e. the smaller samples were cooled faster than the larger ones. The microstructural nature and corresponding morphology of the as-cast alloy samples were examined using X-ray diffraction (XRD) with Cu Kα radiation, optical microscope (OM) using a Leica DM4000M in strument, and a Talos F200X transmission electron microscope (TEM). The average chemical compositions of glassy matrix in different samples were then characterized by energy dispersive X-ray spectroscopy (EDS) in a Quanta 200FEG scanning electron microscope 2
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Table 1 The average element content of glassy matrix in S2, S3, S4 and S5 samples by EDS analysis. Matrix
Zr/at. %
Cu/at. %
Al/at. %
Nb/at. %
S2 S3 S4 S5
48.08 � 0.26 49.78 � 0.61 49.70 � 0.63 48.29 � 0.23
44.60 � 0.38 42.23 � 0.46 42.30 � 0.36 44.98 � 0.60
3.59 � 0.21 4.03 � 0.28 3.50 � 0.44 3.09 � 0.34
3.74 � 0.18 3.96 � 0.45 3.77 � 0.22 3.65 � 0.49
Fig. 2. (a) Typical load-displacement curves obtained from the nanoindentation tests of the glassy matrix of the CuZrAlNb alloy samples with different diameters, and (b) the corresponding H and Er values.
(SEM). The surface roughness of studied samples was examined by a Dimension Fastscan atomic force microscope (AFM). In order to reveal the atomic level structure of the glassy matrix of the composite samples, high-resolution TEM (HRTEM) images were obtained. Then, the auto-correlation functions (ACF) of HRTEM images (Fan and Cowley, 1985; Huang et al., 2014c; Liang and Chen, 1994; Wu et al., 2010a) were obtained to characterize the local ordering of the glassy matrix of the BMGC samples. Nanoindentation tests were carried out on the glassy matrix of the as-cast samples at room temperature using an Agilent G200 Nanoindenter equipped with a Berkovich indenter, which provides a load resolution of 3 nN within the loading range of 30 mN and a displacement resolution of 0.01 nm in the depth range of 2 μm. The diamond indenter radius calibration is performed on the fused quartz (R is ~20 nm). A constant loading rate of 0.1 mN/s was adopted and the maximum load is 10 mN. To verify the data reliability, at least twenty-five indentation tests were repeated on different locations randomly selected on the matrix for each group of samples under identical conditions. The standard deviation has been found to be less than 5%. Also, the morphologies of indentation im pressions were examined by a Helios Nanolab 600i SEM. 3. Results and discussion 3.1. Microstructure and mechanical properties of glassy matrix from Cu47.5Zr48Al4Nb
0.5
BMGCs
Fig. 1a displays the typical XRD patterns of Cu47.5Zr48Al4Nb0.5 alloy samples with various diameters. The XRD pattern for the S2 sample shows a sharp crystalline peak indexed as B2–CuZr phase (bcc) appearing on a diffraction hump, demonstrating a mixture structure of secondary phase and glassy matrix. When the sample diameter increases to 5 mm, the corresponding XRD pattern shows a series of sharp peaks superimposed on broad ones. Meanwhile, the increase in the sample diameter causes a significant increase in the area of the sharp Bragg peak, suggesting an increase in the volume fraction of the crystalline phases. Such microstructural change with specimen diameter was further observed by OM as shown in Fig. 1b–e. The S2 sample exhibits a composite structure with few spherical B2 crystals embedded in the glassy matrix (Fig. 1b), agreeing well with the above XRD results. For the S3 sample, the B2 phases with a size range of 30–150 μm are homogeneously distributed in glassy matrix (Fig. 1c). For the S4 sample cooled at a lower rate, B2 phases pool into a number of large clusters and distribute inhomogeneously across the glassy matrix (Fig. 1d). Upon further decreasing the cooling rate (the S5 sample), the B2 phase occupies almost the entire cross-section with only a small amount of amorphous matrix near the surface of the rod sample (Fig. 1e). It can be seen that the volume fraction of the amorphous phase increases with cooling rates. The EDS analysis demonstrates that no obvious difference in the chemical composition of the glassy matrix can be found for the BMGC samples with different amorphous phase fraction, as shown in Table 1. The composition of the glassy matrix for all the four ingots S2 to S5 is very close to the overall composition of the composite, and also to the stoichiometric ratio of Cu:Zr ¼ 1:1 of the B2 intermetallic phase. This is exactly the condition needed for the simultaneous formation of the glassy matrix and the B2 phase during a rapid so lidification process, during which significant elemental segregation cannot occur. Fig. 2a exhibits representative load versus displacement (P-h) curves acquired from the nanoindentation measurements on the glassy matrix of the studied composite samples with various diameters. The indentation depth at maximum load gradually decreases 3
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Table 2 The maximum depth, first burst size, activation volume and corresponding STZ volume of glassy matrix in the studied samples. Matrix
Maximum depth dmax/nm
First burst size Δh/nm
Activation volume V*/nm3
STZ volume Ω/nm3
S2 S3 S4 S5
338.55 � 13.35 301.08 � 8.55 239.26 � 11.48 218.15 � 11.30
0.91 � 0.06153 0.79 � 0.06903 0.74 � 0.04011 0.69 � 0.05143
(1.70 � 0.103) � 10 3 (1.49 � 0.112) � 10 3 (1.12 � 0.094) � 10 3 (9.51 � 1.08) � 10 4
(3.75 � 0.159) � 10 (3.29 � 0.147) � 10 (2.47 � 0.216) � 10 (2.10 � 0.105) � 10
2 2 2 2
Fig. 3. (a) The typical load-displacement curve of the glassy matrix from a given sample showing the raw and the fitted data using Eq. (1). The inset shows the bursts obtained from the difference between the smoothed displacement data and the fitted data, (b) the plots of survival probability of first burst versus maximum shear stress gathered from 25 independent nanoindentation tests of the glassy matrix of alloy samples with different diameters, (c) the plots of ln(ln(F 1)) as a function of maximum shear stress τmax and corresponding fitted lines in order to characterize the acti vation volume and subsequent STZ size, and (d) the STZ volume of glassy matrix as a function of first burst size.
with the sample diameter and the average maximum indentation depths of the amorphous phase are listed in Table 2. The hardness and elastic modulus of metallic materials are closely related to the contact stiffness S. In order to eliminate the influence of external factors on S as far as possible in nanoindentation tests, an improved method proposed by Feng and Ngan has been adopted (Feng and Ngan, 2002). In the Feng-Ngan method, the corrected contact stiffness Sc is obtained from
1 Sc
¼
1 Su
þ
h_h , jP_u j
here Su is the apparent contact
stiffness at the onset of unloading, i.e.dPu =dh, h_h is the displacement rate just before unloading, and P_ u is the unloading rate. Therefore, based on the program of Oliver-Pharr method (Oliver and Pharr, 1992) in the nanoindentation instrument and the corrected contact stiffness from Feng-Ngan method, the average hardness and elastic modulus are calculated to be 4.65 � 0.22 GPa and 75.48 � 2.12 GPa, 5.62 � 0.78 GPa and 82.91 � 3.84 GPa, 6.20 � 0.93 GPa and 89.48 � 4.72 GPa, and 6.52 � 0.94 GPa and 96.99 � 5.80 GPa for the glassy matrix of S2, S3, S4, and S5, respectively. The corresponding results are plotted in Fig. 2b. Clearly, as the sample diameter increases from 2 mm to 5 mm, both the elastic modulus and hardness of the glassy matrix increase. 3.2. Stochastic deformation of glassy matrix in nanoindentation tests It has been well documented that, in nanoindentation tests, the first burst event can be closely related with the incipient plasticity of the tested materials (Chiu and Ngan, 2002; Gerberich et al., 1996; Schuh and Lund, 2004). Here, to study the incipient plasticity of the 4
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 4. The two-dimensional (a) and three-dimensional (b) images of the representative sample surface scanned by AFM.
glassy matrix, a series of nanoindentation tests were conducted. The P-h curves were found to be jerky during the deformation. To make the discrete bursts more visible, a mean-field curve was first obtained from the experimental P-h curve by fitting the latter by the following equation (Li et al., 2005), h ¼ α1 P8 þ α2 P7 þ α3 P6 þ α4 P5 þ α5 P4 þ α6 P3 þ α7 P2 þ α8 P þ β;
(1)
where α1, α2, α3, α4, α5, α6, α7, α8, and β are fitting constants. Furthermore, the raw data were also smoothened through a least squares method developed by Savitzky and Golay to minimize the noise from indentation instrument (Savitzky and Golay, 1964). As an example, Fig. 3a shows a typical P-h curve for the loading regime of nanoindentation tests. To characterize the first displacement burst, the operation of subtracting the fitted data from the smoothened data was performed. The inset of Fig. 3a shows the net difference between the smoothened data and the fitted mean-field data of a representative P-h curve obtained from the glassy matrix of the studied composite sample. The first displacement burst identified from the starting point (SP) and ending point (EP) is highlighted by the red arrow in the inset of Fig. 3a. Besides, the average sizes of the first displacement bursts of the glassy matrix in the current samples were measured from the nanoindentation displacement data, and these are shown in Table 2. As shown from the example in Fig. 3a, there are successive displacement bursts, corresponding to sudden softening (Ng et al., 2009), and decorating all the P-h curves of the glassy matrix of the studied composite samples. In the current glassy matrix, the maximum shear stress at which the first burst occurs indicates the critical shear strength of incipient plastic deformation. In addition, a Berkovich indenter tip must have a certain degree of roundness under small displacements (Chen et al., 2003; Zhang et al., 2014). Therefore, based on contact mechanics, the maximum shear stress τmax of the elastic field underneath a spherical tip, at the load P1st at which the first burst occurs, is given by (Johnson, 1985) �
τmax ¼ 0:31 6E2r P1st
�
π 3 R2
��1=3
(2)
where Er is the reduced elastic modulus and R (~ 20 nm) is curvature radius of indenter tip. To make sure the validity of the estimated shear stress, the surface roughness of studied samples should be smaller than the radius of indenter tip. The representative AFM image (Fig. 4a and 4b) shows that the average roughness Ra of the sample surface is only 0.107 nm, which is much smaller than tip radius. In the ensemble of repeated runs of the indentation experiments under the identical external conditions, the τmax at which the first burst occurred in each run of the experiments was recorded, and then all the τmax in the ensemble were ranked in ascending order. Under a given stress level, the stressed region in the glassy matrix of a typical replica in the ensemble may or may not emit the first burst, and the probability at which the first burst is emitted is described by an ensemble survival probability F which is just the fraction of the experiments in the ensemble without emitting the first burst (Ng et al., 2009; Ngan and Ng, 2010). For the observed first-burst stress of rank i in ascending order in the ensemble, F is then calculated using the following equation (Ng et al., 2009; Ngan and Ng, 2010), F¼1
(3)
i=ðN þ 1Þ;
where N is the number of experiments for the ensemble. Fig. 3b shows scattered plots of the survival probability F versus τmax at first burst for the glassy matrix of the S2, S3, S4 and S5 samples. As the shear stress increases, the survival probability drops from 1 to 0. At the transition region, the survival probability of the first burst of the glassy matrix exhibits a nearly linear trend and the maximum shear stress range for the nearly line regime is larger in the larger sample which was fabricated with a lower cooling rate. This indicates that the glassy matrix of the composite sample that is cooled at a slower rate exhibits more pronounced stochastic nature in terms of the incipient plastic deformation. To understand the deformation mechanism, the activated STZs during nanoindentation are examined. The first burst event associated with incipient plasticity is a stress-assisted thermal activation process. With ample local thermal energy, the first burst event may occur at any stress level, but the survival probability of the event will decrease exponentially with the shear stress. Based on the analysis, the survival probability for the first burst event can be described as a function of maximum shear 5
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 5. HRTEM images with inset showing the selected area electron diffraction pattern, and the corresponding ACF images of the glassy matrix of the CuZrAlNb composite sample with (a) (b) 2 mm, (c) (d) 3 mm, (e) (f) 4 mm, and (g) (h) 5 mm in diameter.
stress as follows (Schuh and Lund, 2004): (4)
F ¼ exp½ aexpðbτÞ�;
where a ¼ kTAexp½ W=ðkTÞ�=ð_τV � Þ b ¼ V � =ðkTÞ, A is a pre-exponential factor, k is the Boltzmann constant, T is Kelvin temper ature, W is activation energy, τ_ is shear rate, and V* is the activation volume related to the initiation of STZs during the loading stage in nanoindentation. The overall trend of the data distribution for all curves is hardly affected by the data at the end of each curve in Fig. 3b, and the correlation coefficient R2 for each fitted curve is higher than 0.9. Therefore, the agreement between the experimental data and fitted results as the dash dot lines shown in Fig. 3b is reasonable. To characterize the activation volume V*, Eq. (4) can be expressed in a log-log form (Choi et al., 2012) � ln lnF 1 ¼ lna þ bτ: (5) It can be seen that the V* can be obtained from the slope of lnðlnF 1 Þ versus τ when τ is equal to τmax (see Fig. 3c). The V* of glassy matrix from S2 to S5 is shown in Table 2. It can be seen from Table 2 that the average maximum depths of nanoindentation tests in all samples exceed 200 nm and the average deformation volume estimated approximately during nanoindentation tests is higher than 8 � 106 nm3. The deformation can be considered to be homogeneous due to the sub-nanometric size of the fundamental deformation unit (Cheng and Cheng, 2004; Pan et al., 2008). Theoretically, the STZ volume Ω can be quantitatively estimated by cooperative shear model (Johnson and Samwer, 2005): 6
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 6. The operation of fast-Fourier-transformation (FFT) of the sub-images from Fig. 5(b): the FFT pattern of the sub-image with coordinate (1, 1) exhibits certain crystal-like diffraction spots and then is selected as the reference. The FFT patterns with coordinates (3, 2), (3, 4), (6, 5) and (7, 4) showing more crystal-like diffraction spots are considered as being ordered.
Ω¼
τS0 6CGS γ 2S ξ
� 1
τST τS0
* �12 V ;
(6)
where C � 1/4, ξ � 3, τS0 and τST are the threshold shear resistances at temperature 0 and T K, respectively (Johnson and Samwer, 2005), V* is the activation volume, GS is shear modulus at 0 K, γS is the critical shear strain, τS0 =GS ¼ 0:036, which can be expressed as (Johnson and Samwer, 2005): � �M τST T γS ¼ ¼ γ S0 γS1 ; (7) Tg GS where γ S0 ¼ 0:036 � 0:002, γ S1 ¼ 0:016 � 0:002 and M ¼ 0:62 � 0:2 (Ma et al., 2016), and Tg is glass transition temperature of studied CuZrAlNb alloy, which was measured as 683 K by differential scanning calorimetry at a heating rate of 20 K/min. For a certain GS � �M and Tg , the ratio of τS0 and τST can be calculated from the equation, i.e. τST =τS0 ¼ 1 0:444 TTg (Johnson and Samwer, 2005). Consequently, the average volume of STZs for glassy matrix in studied composite samples at loading segment is estimated as shown in Table 2. Theoretically, the onset of plastic deformation is also controlled by the initiation of STZs at a micro-scale (Argon, 1979). Therefore, the correlation between the first burst size and the STZ volume of glassy matrix in studied samples can be achieved by plotting the STZ volume as a function of first burst size in Fig. 3d. From Fig. 3d, it is apparent that the larger STZs activated in the glassy matrix facilitate the formation of larger incipient bursts.
7
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 7. The content of local ordering of the glassy matrix of composite sample with different diameters.
3.3. Nano-scale deformation mechanism for glassy matrix of the composite samples with different cooling rates The activation of STZs is closely related to the structural features of the amorphous phase, i.e. initial free volume. Next, in order to further explain the origin of the incipient plasticity for the amorphous phase, the free-volume contents of the glassy matrix in all the studied samples are analyzed using the concept of the local ordering. As is seen in Fig. 5a (S2), 5c (S3), 5e (S4) and 5g (S5), the HRTEM images exhibit a typical amorphous feature with long-range atomic disorder, which is also supported by the corresponding selected area electron diffraction (SAED) pattern. In order to quanti tatively measure the extent of local ordering of the amorphous phase, the ACF method, combining with HRTEM image analyses, was employed (Fan and Cowley, 1985; Huang et al., 2014c). Firstly, each HRTEM image of the glassy matrix is divided into 49 sub-images to make sure that each sub-image has a dimension of 2.1 nm � 2.1 nm, approximating to the size of medium-range-order atomic cluster (see Fig. 5b, d, f and h). Secondly, fast-Fourier-transformation (FFT) of the sub-images is carried out. Subsequently, a sub-image with certain crystal-like diffraction spots is selected as the reference image to characterize the local ordering of other sub-figures (see Fig. 6), such as the one with a red rectangle shown in Fig. 5b. The sub-images with clearer atomic fringe features (indicating local-ordered atomic arrangement) than the reference pattern are considered as ordered. Finally, the extent of local ordering in the amorphous phase is obtained by counting the ratio of ordered sub-images to total sub-images. It can be seen that the local ordering level in the glassy matrix of S2, resulted from the statistical interpretation of all the sub-images in Fig. 5b, is 10 � 1%. Along this line, the local ordering levels in the glassy matrix of S3, S4 and S5 are quantitatively measured to be 14 � 1%, 20 � 1% and 22 � 1%, respectively, as shown in Fig. 7. Clearly, the local ordering level of the glassy matrix of the studied BMGCs increases with the decrease of cooling rate during sample fabrication, indicating that the initial free volume content in glassy matrix decreases from S2 to S5. There exists a process for the creation and annihilation of excess free volume during plastic deformation of amorphous phase (Spaepen, 1977). The creation rate of free volume is larger than its annihilation rate before the steady state and thus the amount of free volume increases. The creation and annihilation of free volume reaches a balance when the deformation is in a steady state. It can be seen from Fig. 3b and c that the shear stress range for initiation of the first burst increases from S2 to S5, meaning the easier formation of STZs from S5 to S2. Generally, the dense free volumes can ease the formation of STZs. Therefore, the larger amount of excess free volume of amorphous matrix creates from S5 to S2 during nanoindentation, causing a smallest atomic binding strength and a loosest interatomic spacing of amorphous phase in S2 among studied samples (Jiang et al., 2006; Liu and Chan, 2005; Van Steenberge et al., 2007). It is expected to cause an obvious decrease in both the hardness and the elastic modulus of glassy matrix from S5 to S2. Furthermore, the evolution of free volumes and STZs from S5 to S2 lead to a less stochastic behavior of incipient plasticity. Thus, it is easily understood that among the studied samples, the glassy matrix in sample S2 exhibits the weakest stochastic behavior. Based on the above analysis, the glassy matrix of S2 has the highest initial free volumes and free volumes generated during nanoindentation among the four studied samples. Consequently, more STZs form in the glassy matrix of S2. Moreover, larger STZs in the glassy matrix of the studied samples can promote the nucleation of shear bands leading to the onset of plasticity, which corresponds to the occurrence of displacement bursts. In addition, larger STZs can assist the formation of multiple shear bands (Argon, 1979; Greer et al., 2013; Perepezko et al., 2014). This explains the trend of the size of the first displacement burst as shown in Fig. 3d and Table 2. For the glassy matrix of S2, in which the STZs possess the largest density and size, the shear deformation capability can be dramatically enhanced, leading to the largest plastic deformation. Contrarily, the glassy matrix of S5 with the sparsest and smallest STZs exhibits the highest deformation resistance. The observations indicate that the higher local ordering of the glassy matrix induces stronger heterogeneity in it, resulting in more stochastic STZ initiation. The initiation of STZs is closely related to shear banding events corresponding to incipient plasticity in the glassy matrix. To sum up, a more stochastic feature owes to microstructure evolution induced by cooling rate. 8
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 8. SEM images of the indentation marks of the glassy matrix of (a) S2, (b) S3, (c) S4, and (d) S5 with black arrows highlighting the shear bands.
To further understand the nanoindentation deformation feature of the glassy matrix of the composite samples with different di ameters, indentation marks were observed by SEM and the corresponding images are shown in Fig. 8. Pile-ups in the form of semicircular shear bands can be clearly observed around the indentation marks, as shown by the black arrows in Fig. 8. For strainsoftening materials like BMGs, the highly stressed volume immediately underneath the indenter continues to deform more and ma terial moves upwards around the nanoindenter, causing the formation of pile-up (Bolshakov and Pharr, 2011). For the case of BMGs, these pile-ups are characterized as discrete steps due to the inhomogeneous plastic deformation in them. From the indentation in the glassy matrix of S2 (Fig. 8a) to that in glassy matrix of S5 (Fig. 8d), the number of shear bands exhibits a decreasing trend. That is, the shear bands are more pronounced in the glassy matrix with more initial free volumes, which is in agreement with the above results. Therefore, it is reasonable that the larger amount of initial free volumes in the glassy matrix of the current studied samples leads to the formation of larger STZs, and promotes the initiation of more pronounced shear bands. 4. Conclusions In the present study, the deformation behavior of the glassy matrix in Cu47.5Zr48Al4Nb0.5 alloy samples with different casting diameters was systematically investigated by nanoindentation. The following major conclusions can be drawn: 1. By varying the sample size and thus the cooling rate during sample fabrication, Cu47.5Zr48Al4Nb0.5 BMGCs with various contents of amorphous phase were successfully synthesized. The hardness increases from 4.65 � 0.22 GPa for the glassy matrix in S2 to 6.52 � 0.94 GPa for that in S5. The elastic modulus of glassy matrix also obeys an increasing trend from 75.48 � 2.12 GPa for S2 to 96.99 � 5.80 GPa for S5. 2. Statistical analysis of the P-h curves reveals that the survival probability of the first burst in the glassy matrix decreases from 1 to 0 with the increase of shear stress. Furthermore, the incipient plastic deformation of glassy matrix from S2 to S5 exhibits a more stochastic nature. The average first burst size (from 0.91 � 0.06153 nm of S2 to 0.69 � 0.05143 nm of S5), as well as the average STZ volume (from (3.75 � 0.159) � 10 2 nm3 of S2 to (2.10 � 0.105) � 10 2 nm3 of S5) estimated by the cooperative shear model, of the glassy matrix from S2 to S5 exhibits a decreasing trend. Besides, the STZ of larger volume promotes larger first burst size. 3. Based on HRTEM and ACF analyses, the incipient plasticity for amorphous phase as well as variation of hardness, and elastic modulus is attributed to the reduced initial free volume content and the amount of excess free volume created during nano indentation of the glassy matrix from S2 to S5. Theoretical analysis demonstrates that the STZ volume is directly proportional to the
9
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
content of the initial free volume. The glassy matrix with higher density and larger size of STZs can enhance the shear capability, promote the formation of multiple shear bands and lead to a more obvious plastic deformation. Acknowledgements The financial support from National Natural Science Foundation of China under Grant Nos. 51871076, 51671070, 51827801, 51671071, and 51671067, and the Kingboard Professorship Endowment of the University of Hong Kong are grateful acknowledged. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijplas.2019.09.005.
References Argon, A.S., 1979. Plastic deformation in metallic glasses. Acta Metall. 27, 47–58. Bian, Z., Kato, H., Qin, C.L., Zhang, W., Inoue, A., 2005. Cu–Hf–Ti–Ag–Ta bulk metallic glass composites and their properties. Acta Mater. 53, 2037–2048. Bolshakov, A., Pharr, G.M., 2011. Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques. J. Mater. Res. 13, 1049–1058. Chen, J., Wang, W., Qian, L.H., Lu, K., 2003. Critical shear stress for onset of plasticity in a nanocrystalline Cu determined by using nanoindentation. Scr. Mater. 49, 645–650. Chen, J.H., Chen, Y., Jiang, M.Q., Chen, X.W., Zhang, H.F., Dai, L.H., 2015. On the compressive failure of tungsten fiber reinforced Zr-based bulk metallic glass composite. Int. J. Solids Struct. 69–70, 428–441. Cheng, Y.-T., Cheng, C.-M., 2004. Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R 44, 91–149. Cheng, Y.Q., Ma, E., 2011. Atomic-level structure and structure–property relationship in metallic glasses. Prog. Mater. Sci. 56, 379–473. Chiu, Y.L., Ngan, A.H.W., 2002. Time-dependent characteristics of incipient plasticity in nanoindentation of a Ni3Al single crystal. Acta Mater. 50, 1599–1611. Choi, I.C., Zhao, Y., Kim, Y.J., Yoo, B.G., Suh, J.Y., Ramamurty, U., Jang, J.I., 2012. Indentation size effect and shear transformation zone size in a bulk metallic glass in two different structural states. Acta Mater. 60, 6862–6868. Dong, J., Gao, M., Huan, Y., Feng, Y.H., Liu, W., Wang, W.H., 2017. Enhanced tensile plasticity of Zr based bulk metallic glasses by a stress induced large scale flow. J. Alloy. Comp. 727, 297–303. Fan, G.Y., Cowley, J.M., 1985. Auto-correlation analysis of high resolution electron micrographs of near-amorphous thin films. Ultramicroscopy 17, 345–355. Feng, G., Ngan, A.H.W., 2002. Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J. Mater. Res. 17, 660–668. Gerberich, W.W., Nelson, J.C., Lilleodden, E.T., Anderson, P., Wyrobek, J.T., 1996. Indentation induced dislocation nucleation: the initial yield point. Acta Mater. 44, 3585–3598. Greer, A.L., Cheng, Y.Q., Ma, E., 2013. Shear bands in metallic glasses. Mater. Sci. Eng. R 74, 71–132. Huang, Y.J., Khong, J.C., Connolley, T., Mi, J., 2014. The onset of plasticity of a Zr-based bulk metallic glass. Int. J. Plast. 60, 87–100. Huang, Y.J., Khong, J.C., Connolley, T., Mi, J., 2014. Understanding the deformation mechanism of individual phases of a ZrTi-based bulk metallic glass matrix composite using in situ diffraction and imaging methods. Appl. Phys. Lett. 104, 031912. Huang, Y.J., Shen, J., Chen, J.J.J., Sun, J.F., 2009. Critical cooling rate and thermal stability for a Ti–Zr–Ni–Cu–Be metallic glass. J. Alloy. Comp. 477, 920–924. Huang, Y.J., Shen, J., Sun, J.F., 2007. Bulk metallic glasses: smaller is softer. Appl. Phys. Lett. 90, 081919. Huang, Y.J., Zhou, B.J., Chiu, Y.L., Fan, H.B., Wang, D.J., Sun, J.F., Shen, J., 2014. The structural relaxation effect on the nanomechanical properties of a Ti-based bulk metallic glass. J. Alloy. Comp. 608, 148–152. Jiang, S.S., Huang, Y.J., Wu, F.F., Xue, P., Sun, J.F., 2018. A CuZr-based bulk metallic glass composite with excellent mechanical properties by optimizing microstructure. J. Non-Cryst. Solids 483, 94–98. Jiang, W.H., Liu, F.X., Wang, Y.D., Zhang, H.F., Choo, H., Liaw, P.K., 2006. Comparison of mechanical behavior between bulk and ribbon Cu-based metallic glasses. Mater. Sci. Eng. A 430, 350–354. Johnson, K.L., 1985. Contact Mechanics. Cambridge University Press, Cambridge. Johnson, W.L., 1999. Bulk glass-forming metallic alloys: science and technology. MRS Bull. 24, 42–56. Johnson, W.L., Samwer, K., 2005. A universal criterion for plastic yielding of metallic glasses with a (T/Tg) 2/3 temperature dependence. Phys. Rev. Lett. 95, 195501. Lee, M.L., Li, Y., Schuh, C.A., 2004. Effect of a controlled volume fraction of dendritic phases on tensile and compressive ductility in La-based metallic glass matrix composites. Acta Mater. 52, 4121–4131. Li, H., Ngan, A.H.W., Wang, M.G., 2005. Continuous strain bursts in crystalline and amorphous metals during plastic deformation by nanoindentation. J. Mater. Res. 20, 3072–3081. Liang, J.M., Chen, L.J., 1994. Autocorrelation function analysis of phase formation in the initial stage of interfacial reactions of molybdenum thin films on (111)Si. Appl. Phys. Lett. 64, 1224–1226. Liu, L., Chan, K.C., 2005. Plastic deformation of Zr-based bulk metallic glasses under nanoindentation. Mater. Lett. 59, 3090–3094. Liu, Y.Y., Liu, P.Z., Li, J.J., Liaw, P.K., Spieckermann, F., Kiener, D., Qiao, J.W., Eckert, J., 2018. Universally scaling Hall-Petch-like relationship in metallic glass matrix composites. Int. J. Plast. 105, 225–238. Liu, Z.Q., Li, R., Liu, G., Su, W.H., Wang, H., Li, Y., Shi, M.J., Luo, X.K., Wu, G.J., Zhang, T., 2012. Microstructural tailoring and improvement of mechanical properties in CuZr-based bulk metallic glass composites. Acta Mater. 60, 3128–3139. Ma, Y., Peng, G.J., Feng, Y.H., Zhang, T.H., 2016. Nanoindentation investigation on the creep mechanism in metallic glassy films. Mater. Sci. Eng. A 651, 548–555. Narayan, R.L., Raut, D., Ramamurty, U., 2018. A quantitative connection between shear band mediated plasticity and fracture initiation toughness of metallic glasses. Acta Mater. 150, 69–77. Narayan, R.L., Singh, P.S., Hofmann, D.C., Hutchinson, N., Flores, K.M., Ramamurty, U., 2012. On the microstructure–tensile property correlations in bulk metallic glass matrix composites with crystalline dendrites. Acta Mater. 60, 5089–5100. Ng, K.Y., Zuo, L., Ngan, A.H.W., 2009. Steady-state serrated deformation of metallic glass during indentation. Scr. Mater. 61, 955–958. Ngan, A.H.W., Ng, K.S., 2010. Transition from deterministic to stochastic deformation. Philos. Mag. 90, 1937–1954. Oliver, W.C., Pharr, G.M., 1992. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583. Pan, D., Inoue, A., Sakurai, T., Chen, M.W., 2008. Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses. Proc. Natl. Acad. Sci. U.S.A. 105, 14769–14772. Pan, J., Wang, Y.X., Li, Y., 2017. Ductile fracture in notched bulk metallic glasses. Acta Mater. 136, 126–133. Pauly, S., Gorantla, S., Wang, G., Kuhn, U., Eckert, J., 2010. Transformation-mediated ductility in CuZr-based bulk metallic glasses. Nat. Mater. 9, 473–477.
10
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Perepezko, J.H., Imhoff, S.D., Chen, M.W., Wang, J.Q., Gonzalez, S., 2014. Nucleation of shear bands in amorphous alloys. Proc. Natl. Acad. Sci. U.S.A. 111, 3938–3942. Qiao, J.C., Pelletier, J.M., 2014. Dynamic mechanical relaxation in bulk metallic glasses: a review. J. Mater. Sci. Technol. 30, 523–545. Qiao, J.C., Yao, Y., Pelletier, J.M., Keer, L.M., 2016. Understanding of micro-alloying on plasticity in Cu46Zr47 xAl7Dyx (0�x� 8) bulk metallic glasses under compression: based on mechanical relaxations and theoretical analysis. Int. J. Plast. 82, 62–75. Qiao, J.W., Sun, A.C., Huang, E.W., Zhang, Y., Liaw, P.K., Chuang, C.P., 2011. Tensile deformation micromechanisms for bulk metallic glass matrix composites: from work-hardening to softening. Acta Mater. 59, 4126–4137. Savitzky, A., Golay, M.J.E., 1964. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639. Schuh, C.A., Lund, A.C., 2004. Application of nucleation theory to the rate dependence of incipient plasticity during nanoindentation. J. Mater. Res. 19, 2152–2158. Sha, Z., Branicio, P.S., Lee, H.P., Tay, T.E., 2017. Strong and ductile nanolaminate composites combining metallic glasses and nanoglasses. Int. J. Plast. 90, 231–241. Song, K.K., Pauly, S., Zhang, Y., Li, R., Gorantla, S., Narayanan, N., Kühn, U., Gemming, T., Eckert, J., 2012. Triple yielding and deformation mechanisms in metastable Cu47.5Zr47.5Al5 composites. Acta Mater. 60, 6000–6012. Spaepen, F., 1977. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall. 25, 407–415. Sun, B.A., Song, K.K., Pauly, S., Gargarella, P., Yi, J., Wang, G., Liu, C.T., Eckert, J., Yang, Y., 2016. Transformation-mediated plasticity in CuZr based metallic glass composites: a quantitative mechanistic understanding. Int. J. Plast. 85, 34–51. Van Steenberge, N., Sort, J., Concustell, A., Das, J., Scudino, S., Suri~ nach, S., Eckert, J., Bar� o, M.D., 2007. Dynamic softening and indentation size effect in a Zr-based bulk glass-forming alloy. Scr. Mater. 56, 605–608. Wang, D.M., Chen, Y., Mu, J., Zhu, Z.W., Zhang, H.F., Wang, Y.D., An, K., 2018. An in situ neutron diffraction study of plastic deformation in a Cu46.5Zr46.5Al7 bulk metallic glass composite. Scr. Mater. 153, 118–121. Wang, G., Huang, Y.J., Shen, J., 2012. Novel TiCuNiCo composites with high fracture strength and plasticity. Mater. Des. 33, 226–230. Wang, W.H., Dong, C., Shek, C.H., 2004. Bulk metallic glasses. Mater. Sci. Eng. R 44, 45–89. Wu, F.F., Chan, K.C., Jiang, S.S., Chen, S.H., Wang, G., 2014. Bulk metallic glass composite with good tensile ductility, high strength and large elastic strain limit. Sci. Rep. 4, 5302. Wu, F.F., Chan, K.C., Li, S.T., Wang, G., 2013. Stabilized shear banding of ZrCu-based metallic glass composites under tensile loading. J. Mater. Sci. 49, 2164–2170. Wu, Y., Ma, D., Li, Q.K., Stoica, A.D., Song, W.L., Wang, H., Liu, X.J., Stoica, G.M., Wang, G.Y., An, K., Wang, X.L., Li, M., Lu, Z.P., 2017. Transformation-induced plasticity in bulk metallic glass composites evidenced by in-situ neutron diffraction. Acta Mater. 124, 478–488. Wu, Y., Wang, H., Wu, H.H., Zhang, Z.Y., Hui, X.D., Chen, G.L., Ma, D., Wang, X.L., Lu, Z.P., 2011. Formation of Cu–Zr–Al bulk metallic glass composites with improved tensile properties. Acta Mater. 59, 2928–2936. Wu, Y., Wu, H.H., Hui, X.D., Chen, G.L., Lu, Z.P., 2010. Effects of drawing on the tensile fracture strength and its reliability of small-sized metallic glasses. Acta Mater. 58, 2564–2576. Wu, Y., Xiao, Y.H., Chen, G.L., Liu, C.T., Lu, Z.P., 2010. Bulk metallic glass composites with transformation-mediated work-hardening and ductility. Adv. Mater. 22, 2770–2773. Zhang, Z.Y., Yang, S., Xu, C.G., Wang, B., Duan, N.D., 2014. Deformation and stress at pop-in of lithium niobate induced by nanoindentation. Scr. Mater. 77, 56–59.
11
Contents lists available at ScienceDirect
International Journal of Plasticity journal homepage: http://www.elsevier.com/locate/ijplas
Stochastic deformation and shear transformation zones of the glassy matrix in CuZr-based metallic-glass composites S.S. Jiang a, b, c, K.F. Gan d, Y.J. Huang a, b, c, *, P. Xue a, b, c, Z.L. Ning b, J.F. Sun a, b, A.H. W. Ngan d a
State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China c Key Laboratory of Micro-systems and Micro-structures Manufacturing (Harbin Institute of Technology), Ministry of Education, Harbin, China d Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Metallic glass Cooling rate Incipient plasticity Stochastic deformation Free volume Shear transformation zone
The incipient plasticity of an amorphous solid represents the onset of shear deformation, which is a stochastic progress closely related to microstructure evolution. It is well known that the cooling rate plays a crucial role in the microstructure evolution of a glass. Nevertheless, how the cooling rate affects the incipient plasticity is still unclear. In this work, the incipient plastic deformation of the amorphous phase in Cu47.5Zr48Al4Nb0.5 bulk metallic glass composites (BMGCs) cast with different cooling rates is systematically studied. The incipient plasticity of the glassy matrix of the BMGCs is found to occur via a first displacement burst, the occurrence of which is more stochastic as the cooling rate decreases. According to the auto-correlation functions and cooperative shear model, the stochastic behavior is attributed to the effects of the cooling rate on the initial free volume and subsequent activated shear transformation zones (STZs). A higher content of free volume is present in the glassy matrix of the studied samples cooled at a faster rate, which fa cilitates the operation of STZs. Moreover, the larger incipient burst size is correlated with the higher content of free volume and larger STZs in the glassy matrix. The larger STZs result in more preferable propagation of multiple shear bands, leading to less stochastic deformation and more obvious plastic deformation. This study provides further understanding on the incipient plasticity of glassy matrix in BMGCs.
1. Introduction Owing to the unique structure free of crystalline defects, bulk metallic glasses (BMGs) often offer high strength and elastic limit compared with traditional crystalline materials (Huang et al., 2009; Johnson, 1999; Pan et al., 2017; Qiao and Pelletier, 2014; Wang et al., 2004). However, the room-temperature brittleness and work softening largely restrict their wide applications in engineering (Greer et al., 2013; Huang et al., 2014a). BMGs usually experience shear localization within nano-scaled narrow shear bands, resulting in catastrophic fracture under tensile loading. To overcome this limitation, numerous strategies have been proposed (Dong et al., 2017; Huang et al., 2014b; Jiang et al., 2018; Narayan et al., 2018; Pauly et al., 2010; Qiao et al., 2016). Among them, developing BMG composites (BMGCs) comprising crystalline phases of different length scales distributed in the amorphous matrix has been proven to be
* Corresponding author. State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin, China. E-mail address: [email protected] (Y.J. Huang). https://doi.org/10.1016/j.ijplas.2019.09.005 Received 4 January 2019; Received in revised form 15 June 2019; Accepted 4 September 2019 Available online 7 September 2019 0749-6419/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: S.S. Jiang, International Journal of Plasticity, https://doi.org/10.1016/j.ijplas.2019.09.005
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 1. (a) XRD patterns of Cu47.5Zr48Al4Nb0.5 (at. %) alloy samples with different diameters (The sample with 2 mm, 3 mm, 4 mm, or 5 mm in diameter is labeled as S2, S3, S4, and S5, respectively), and optical micrograph images of (b) S2, (c) S3, (d)S4 and (e) S5 samples.
effective in improving toughness and plasticity, because the ductile secondary phases can effectively distribute the plastic strain over a larger volume of materials (Bian et al., 2005; Chen et al., 2015; Lee et al., 2004; Liu et al., 2018; Narayan et al., 2012; Qiao et al., 2011; Sha et al., 2017; Wang et al., 2012). Nevertheless, such BMGCs exhibit a disappointing strain softening behavior in tension, resulting in unstable deformation. Recently, this shortcoming has been successfully circumvented by adopting the concept of transformation-induced plasticity (TRIP) in BMG composites (Wu et al., 2010b). Pronounced tensile properties have been achieved through introducing an in situ B2 phase into the glassy matrix (Liu et al., 2012; Song et al., 2012; Wang et al., 2018; Wu et al., 2014, 2017). B2 phase reinforced BMGCs consist of a crystalline phase and an amorphous phase. Considerable attention has been put in the crystalline B2 phase in relation to the deformation mechanism of the entire composite. While the work-hardening ability originates mainly from the deformation-induced martensitic transformation of cubic B2 CuZr into monoclinic B190 phase (Song et al., 2012; Wu et al., 2014, 2017) and the high elastic limit and ductility are attributable to the interaction of the B2 phase with the glassy matrix (Sun et al., 2016; Wu et al., 2011, 2014), numerous studies have shown that the high yield strength of BMGCs is mainly attributed to the amorphous phase (Jiang et al., 2018; Wu et al., 2013, 2017). However, the plastic deformation behavior of the amorphous phase in BMGCs has remained unclear, although this is essential for the further understanding of the intrinsic deformation mechanism of BMGCs. The plastic deformation of the amorphous phase is dominated by the evolution of shear bands (Perepezko et al., 2014), the nucleation of which is intricately related to the initial free volumes and subsequently activated shear transformation zones (STZs) (Greer et al., 2013; Huang et al., 2007; Wang et al., 2004). Although monolithic BMGs have been widely studied (Cheng and Ma, 2011), there is little scientific basis to assume that the structural features and deformation behavior of the glassy matrix in a BMGC are identical in every aspect to those of monolithic BMG alloys. In particular, as the atomic-scale structural features in terms of free volume and STZs in a glassy phase depend sensitively on the preparation method especially the solidification condition, it would be practically impossible to produce a monolithic BMG alloy that could duplicate exactly a composite’s glassy matrix. As such, testing the local properties using a local probe such as nanoindentation is the only reliable way to know the properties of the glassy matrix of a BMGC. Therefore, in the present study, the amorphous matrix of CuZrAlNb B2-reinforced BMGCs prepared by different cooling rates is characterized by nanoindentation. We focus on the onset of plasticity in the amorphous phase as this marks the nucleation of shear banding and the first yielding condition of the glassy matrix (Perepezko et al., 2014). By systematically analyzing the effects of cooling rate on the local mechanical behavior of the glassy matrix, the role of the initial free volumes and the subsequently activated STZs on the incipient plastic deformation behaviors at nano-scale of the glassy matrix in BMGCs will be elucidated. The results will help us further understand the plastic deformation mechanism of the amorphous phase, and the relationship between the fabrication, microstructure and mechanical properties of BMGCs. 2. Experimental details The ingots of Cu47.5Zr48Al4Nb0.5 (at. %) alloy samples were fabricated through arc melting mixtures of Cu, Zr, Nb, and Al metals (purity > 99.99 wt %) in a Ti-gettered Ar atmosphere. To avoid compositional inhomogeneity and segregation, the ingots were remelted at least five times with electromagnetic stirring. Cylindrical alloy samples with diameters of 2 mm, 3 mm, 4 mm and 5 mm, hereafter labeled as S2, S3, S4 and S5, respectively, were fabricated using drop casting the alloy melt into a copper mold under the argon atmosphere. Due to the difference in their dimensions, these samples correspond to different cooling rates from the melt, i.e. the smaller samples were cooled faster than the larger ones. The microstructural nature and corresponding morphology of the as-cast alloy samples were examined using X-ray diffraction (XRD) with Cu Kα radiation, optical microscope (OM) using a Leica DM4000M in strument, and a Talos F200X transmission electron microscope (TEM). The average chemical compositions of glassy matrix in different samples were then characterized by energy dispersive X-ray spectroscopy (EDS) in a Quanta 200FEG scanning electron microscope 2
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Table 1 The average element content of glassy matrix in S2, S3, S4 and S5 samples by EDS analysis. Matrix
Zr/at. %
Cu/at. %
Al/at. %
Nb/at. %
S2 S3 S4 S5
48.08 � 0.26 49.78 � 0.61 49.70 � 0.63 48.29 � 0.23
44.60 � 0.38 42.23 � 0.46 42.30 � 0.36 44.98 � 0.60
3.59 � 0.21 4.03 � 0.28 3.50 � 0.44 3.09 � 0.34
3.74 � 0.18 3.96 � 0.45 3.77 � 0.22 3.65 � 0.49
Fig. 2. (a) Typical load-displacement curves obtained from the nanoindentation tests of the glassy matrix of the CuZrAlNb alloy samples with different diameters, and (b) the corresponding H and Er values.
(SEM). The surface roughness of studied samples was examined by a Dimension Fastscan atomic force microscope (AFM). In order to reveal the atomic level structure of the glassy matrix of the composite samples, high-resolution TEM (HRTEM) images were obtained. Then, the auto-correlation functions (ACF) of HRTEM images (Fan and Cowley, 1985; Huang et al., 2014c; Liang and Chen, 1994; Wu et al., 2010a) were obtained to characterize the local ordering of the glassy matrix of the BMGC samples. Nanoindentation tests were carried out on the glassy matrix of the as-cast samples at room temperature using an Agilent G200 Nanoindenter equipped with a Berkovich indenter, which provides a load resolution of 3 nN within the loading range of 30 mN and a displacement resolution of 0.01 nm in the depth range of 2 μm. The diamond indenter radius calibration is performed on the fused quartz (R is ~20 nm). A constant loading rate of 0.1 mN/s was adopted and the maximum load is 10 mN. To verify the data reliability, at least twenty-five indentation tests were repeated on different locations randomly selected on the matrix for each group of samples under identical conditions. The standard deviation has been found to be less than 5%. Also, the morphologies of indentation im pressions were examined by a Helios Nanolab 600i SEM. 3. Results and discussion 3.1. Microstructure and mechanical properties of glassy matrix from Cu47.5Zr48Al4Nb
0.5
BMGCs
Fig. 1a displays the typical XRD patterns of Cu47.5Zr48Al4Nb0.5 alloy samples with various diameters. The XRD pattern for the S2 sample shows a sharp crystalline peak indexed as B2–CuZr phase (bcc) appearing on a diffraction hump, demonstrating a mixture structure of secondary phase and glassy matrix. When the sample diameter increases to 5 mm, the corresponding XRD pattern shows a series of sharp peaks superimposed on broad ones. Meanwhile, the increase in the sample diameter causes a significant increase in the area of the sharp Bragg peak, suggesting an increase in the volume fraction of the crystalline phases. Such microstructural change with specimen diameter was further observed by OM as shown in Fig. 1b–e. The S2 sample exhibits a composite structure with few spherical B2 crystals embedded in the glassy matrix (Fig. 1b), agreeing well with the above XRD results. For the S3 sample, the B2 phases with a size range of 30–150 μm are homogeneously distributed in glassy matrix (Fig. 1c). For the S4 sample cooled at a lower rate, B2 phases pool into a number of large clusters and distribute inhomogeneously across the glassy matrix (Fig. 1d). Upon further decreasing the cooling rate (the S5 sample), the B2 phase occupies almost the entire cross-section with only a small amount of amorphous matrix near the surface of the rod sample (Fig. 1e). It can be seen that the volume fraction of the amorphous phase increases with cooling rates. The EDS analysis demonstrates that no obvious difference in the chemical composition of the glassy matrix can be found for the BMGC samples with different amorphous phase fraction, as shown in Table 1. The composition of the glassy matrix for all the four ingots S2 to S5 is very close to the overall composition of the composite, and also to the stoichiometric ratio of Cu:Zr ¼ 1:1 of the B2 intermetallic phase. This is exactly the condition needed for the simultaneous formation of the glassy matrix and the B2 phase during a rapid so lidification process, during which significant elemental segregation cannot occur. Fig. 2a exhibits representative load versus displacement (P-h) curves acquired from the nanoindentation measurements on the glassy matrix of the studied composite samples with various diameters. The indentation depth at maximum load gradually decreases 3
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Table 2 The maximum depth, first burst size, activation volume and corresponding STZ volume of glassy matrix in the studied samples. Matrix
Maximum depth dmax/nm
First burst size Δh/nm
Activation volume V*/nm3
STZ volume Ω/nm3
S2 S3 S4 S5
338.55 � 13.35 301.08 � 8.55 239.26 � 11.48 218.15 � 11.30
0.91 � 0.06153 0.79 � 0.06903 0.74 � 0.04011 0.69 � 0.05143
(1.70 � 0.103) � 10 3 (1.49 � 0.112) � 10 3 (1.12 � 0.094) � 10 3 (9.51 � 1.08) � 10 4
(3.75 � 0.159) � 10 (3.29 � 0.147) � 10 (2.47 � 0.216) � 10 (2.10 � 0.105) � 10
2 2 2 2
Fig. 3. (a) The typical load-displacement curve of the glassy matrix from a given sample showing the raw and the fitted data using Eq. (1). The inset shows the bursts obtained from the difference between the smoothed displacement data and the fitted data, (b) the plots of survival probability of first burst versus maximum shear stress gathered from 25 independent nanoindentation tests of the glassy matrix of alloy samples with different diameters, (c) the plots of ln(ln(F 1)) as a function of maximum shear stress τmax and corresponding fitted lines in order to characterize the acti vation volume and subsequent STZ size, and (d) the STZ volume of glassy matrix as a function of first burst size.
with the sample diameter and the average maximum indentation depths of the amorphous phase are listed in Table 2. The hardness and elastic modulus of metallic materials are closely related to the contact stiffness S. In order to eliminate the influence of external factors on S as far as possible in nanoindentation tests, an improved method proposed by Feng and Ngan has been adopted (Feng and Ngan, 2002). In the Feng-Ngan method, the corrected contact stiffness Sc is obtained from
1 Sc
¼
1 Su
þ
h_h , jP_u j
here Su is the apparent contact
stiffness at the onset of unloading, i.e.dPu =dh, h_h is the displacement rate just before unloading, and P_ u is the unloading rate. Therefore, based on the program of Oliver-Pharr method (Oliver and Pharr, 1992) in the nanoindentation instrument and the corrected contact stiffness from Feng-Ngan method, the average hardness and elastic modulus are calculated to be 4.65 � 0.22 GPa and 75.48 � 2.12 GPa, 5.62 � 0.78 GPa and 82.91 � 3.84 GPa, 6.20 � 0.93 GPa and 89.48 � 4.72 GPa, and 6.52 � 0.94 GPa and 96.99 � 5.80 GPa for the glassy matrix of S2, S3, S4, and S5, respectively. The corresponding results are plotted in Fig. 2b. Clearly, as the sample diameter increases from 2 mm to 5 mm, both the elastic modulus and hardness of the glassy matrix increase. 3.2. Stochastic deformation of glassy matrix in nanoindentation tests It has been well documented that, in nanoindentation tests, the first burst event can be closely related with the incipient plasticity of the tested materials (Chiu and Ngan, 2002; Gerberich et al., 1996; Schuh and Lund, 2004). Here, to study the incipient plasticity of the 4
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 4. The two-dimensional (a) and three-dimensional (b) images of the representative sample surface scanned by AFM.
glassy matrix, a series of nanoindentation tests were conducted. The P-h curves were found to be jerky during the deformation. To make the discrete bursts more visible, a mean-field curve was first obtained from the experimental P-h curve by fitting the latter by the following equation (Li et al., 2005), h ¼ α1 P8 þ α2 P7 þ α3 P6 þ α4 P5 þ α5 P4 þ α6 P3 þ α7 P2 þ α8 P þ β;
(1)
where α1, α2, α3, α4, α5, α6, α7, α8, and β are fitting constants. Furthermore, the raw data were also smoothened through a least squares method developed by Savitzky and Golay to minimize the noise from indentation instrument (Savitzky and Golay, 1964). As an example, Fig. 3a shows a typical P-h curve for the loading regime of nanoindentation tests. To characterize the first displacement burst, the operation of subtracting the fitted data from the smoothened data was performed. The inset of Fig. 3a shows the net difference between the smoothened data and the fitted mean-field data of a representative P-h curve obtained from the glassy matrix of the studied composite sample. The first displacement burst identified from the starting point (SP) and ending point (EP) is highlighted by the red arrow in the inset of Fig. 3a. Besides, the average sizes of the first displacement bursts of the glassy matrix in the current samples were measured from the nanoindentation displacement data, and these are shown in Table 2. As shown from the example in Fig. 3a, there are successive displacement bursts, corresponding to sudden softening (Ng et al., 2009), and decorating all the P-h curves of the glassy matrix of the studied composite samples. In the current glassy matrix, the maximum shear stress at which the first burst occurs indicates the critical shear strength of incipient plastic deformation. In addition, a Berkovich indenter tip must have a certain degree of roundness under small displacements (Chen et al., 2003; Zhang et al., 2014). Therefore, based on contact mechanics, the maximum shear stress τmax of the elastic field underneath a spherical tip, at the load P1st at which the first burst occurs, is given by (Johnson, 1985) �
τmax ¼ 0:31 6E2r P1st
�
π 3 R2
��1=3
(2)
where Er is the reduced elastic modulus and R (~ 20 nm) is curvature radius of indenter tip. To make sure the validity of the estimated shear stress, the surface roughness of studied samples should be smaller than the radius of indenter tip. The representative AFM image (Fig. 4a and 4b) shows that the average roughness Ra of the sample surface is only 0.107 nm, which is much smaller than tip radius. In the ensemble of repeated runs of the indentation experiments under the identical external conditions, the τmax at which the first burst occurred in each run of the experiments was recorded, and then all the τmax in the ensemble were ranked in ascending order. Under a given stress level, the stressed region in the glassy matrix of a typical replica in the ensemble may or may not emit the first burst, and the probability at which the first burst is emitted is described by an ensemble survival probability F which is just the fraction of the experiments in the ensemble without emitting the first burst (Ng et al., 2009; Ngan and Ng, 2010). For the observed first-burst stress of rank i in ascending order in the ensemble, F is then calculated using the following equation (Ng et al., 2009; Ngan and Ng, 2010), F¼1
(3)
i=ðN þ 1Þ;
where N is the number of experiments for the ensemble. Fig. 3b shows scattered plots of the survival probability F versus τmax at first burst for the glassy matrix of the S2, S3, S4 and S5 samples. As the shear stress increases, the survival probability drops from 1 to 0. At the transition region, the survival probability of the first burst of the glassy matrix exhibits a nearly linear trend and the maximum shear stress range for the nearly line regime is larger in the larger sample which was fabricated with a lower cooling rate. This indicates that the glassy matrix of the composite sample that is cooled at a slower rate exhibits more pronounced stochastic nature in terms of the incipient plastic deformation. To understand the deformation mechanism, the activated STZs during nanoindentation are examined. The first burst event associated with incipient plasticity is a stress-assisted thermal activation process. With ample local thermal energy, the first burst event may occur at any stress level, but the survival probability of the event will decrease exponentially with the shear stress. Based on the analysis, the survival probability for the first burst event can be described as a function of maximum shear 5
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 5. HRTEM images with inset showing the selected area electron diffraction pattern, and the corresponding ACF images of the glassy matrix of the CuZrAlNb composite sample with (a) (b) 2 mm, (c) (d) 3 mm, (e) (f) 4 mm, and (g) (h) 5 mm in diameter.
stress as follows (Schuh and Lund, 2004): (4)
F ¼ exp½ aexpðbτÞ�;
where a ¼ kTAexp½ W=ðkTÞ�=ð_τV � Þ b ¼ V � =ðkTÞ, A is a pre-exponential factor, k is the Boltzmann constant, T is Kelvin temper ature, W is activation energy, τ_ is shear rate, and V* is the activation volume related to the initiation of STZs during the loading stage in nanoindentation. The overall trend of the data distribution for all curves is hardly affected by the data at the end of each curve in Fig. 3b, and the correlation coefficient R2 for each fitted curve is higher than 0.9. Therefore, the agreement between the experimental data and fitted results as the dash dot lines shown in Fig. 3b is reasonable. To characterize the activation volume V*, Eq. (4) can be expressed in a log-log form (Choi et al., 2012) � ln lnF 1 ¼ lna þ bτ: (5) It can be seen that the V* can be obtained from the slope of lnðlnF 1 Þ versus τ when τ is equal to τmax (see Fig. 3c). The V* of glassy matrix from S2 to S5 is shown in Table 2. It can be seen from Table 2 that the average maximum depths of nanoindentation tests in all samples exceed 200 nm and the average deformation volume estimated approximately during nanoindentation tests is higher than 8 � 106 nm3. The deformation can be considered to be homogeneous due to the sub-nanometric size of the fundamental deformation unit (Cheng and Cheng, 2004; Pan et al., 2008). Theoretically, the STZ volume Ω can be quantitatively estimated by cooperative shear model (Johnson and Samwer, 2005): 6
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 6. The operation of fast-Fourier-transformation (FFT) of the sub-images from Fig. 5(b): the FFT pattern of the sub-image with coordinate (1, 1) exhibits certain crystal-like diffraction spots and then is selected as the reference. The FFT patterns with coordinates (3, 2), (3, 4), (6, 5) and (7, 4) showing more crystal-like diffraction spots are considered as being ordered.
Ω¼
τS0 6CGS γ 2S ξ
� 1
τST τS0
* �12 V ;
(6)
where C � 1/4, ξ � 3, τS0 and τST are the threshold shear resistances at temperature 0 and T K, respectively (Johnson and Samwer, 2005), V* is the activation volume, GS is shear modulus at 0 K, γS is the critical shear strain, τS0 =GS ¼ 0:036, which can be expressed as (Johnson and Samwer, 2005): � �M τST T γS ¼ ¼ γ S0 γS1 ; (7) Tg GS where γ S0 ¼ 0:036 � 0:002, γ S1 ¼ 0:016 � 0:002 and M ¼ 0:62 � 0:2 (Ma et al., 2016), and Tg is glass transition temperature of studied CuZrAlNb alloy, which was measured as 683 K by differential scanning calorimetry at a heating rate of 20 K/min. For a certain GS � �M and Tg , the ratio of τS0 and τST can be calculated from the equation, i.e. τST =τS0 ¼ 1 0:444 TTg (Johnson and Samwer, 2005). Consequently, the average volume of STZs for glassy matrix in studied composite samples at loading segment is estimated as shown in Table 2. Theoretically, the onset of plastic deformation is also controlled by the initiation of STZs at a micro-scale (Argon, 1979). Therefore, the correlation between the first burst size and the STZ volume of glassy matrix in studied samples can be achieved by plotting the STZ volume as a function of first burst size in Fig. 3d. From Fig. 3d, it is apparent that the larger STZs activated in the glassy matrix facilitate the formation of larger incipient bursts.
7
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 7. The content of local ordering of the glassy matrix of composite sample with different diameters.
3.3. Nano-scale deformation mechanism for glassy matrix of the composite samples with different cooling rates The activation of STZs is closely related to the structural features of the amorphous phase, i.e. initial free volume. Next, in order to further explain the origin of the incipient plasticity for the amorphous phase, the free-volume contents of the glassy matrix in all the studied samples are analyzed using the concept of the local ordering. As is seen in Fig. 5a (S2), 5c (S3), 5e (S4) and 5g (S5), the HRTEM images exhibit a typical amorphous feature with long-range atomic disorder, which is also supported by the corresponding selected area electron diffraction (SAED) pattern. In order to quanti tatively measure the extent of local ordering of the amorphous phase, the ACF method, combining with HRTEM image analyses, was employed (Fan and Cowley, 1985; Huang et al., 2014c). Firstly, each HRTEM image of the glassy matrix is divided into 49 sub-images to make sure that each sub-image has a dimension of 2.1 nm � 2.1 nm, approximating to the size of medium-range-order atomic cluster (see Fig. 5b, d, f and h). Secondly, fast-Fourier-transformation (FFT) of the sub-images is carried out. Subsequently, a sub-image with certain crystal-like diffraction spots is selected as the reference image to characterize the local ordering of other sub-figures (see Fig. 6), such as the one with a red rectangle shown in Fig. 5b. The sub-images with clearer atomic fringe features (indicating local-ordered atomic arrangement) than the reference pattern are considered as ordered. Finally, the extent of local ordering in the amorphous phase is obtained by counting the ratio of ordered sub-images to total sub-images. It can be seen that the local ordering level in the glassy matrix of S2, resulted from the statistical interpretation of all the sub-images in Fig. 5b, is 10 � 1%. Along this line, the local ordering levels in the glassy matrix of S3, S4 and S5 are quantitatively measured to be 14 � 1%, 20 � 1% and 22 � 1%, respectively, as shown in Fig. 7. Clearly, the local ordering level of the glassy matrix of the studied BMGCs increases with the decrease of cooling rate during sample fabrication, indicating that the initial free volume content in glassy matrix decreases from S2 to S5. There exists a process for the creation and annihilation of excess free volume during plastic deformation of amorphous phase (Spaepen, 1977). The creation rate of free volume is larger than its annihilation rate before the steady state and thus the amount of free volume increases. The creation and annihilation of free volume reaches a balance when the deformation is in a steady state. It can be seen from Fig. 3b and c that the shear stress range for initiation of the first burst increases from S2 to S5, meaning the easier formation of STZs from S5 to S2. Generally, the dense free volumes can ease the formation of STZs. Therefore, the larger amount of excess free volume of amorphous matrix creates from S5 to S2 during nanoindentation, causing a smallest atomic binding strength and a loosest interatomic spacing of amorphous phase in S2 among studied samples (Jiang et al., 2006; Liu and Chan, 2005; Van Steenberge et al., 2007). It is expected to cause an obvious decrease in both the hardness and the elastic modulus of glassy matrix from S5 to S2. Furthermore, the evolution of free volumes and STZs from S5 to S2 lead to a less stochastic behavior of incipient plasticity. Thus, it is easily understood that among the studied samples, the glassy matrix in sample S2 exhibits the weakest stochastic behavior. Based on the above analysis, the glassy matrix of S2 has the highest initial free volumes and free volumes generated during nanoindentation among the four studied samples. Consequently, more STZs form in the glassy matrix of S2. Moreover, larger STZs in the glassy matrix of the studied samples can promote the nucleation of shear bands leading to the onset of plasticity, which corresponds to the occurrence of displacement bursts. In addition, larger STZs can assist the formation of multiple shear bands (Argon, 1979; Greer et al., 2013; Perepezko et al., 2014). This explains the trend of the size of the first displacement burst as shown in Fig. 3d and Table 2. For the glassy matrix of S2, in which the STZs possess the largest density and size, the shear deformation capability can be dramatically enhanced, leading to the largest plastic deformation. Contrarily, the glassy matrix of S5 with the sparsest and smallest STZs exhibits the highest deformation resistance. The observations indicate that the higher local ordering of the glassy matrix induces stronger heterogeneity in it, resulting in more stochastic STZ initiation. The initiation of STZs is closely related to shear banding events corresponding to incipient plasticity in the glassy matrix. To sum up, a more stochastic feature owes to microstructure evolution induced by cooling rate. 8
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Fig. 8. SEM images of the indentation marks of the glassy matrix of (a) S2, (b) S3, (c) S4, and (d) S5 with black arrows highlighting the shear bands.
To further understand the nanoindentation deformation feature of the glassy matrix of the composite samples with different di ameters, indentation marks were observed by SEM and the corresponding images are shown in Fig. 8. Pile-ups in the form of semicircular shear bands can be clearly observed around the indentation marks, as shown by the black arrows in Fig. 8. For strainsoftening materials like BMGs, the highly stressed volume immediately underneath the indenter continues to deform more and ma terial moves upwards around the nanoindenter, causing the formation of pile-up (Bolshakov and Pharr, 2011). For the case of BMGs, these pile-ups are characterized as discrete steps due to the inhomogeneous plastic deformation in them. From the indentation in the glassy matrix of S2 (Fig. 8a) to that in glassy matrix of S5 (Fig. 8d), the number of shear bands exhibits a decreasing trend. That is, the shear bands are more pronounced in the glassy matrix with more initial free volumes, which is in agreement with the above results. Therefore, it is reasonable that the larger amount of initial free volumes in the glassy matrix of the current studied samples leads to the formation of larger STZs, and promotes the initiation of more pronounced shear bands. 4. Conclusions In the present study, the deformation behavior of the glassy matrix in Cu47.5Zr48Al4Nb0.5 alloy samples with different casting diameters was systematically investigated by nanoindentation. The following major conclusions can be drawn: 1. By varying the sample size and thus the cooling rate during sample fabrication, Cu47.5Zr48Al4Nb0.5 BMGCs with various contents of amorphous phase were successfully synthesized. The hardness increases from 4.65 � 0.22 GPa for the glassy matrix in S2 to 6.52 � 0.94 GPa for that in S5. The elastic modulus of glassy matrix also obeys an increasing trend from 75.48 � 2.12 GPa for S2 to 96.99 � 5.80 GPa for S5. 2. Statistical analysis of the P-h curves reveals that the survival probability of the first burst in the glassy matrix decreases from 1 to 0 with the increase of shear stress. Furthermore, the incipient plastic deformation of glassy matrix from S2 to S5 exhibits a more stochastic nature. The average first burst size (from 0.91 � 0.06153 nm of S2 to 0.69 � 0.05143 nm of S5), as well as the average STZ volume (from (3.75 � 0.159) � 10 2 nm3 of S2 to (2.10 � 0.105) � 10 2 nm3 of S5) estimated by the cooperative shear model, of the glassy matrix from S2 to S5 exhibits a decreasing trend. Besides, the STZ of larger volume promotes larger first burst size. 3. Based on HRTEM and ACF analyses, the incipient plasticity for amorphous phase as well as variation of hardness, and elastic modulus is attributed to the reduced initial free volume content and the amount of excess free volume created during nano indentation of the glassy matrix from S2 to S5. Theoretical analysis demonstrates that the STZ volume is directly proportional to the
9
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
content of the initial free volume. The glassy matrix with higher density and larger size of STZs can enhance the shear capability, promote the formation of multiple shear bands and lead to a more obvious plastic deformation. Acknowledgements The financial support from National Natural Science Foundation of China under Grant Nos. 51871076, 51671070, 51827801, 51671071, and 51671067, and the Kingboard Professorship Endowment of the University of Hong Kong are grateful acknowledged. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijplas.2019.09.005.
References Argon, A.S., 1979. Plastic deformation in metallic glasses. Acta Metall. 27, 47–58. Bian, Z., Kato, H., Qin, C.L., Zhang, W., Inoue, A., 2005. Cu–Hf–Ti–Ag–Ta bulk metallic glass composites and their properties. Acta Mater. 53, 2037–2048. Bolshakov, A., Pharr, G.M., 2011. Influences of pileup on the measurement of mechanical properties by load and depth sensing indentation techniques. J. Mater. Res. 13, 1049–1058. Chen, J., Wang, W., Qian, L.H., Lu, K., 2003. Critical shear stress for onset of plasticity in a nanocrystalline Cu determined by using nanoindentation. Scr. Mater. 49, 645–650. Chen, J.H., Chen, Y., Jiang, M.Q., Chen, X.W., Zhang, H.F., Dai, L.H., 2015. On the compressive failure of tungsten fiber reinforced Zr-based bulk metallic glass composite. Int. J. Solids Struct. 69–70, 428–441. Cheng, Y.-T., Cheng, C.-M., 2004. Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng. R 44, 91–149. Cheng, Y.Q., Ma, E., 2011. Atomic-level structure and structure–property relationship in metallic glasses. Prog. Mater. Sci. 56, 379–473. Chiu, Y.L., Ngan, A.H.W., 2002. Time-dependent characteristics of incipient plasticity in nanoindentation of a Ni3Al single crystal. Acta Mater. 50, 1599–1611. Choi, I.C., Zhao, Y., Kim, Y.J., Yoo, B.G., Suh, J.Y., Ramamurty, U., Jang, J.I., 2012. Indentation size effect and shear transformation zone size in a bulk metallic glass in two different structural states. Acta Mater. 60, 6862–6868. Dong, J., Gao, M., Huan, Y., Feng, Y.H., Liu, W., Wang, W.H., 2017. Enhanced tensile plasticity of Zr based bulk metallic glasses by a stress induced large scale flow. J. Alloy. Comp. 727, 297–303. Fan, G.Y., Cowley, J.M., 1985. Auto-correlation analysis of high resolution electron micrographs of near-amorphous thin films. Ultramicroscopy 17, 345–355. Feng, G., Ngan, A.H.W., 2002. Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J. Mater. Res. 17, 660–668. Gerberich, W.W., Nelson, J.C., Lilleodden, E.T., Anderson, P., Wyrobek, J.T., 1996. Indentation induced dislocation nucleation: the initial yield point. Acta Mater. 44, 3585–3598. Greer, A.L., Cheng, Y.Q., Ma, E., 2013. Shear bands in metallic glasses. Mater. Sci. Eng. R 74, 71–132. Huang, Y.J., Khong, J.C., Connolley, T., Mi, J., 2014. The onset of plasticity of a Zr-based bulk metallic glass. Int. J. Plast. 60, 87–100. Huang, Y.J., Khong, J.C., Connolley, T., Mi, J., 2014. Understanding the deformation mechanism of individual phases of a ZrTi-based bulk metallic glass matrix composite using in situ diffraction and imaging methods. Appl. Phys. Lett. 104, 031912. Huang, Y.J., Shen, J., Chen, J.J.J., Sun, J.F., 2009. Critical cooling rate and thermal stability for a Ti–Zr–Ni–Cu–Be metallic glass. J. Alloy. Comp. 477, 920–924. Huang, Y.J., Shen, J., Sun, J.F., 2007. Bulk metallic glasses: smaller is softer. Appl. Phys. Lett. 90, 081919. Huang, Y.J., Zhou, B.J., Chiu, Y.L., Fan, H.B., Wang, D.J., Sun, J.F., Shen, J., 2014. The structural relaxation effect on the nanomechanical properties of a Ti-based bulk metallic glass. J. Alloy. Comp. 608, 148–152. Jiang, S.S., Huang, Y.J., Wu, F.F., Xue, P., Sun, J.F., 2018. A CuZr-based bulk metallic glass composite with excellent mechanical properties by optimizing microstructure. J. Non-Cryst. Solids 483, 94–98. Jiang, W.H., Liu, F.X., Wang, Y.D., Zhang, H.F., Choo, H., Liaw, P.K., 2006. Comparison of mechanical behavior between bulk and ribbon Cu-based metallic glasses. Mater. Sci. Eng. A 430, 350–354. Johnson, K.L., 1985. Contact Mechanics. Cambridge University Press, Cambridge. Johnson, W.L., 1999. Bulk glass-forming metallic alloys: science and technology. MRS Bull. 24, 42–56. Johnson, W.L., Samwer, K., 2005. A universal criterion for plastic yielding of metallic glasses with a (T/Tg) 2/3 temperature dependence. Phys. Rev. Lett. 95, 195501. Lee, M.L., Li, Y., Schuh, C.A., 2004. Effect of a controlled volume fraction of dendritic phases on tensile and compressive ductility in La-based metallic glass matrix composites. Acta Mater. 52, 4121–4131. Li, H., Ngan, A.H.W., Wang, M.G., 2005. Continuous strain bursts in crystalline and amorphous metals during plastic deformation by nanoindentation. J. Mater. Res. 20, 3072–3081. Liang, J.M., Chen, L.J., 1994. Autocorrelation function analysis of phase formation in the initial stage of interfacial reactions of molybdenum thin films on (111)Si. Appl. Phys. Lett. 64, 1224–1226. Liu, L., Chan, K.C., 2005. Plastic deformation of Zr-based bulk metallic glasses under nanoindentation. Mater. Lett. 59, 3090–3094. Liu, Y.Y., Liu, P.Z., Li, J.J., Liaw, P.K., Spieckermann, F., Kiener, D., Qiao, J.W., Eckert, J., 2018. Universally scaling Hall-Petch-like relationship in metallic glass matrix composites. Int. J. Plast. 105, 225–238. Liu, Z.Q., Li, R., Liu, G., Su, W.H., Wang, H., Li, Y., Shi, M.J., Luo, X.K., Wu, G.J., Zhang, T., 2012. Microstructural tailoring and improvement of mechanical properties in CuZr-based bulk metallic glass composites. Acta Mater. 60, 3128–3139. Ma, Y., Peng, G.J., Feng, Y.H., Zhang, T.H., 2016. Nanoindentation investigation on the creep mechanism in metallic glassy films. Mater. Sci. Eng. A 651, 548–555. Narayan, R.L., Raut, D., Ramamurty, U., 2018. A quantitative connection between shear band mediated plasticity and fracture initiation toughness of metallic glasses. Acta Mater. 150, 69–77. Narayan, R.L., Singh, P.S., Hofmann, D.C., Hutchinson, N., Flores, K.M., Ramamurty, U., 2012. On the microstructure–tensile property correlations in bulk metallic glass matrix composites with crystalline dendrites. Acta Mater. 60, 5089–5100. Ng, K.Y., Zuo, L., Ngan, A.H.W., 2009. Steady-state serrated deformation of metallic glass during indentation. Scr. Mater. 61, 955–958. Ngan, A.H.W., Ng, K.S., 2010. Transition from deterministic to stochastic deformation. Philos. Mag. 90, 1937–1954. Oliver, W.C., Pharr, G.M., 1992. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564–1583. Pan, D., Inoue, A., Sakurai, T., Chen, M.W., 2008. Experimental characterization of shear transformation zones for plastic flow of bulk metallic glasses. Proc. Natl. Acad. Sci. U.S.A. 105, 14769–14772. Pan, J., Wang, Y.X., Li, Y., 2017. Ductile fracture in notched bulk metallic glasses. Acta Mater. 136, 126–133. Pauly, S., Gorantla, S., Wang, G., Kuhn, U., Eckert, J., 2010. Transformation-mediated ductility in CuZr-based bulk metallic glasses. Nat. Mater. 9, 473–477.
10
International Journal of Plasticity xxx (xxxx) xxx
S.S. Jiang et al.
Perepezko, J.H., Imhoff, S.D., Chen, M.W., Wang, J.Q., Gonzalez, S., 2014. Nucleation of shear bands in amorphous alloys. Proc. Natl. Acad. Sci. U.S.A. 111, 3938–3942. Qiao, J.C., Pelletier, J.M., 2014. Dynamic mechanical relaxation in bulk metallic glasses: a review. J. Mater. Sci. Technol. 30, 523–545. Qiao, J.C., Yao, Y., Pelletier, J.M., Keer, L.M., 2016. Understanding of micro-alloying on plasticity in Cu46Zr47 xAl7Dyx (0�x� 8) bulk metallic glasses under compression: based on mechanical relaxations and theoretical analysis. Int. J. Plast. 82, 62–75. Qiao, J.W., Sun, A.C., Huang, E.W., Zhang, Y., Liaw, P.K., Chuang, C.P., 2011. Tensile deformation micromechanisms for bulk metallic glass matrix composites: from work-hardening to softening. Acta Mater. 59, 4126–4137. Savitzky, A., Golay, M.J.E., 1964. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627–1639. Schuh, C.A., Lund, A.C., 2004. Application of nucleation theory to the rate dependence of incipient plasticity during nanoindentation. J. Mater. Res. 19, 2152–2158. Sha, Z., Branicio, P.S., Lee, H.P., Tay, T.E., 2017. Strong and ductile nanolaminate composites combining metallic glasses and nanoglasses. Int. J. Plast. 90, 231–241. Song, K.K., Pauly, S., Zhang, Y., Li, R., Gorantla, S., Narayanan, N., Kühn, U., Gemming, T., Eckert, J., 2012. Triple yielding and deformation mechanisms in metastable Cu47.5Zr47.5Al5 composites. Acta Mater. 60, 6000–6012. Spaepen, F., 1977. A microscopic mechanism for steady state inhomogeneous flow in metallic glasses. Acta Metall. 25, 407–415. Sun, B.A., Song, K.K., Pauly, S., Gargarella, P., Yi, J., Wang, G., Liu, C.T., Eckert, J., Yang, Y., 2016. Transformation-mediated plasticity in CuZr based metallic glass composites: a quantitative mechanistic understanding. Int. J. Plast. 85, 34–51. Van Steenberge, N., Sort, J., Concustell, A., Das, J., Scudino, S., Suri~ nach, S., Eckert, J., Bar� o, M.D., 2007. Dynamic softening and indentation size effect in a Zr-based bulk glass-forming alloy. Scr. Mater. 56, 605–608. Wang, D.M., Chen, Y., Mu, J., Zhu, Z.W., Zhang, H.F., Wang, Y.D., An, K., 2018. An in situ neutron diffraction study of plastic deformation in a Cu46.5Zr46.5Al7 bulk metallic glass composite. Scr. Mater. 153, 118–121. Wang, G., Huang, Y.J., Shen, J., 2012. Novel TiCuNiCo composites with high fracture strength and plasticity. Mater. Des. 33, 226–230. Wang, W.H., Dong, C., Shek, C.H., 2004. Bulk metallic glasses. Mater. Sci. Eng. R 44, 45–89. Wu, F.F., Chan, K.C., Jiang, S.S., Chen, S.H., Wang, G., 2014. Bulk metallic glass composite with good tensile ductility, high strength and large elastic strain limit. Sci. Rep. 4, 5302. Wu, F.F., Chan, K.C., Li, S.T., Wang, G., 2013. Stabilized shear banding of ZrCu-based metallic glass composites under tensile loading. J. Mater. Sci. 49, 2164–2170. Wu, Y., Ma, D., Li, Q.K., Stoica, A.D., Song, W.L., Wang, H., Liu, X.J., Stoica, G.M., Wang, G.Y., An, K., Wang, X.L., Li, M., Lu, Z.P., 2017. Transformation-induced plasticity in bulk metallic glass composites evidenced by in-situ neutron diffraction. Acta Mater. 124, 478–488. Wu, Y., Wang, H., Wu, H.H., Zhang, Z.Y., Hui, X.D., Chen, G.L., Ma, D., Wang, X.L., Lu, Z.P., 2011. Formation of Cu–Zr–Al bulk metallic glass composites with improved tensile properties. Acta Mater. 59, 2928–2936. Wu, Y., Wu, H.H., Hui, X.D., Chen, G.L., Lu, Z.P., 2010. Effects of drawing on the tensile fracture strength and its reliability of small-sized metallic glasses. Acta Mater. 58, 2564–2576. Wu, Y., Xiao, Y.H., Chen, G.L., Liu, C.T., Lu, Z.P., 2010. Bulk metallic glass composites with transformation-mediated work-hardening and ductility. Adv. Mater. 22, 2770–2773. Zhang, Z.Y., Yang, S., Xu, C.G., Wang, B., Duan, N.D., 2014. Deformation and stress at pop-in of lithium niobate induced by nanoindentation. Scr. Mater. 77, 56–59.
11