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Effect of Aspect Ratio on the Evolution of Shear Bands in Zr61.7Al8Ni13Cu17Sn0.3 Bulk Metallic Glass
ARTICLE IN PRESS Journal of Materials Science & Technology ■■ (2015) ■■–■■
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Effect of Aspect Ratio on the Evolution of Shear Bands in Zr61.7Al8Ni13Cu17Sn0.3 Bulk Metallic Glass Wenli Ma, Yuanli Xu, Bo Shi, Jiangong Li * Institute of Materials Science and Engineering and MOE Key Laboratory for Magnetism and Magnetic Materials, Lanzhou University, Lanzhou 730000, China
A R T I C L E
I N F O
Article history: Received 5 February 2015 Received in revised form 28 April 2015 Accepted 4 May 2015 Available online Key words: Metallic glass Aspect ratio Shear band Compressive deformation
Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with different aspect ratios in the range of 0.25–2.25 were deformed by compression, and the effect of aspect ratio on the evolution of shear bands was investigated. It is found that for the deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass, the average shear band spacing decreases and the shear band density increases monotonically as the aspect ratio increases from 0.25 to 2.25. A minimal average shear band spacing of 0.478 μm is achieved for the sample with an aspect ratio of 2.25. In addition, the fractions of shear bands with spacings below 100 and 50 nm are about 12.84% and 6.76%, respectively, for the sample with an aspect ratio of 2.25. The reason for the formation of a higher density of shear bands can probably be attributed to the increase of the driving force for the sample with a larger aspect ratio. Copyright © 2015, The editorial office of Journal of Materials Science & Technology. Published by Elsevier Limited. All rights reserved.
1. Introduction Metallic glasses possess excellent properties, such as high strength, high hardness, and large elastic limit[1–3]. At low temperatures and high strain rates, the plastic deformation of metallic glasses occurs in an inhomogeneous mode and the plastic flow is localized in narrow regions called “shear bands”[4]. It was found that the density and distribution of shear bands have a significant effect on the properties of metallic glasses[5,6]. For example, the phenomena of “work-hardening” capability and ductility improvement were found in Cu47.5Zr47.5Al5 metallic glass after inhomogeneous plastic deformation, which were attributed to the introduction of multiple intersected shear bands[7]. Obviously, it is important to investigate the distribution of the shear bands as well as the evolution of shear band density in metallic glasses endured inhomogeneous plastic deformation. Theoretically speaking, there are many factors (for example, strain, strain rate, aspect ratio, the stiffness of testing machine, and the size effect) impacting the density and distribution of shear bands[8–12]. Among them, aspect ratio is one of the most important factors, and many efforts have been made to study the effect of the aspect ratio on the mechanical behaviors of metallic glasses in the past decades[12–15]. Zhang et al. investigated the
* Corresponding author. Prof., Ph.D.; Tel.: +86 931 8910364; Fax: +86 931 8910364. E-mail address: [email protected] (J. Li).
compressive deformation and fracture features of Zr59Cu20Al10Ni8Ti3 bulk metallic glass samples with aspect ratios in the range of 0.67– 2.00 and found a large compressive ductility in the sample with an aspect ratio of 0.67[15]. Han et al. pointed out that a better plasticity could be achieved for Zr64.13Cu15.75Ni10.12Al10 bulk metallic glasses with an aspect ratio of 1[14]. Liu et al. performed compression tests on Zr55Al10Ni5Cu30 metallic glass samples with different aspect ratios from 2 to 4, and the sample with an aspect ratio of 2.5 showed the best plasticity[12]. Sha et al. investigated the effect of aspect ratio on plasticity for Cu50Zr50 metallic glass during a tensile deformation process[16]. However, most of these works mentioned above only concerned the effect of aspect ratio on the plasticity of metallic glasses. The effect of aspect ratio on the density and distribution of shear bands for metallic glasses endured inhomogeneous plastic deformation has not been systematically studied so far. Since the density and distribution of shear bands have a significant effect on the properties of metallic glasses, it is undoubtedly of interest to study how aspect ratio affects the evolution of shear bands for metallic glasses endured inhomogeneous deformation. In the present work, the effect of aspect ratio on the distribution of shear bands and the evolution of shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured uniaxial compression deformation was investigated. It is found that the shear band density increases monotonically with increasing aspect ratio. For the sample with an aspect ratio of 2.25 and endured 80% compressive plastic deformation, a minimal shear band spacing with an average value of 0.478 μm is achieved, and the fractions of the shear
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bands with spacings below 100 and 50 nm are about 12.84% and 6.76%, respectively. 2. Experimental Master alloy ingots with a composition of Zr61.7Al8Ni13Cu17Sn0.3 were prepared by arc-melting the mixtures of pure Zr (99.99%), Al (99.99%), Ni (99.99%), Cu (99.99%), and Sn (99.99%) in a Ti-gettered argon atmosphere. The master alloy ingots were re-melted six times to ensure the compositional homogeneity and subsequently suctioncasted into a copper mold with a size of 2 mm × 2 mm × 70 mm. The as-cast metallic glass samples were cut into different heights of 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and 4.5 mm, and hence samples with different aspect ratios in the range of 0.25–2.25 were obtained. Before compression deformation, the samples with different aspect ratios were polished mechanically to make the upper and lower plane parallel. The uniaxial compression deformation was conducted at room temperature using a WDW-100D testing machine at a strain rate of 1.0 × 10−2 s−1. The amorphous nature of the as-cast and deformed samples was examined by a Rigaku D/max-2400 X-ray diffractometer (XRD) using CuKα radiation (wavelength of 0.154187 nm). The morphology of shear bands on the deformed samples was analyzed by scanning electron microscopy (SEM) using a Hitachi S-4800 field emission scanning electron microscope. Transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) observations, and selected area electron diffraction (SAED) analysis were performed on the as-cast and deformed samples using an FEI Tecnai G2 F30 electron microscope operating at a voltage of 300 kV. The process of statistics on the shear bands in this work is as follows: (1) 20 SEM images at the magnification of 50 000 were selected at random for each sample. (2) The center of each SEM image is regarded as the center of a circle and the circle is drawn on the image (the radius of the circle equals to the half of the distance between the upper and the lower sides of the SEM image). (3) Four diameter line segments separating the circle equally are drawn. (4) The intersection number between the diameter line segments and the shear bands is counted. (5) If we use n to represent the whole intersection number between the diameter line segments and the shear band in the corresponding 20 SEM images, d to represent the diameter of the circle, ρ the statistical shear band density, the shear band density of each sample, ρ = n/(20 × 4d). The average shear band spacing in this work equals 1/ρ.
3. Results and Discussion Fig. 1(a) shows the XRD patterns of the as-cast sample and the deformed samples with different aspect ratios. A distinct diffraction halo at about 2θ = 38° without diffraction peaks corresponding to crystalline phases can be observed for the as-cast sample, indicating that the as-cast sample is amorphous. To further confirm the amorphous nature of the as-cast sample, HRTEM analysis was conducted and the corresponding HRTEM image, as well as the SAED pattern, is shown in Fig. 1(b). A homogeneous contrast without obvious lattice fringes can be found in the corresponding HRTEM image. In addition, the SAED pattern shown in the inset of Fig. 1(b) consists of a broad diffraction halo and a faint large one, which are typical for amorphous materials. Therefore, the as-cast Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass is completely amorphous. To examine whether crystallization occurred in the deformed samples, the deformed samples with different aspect ratios of 0.25– 2.25 were analyzed by XRD. The XRD patterns for these samples endured 80% compressive plastic deformation at a strain rate of 1.0 × 10−2 s−1 are shown in Fig. 1(a). Similar to that for the as-cast sample, the XRD patterns for these deformed samples also exhibit only a broad diffraction halo of around 2θ of 38°, indicating that the deformed samples are amorphous. In addition, the bright field TEM image for the 80% deformed sample with an aspect ratio of 2.25 is shown in Fig. 1(c). No other strong contrast than the bright “bandlike” regions can be observed in this image. Obviously, these bright regions should be shear bands as they were usually observed with a bright contrast in the bright field TEM images due to the lower atomic density in these regions[17]. The corresponding SAED pattern in the inset of Fig. 1(c) consists of one broad diffraction halo and a faint larger one without obvious diffraction spots, which are indicative of amorphous nature. Therefore, only shear bands form and no crystallization occurs in the 80% deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass sample with an aspect ratio of 2.25. Fig. 2 shows the side-viewed SEM images of the deformed samples with aspect ratios of 0.25–2.25. Intersected and branched shear bands can be observed on the surfaces of these deformed samples. When the aspect ratio increases from 0.25 to 0.75 (Fig. 2(a–c)), it can be found that parallel shear bands mainly exist, and a few intersected and branched shear bands can be observed along the parallel shear bands. At the same time, fine shear bands begin to appear when the aspect ratio is 0.75. With increasing aspect ratio from 1.00 to 1.50 (Fig. 2(d–f)), intersected and branched shear
Fig. 1. (a) XRD patterns of the as-cast Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass and the deformed samples with a strain of 80% deformed at strain rate of 1.0 × 10−2 s−1 with aspect ratios of 0.25–2.25; (b) HRTEM micrograph and the SAED pattern of the as-cast Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass; and (c) TEM (an SAED pattern in the inset) of the 80% deformed sample with an aspect ratio of 2.25.
Please cite this article in press as: Wenli Ma, Yuanli Xu, Bo Shi, Jiangong Li, Effect of Aspect Ratio on the Evolution of Shear Bands in Zr61.7Al8Ni13Cu17Sn0.3 Bulk Metallic Glass, Journal of Materials Science & Technology (2015), doi: 10.1016/j.jmst.2015.12.020
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Fig. 2. SEM images for the deformed Zr61.7Al8Ni13Cu17Sn0.3 metallic glass samples endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1 with aspect ratios of 0.25 (a), 0.50 (b), 0.75 (c), 1.00 (d), 1.25 (e), 1.50 (f), 1.75 (g), 2.00 (h), and 2.25 (i).
bands gradually increase and the number of fine shear bands continues to grow. It seems that the shear band density increases for these samples compared with that for the sample with low aspect ratios of 0.25 to 0.75. When the aspect ratio increases further (from 1.75 to 2.25) as shown in Fig. 2(g–i), more intersected, branched and fine shear bands can be observed. Especially for the sample with the maximum aspect ratio of 2.25, a high density of intersected, branched and fine shear bands with a minimal spacing forms after 80% compressive plastic deformation (Fig. 2(i)). Hence, the shear band density increases further for these deformed samples with larger aspect ratios. Therefore, a large number of shear bands form on the side surface of these deformed samples with different aspect ratios, and fine shear bands increase with increasing aspect ratio. To further investigate the variation of shear band evolution with increasing aspect ratio for the 80% deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass, statistics was performed on shear band spacing for these deformed samples with different aspect ratios. Fig. 3 presents the statistical distribution of shear band spacing in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with aspect ratios
of 0.25, 1.00, 1.50, and 2.25. It can be observed that the spacings of most shear bands are between 1.1 and 1.2 μm for the sample with the aspect ratio of 0.25 (Fig. 3(a)). For the sample with the aspect ratio of 1.00 (Fig. 3(b)), the spacings of most shear bands are reduced to the range between 0.6 and 0.8 μm. When the aspect ratio increases to 1.50 (Fig. 3(c)), the spacings of most shear bands are reduced to a range of 0.5–0.6 μm. For the sample with the largest aspect ratio of 2.25 (Fig. 3(d)), the spacings of most shear bands are in the range of 0.3–0.4 μm. The statistical results shown here are consistent with the corresponding SEM observations shown in Fig. 2, and both of them indicate that with increasing aspect ratio the average shear band spacing decreases for the deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glasses. Fig. 4 shows the variation of the shear band density and average shear band spacing with increasing aspect ratio for the 80% deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples. For the sample with an aspect ratio of 0.25, the average shear band spacing is 1.388 μm and the corresponding shear band density is 0.720 μm−1. When the aspect ratio increases from 0.25 to 1.00, the average shear
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Fig. 3. Statistical distribution of shear band spacing in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1 with aspect ratios of 0.25 (a), 1.00 (b), 1.50 (c), and 2.25 (d).
band spacing decreases from 1.388 to 0.787 μm. Meanwhile, the average shear band spacing decreases from 0.787 to 0.761 μm with increasing aspect ratio from 1.00 to 1.50. The average shear band spacing decreases obviously from 0.761 to 0.478 μm when the aspect ratio increases from 1.50 to 2.25. Accordingly, the variation of the shear band density increases. As compared to the shear band density of 0.720 μm−1 for the sample with an aspect ratio of 0.25, the shear band density increases monotonously to 2.092 μm−1 for the sample with an aspect ratio of 2.25. In one word, the average shear band spacing decreases from 1.388 to 0.478 μm and the corresponding shear band density increases from 0.720 to 2.092 μm−1 with aspect ratio increasing from 0.25 to 2.25. For the sample with an aspect
ratio of 2.25, the average shear band spacing is as small as 0.478 μm and the shear band density is as high as 2.092 μm−1. The variation trend of the shear band density, as well as the corresponding average shear band spacing for the samples endured smaller deformation strains such as 7% and 45% (not shown here), is similar to that for the samples endured a deformation strain of 80%. Hence, the shear band density increases and the corresponding average shear band spacing decreases with increasing aspect ratio for Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass. Fig. 5 shows the fractions of shear bands with spacings below 100 and 50 nm in all shear bands for the Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with different aspect ratios. As the aspect ratio
Fig. 4. Variation trend for the effect of aspect ratio on the average shear band spacing and shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1.
Fig. 5. Ratio distribution of shear bands with spacings below 100 and 50 nm in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1 with different aspect ratios.
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increases from 0.25 to 0.50, no shear band with spacings below 100 nm can be found. For the sample with an aspect ratio of 0.75, the fraction of shear bands with spacings below 100 nm is 1.35%. As the aspect ratio increases from 1.25 to 2.00, the fraction of shear bands with spacings below 100 nm is larger than that for the sample with an aspect ratio of 0.75 and increases with increasing aspect ratio. For the sample with the largest aspect ratio of 2.25, the fraction of shear bands with spacings below 100 nm accounts for about 12.84%, which is maximal in all these samples with different aspect ratios. Furthermore, the variation trend in the fraction of shear bands with spacings below 50 nm with increasing aspect ratio is similar to that in the fraction of shear bands with spacings below 100 nm. For the sample with an aspect ratio of 2.25, the fraction of shear bands with spacings below 50 nm accounts for about 6.76%, which is also maximal in all the samples with different aspect ratios. Therefore, as the aspect ratio increases, the fractions of shear bands with spacings below 100 and 50 nm both increase. Based on the experimental results described above, it can be considered that the evolution of shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glasses is strongly affected by aspect ratio. According to the shear band phase (SBP) model proposed by Liu et al., the initiation and propagation of shear bands may be treated as a quasi-phase transition process[12]. When a new phase (shear bands) forms, the transition results in an increase in volume free energy (the difference in free energy per unit volume between the SBP and glassy matrix) and produces new interfaces between the SBP and glassy matrix, giving rise to an interfacial free energy[18]. It is known that the driving force for SBP transition process is the stored elastic energy in samples[19,20]. Therefore, the driving force for the SBP transition is the stored elastic energy ΔGE, while the resistance is the increasing volume free energy ΔGV and the interfacial free energy ΔGI. If the driving force overcomes the resistance, the SBP transition is theoretically favored[21–25]. Here, we take a metallic glass bar with a square cross section as an example, and the dimension of this metallic glass bar is d02 × L0 (d0 is the side length of the square cross section and L0 is the height of a bar). Because all the samples failure occurs via a single shear band, according to the results proposed by Sha et al.[16], the change in the elastic energy ΔGE of the sample upon forming a shear band with the aspect ratio of λ can be obtained:
ΔG E = Ed 02ε 0kl −
Ed 0l 2k 2 2λ
(1)
where E is the Young’s modulus of the sample, d0 is the side length of the sample, ε0 is the critical strain, at which a shear band forms, and k is a positive constant[12], l is the length of a formed shear band, and λ is the aspect ratio of the sample. According to Eq. (1), because E, d0, ε0, and l are independent of the aspect ratio of metallic glass samples[16], the stored elastic energy ΔGE will be larger when the aspect ratio is larger[16]. From this respect, the elastic energy may be an important factor affecting the shear band density as well as shear band spacing, as proposed by Chen et al.[26]. According to the results presented by Liu et al., the increase in the volume free energy after the formation of a shear band can be expressed as
ΔG V = g 0V max
ΔG I = σ S max
where σ is the interfacial free energy per unit interface area, and Smax represents the total area of the upper and lower interfacial areas between the SBP and MG phases, as well as the interfacial area at shear band tip[12]. Theoretically, for a formed shear band, Vmax in Eq. (2) and Smax in Eq. (3) are both constant, so ΔGV and ΔGI are constant, too. According to what was mentioned above, the driving force for the initiation and propagation of shear bands will be larger when the aspect ratio is larger[16], and the resistance (the increase in the volume free energy and the newly generated interfacial free energy induced by forming a shear band) is constant. Therefore, with increasing aspect ratio, the change of the total energy ΔG = ΔGE + ΔGV + ΔGI increases. This means that the stored energy in the sample is increased. This energy is the driving force to form another shear band. On this basis, the driving force for the formation of new shear bands is higher for a metallic glass sample with a larger aspect ratio. Therefore, it becomes easier for more shear bands to initiate and propagate as the aspect ratio increases. According to the above analysis, a higher aspect ratio is favorable for forming greater amount of shear bands. This is consistent with our results. Namely, Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass sample with a higher aspect ratio exhibits a higher density of shear bands after uniaxial compressive deformation.
4. Conclusion It is found that the distribution of the shear bands and the evolution of shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass strongly depend on the aspect ratio during the compressive deformation. For the deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass, the shear band density increases with increasing aspect ratio. A minimal shear band spacing with an average spacing of 0.478 μm was achieved for the sample with an aspect ratio of 2.25. In addition, the fractions of shear bands with spacings below 100 and 50 nm are about 12.84% and 6.76%, respectively, for the sample with an aspect ratio of 2.25. The driving force for the initiation and propagation of shear bands will be larger if the aspect ratio is larger. Obviously, the driving force for the formation of new shear bands is higher for the sample with a larger aspect ratio. This can probably explain why the Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with a higher aspect ratio exhibit a higher density of shear bands after uniaxial compression deformation.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51071079, 51272098, and 51301080).
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(2) [7]
where g0 is the increase in the volume free energy per unit volume, and Vmax is the total volume of forming a SBP zone[12]. Moreover, the newly generated interfacial free energy after the formation of a shear band can be given by (3)
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Contents lists available at ScienceDirect
Journal of Materials Science & Technology j o u r n a l h o m e p a g e : w w w. j m s t . o r g
Effect of Aspect Ratio on the Evolution of Shear Bands in Zr61.7Al8Ni13Cu17Sn0.3 Bulk Metallic Glass Wenli Ma, Yuanli Xu, Bo Shi, Jiangong Li * Institute of Materials Science and Engineering and MOE Key Laboratory for Magnetism and Magnetic Materials, Lanzhou University, Lanzhou 730000, China
A R T I C L E
I N F O
Article history: Received 5 February 2015 Received in revised form 28 April 2015 Accepted 4 May 2015 Available online Key words: Metallic glass Aspect ratio Shear band Compressive deformation
Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with different aspect ratios in the range of 0.25–2.25 were deformed by compression, and the effect of aspect ratio on the evolution of shear bands was investigated. It is found that for the deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass, the average shear band spacing decreases and the shear band density increases monotonically as the aspect ratio increases from 0.25 to 2.25. A minimal average shear band spacing of 0.478 μm is achieved for the sample with an aspect ratio of 2.25. In addition, the fractions of shear bands with spacings below 100 and 50 nm are about 12.84% and 6.76%, respectively, for the sample with an aspect ratio of 2.25. The reason for the formation of a higher density of shear bands can probably be attributed to the increase of the driving force for the sample with a larger aspect ratio. Copyright © 2015, The editorial office of Journal of Materials Science & Technology. Published by Elsevier Limited. All rights reserved.
1. Introduction Metallic glasses possess excellent properties, such as high strength, high hardness, and large elastic limit[1–3]. At low temperatures and high strain rates, the plastic deformation of metallic glasses occurs in an inhomogeneous mode and the plastic flow is localized in narrow regions called “shear bands”[4]. It was found that the density and distribution of shear bands have a significant effect on the properties of metallic glasses[5,6]. For example, the phenomena of “work-hardening” capability and ductility improvement were found in Cu47.5Zr47.5Al5 metallic glass after inhomogeneous plastic deformation, which were attributed to the introduction of multiple intersected shear bands[7]. Obviously, it is important to investigate the distribution of the shear bands as well as the evolution of shear band density in metallic glasses endured inhomogeneous plastic deformation. Theoretically speaking, there are many factors (for example, strain, strain rate, aspect ratio, the stiffness of testing machine, and the size effect) impacting the density and distribution of shear bands[8–12]. Among them, aspect ratio is one of the most important factors, and many efforts have been made to study the effect of the aspect ratio on the mechanical behaviors of metallic glasses in the past decades[12–15]. Zhang et al. investigated the
* Corresponding author. Prof., Ph.D.; Tel.: +86 931 8910364; Fax: +86 931 8910364. E-mail address: [email protected] (J. Li).
compressive deformation and fracture features of Zr59Cu20Al10Ni8Ti3 bulk metallic glass samples with aspect ratios in the range of 0.67– 2.00 and found a large compressive ductility in the sample with an aspect ratio of 0.67[15]. Han et al. pointed out that a better plasticity could be achieved for Zr64.13Cu15.75Ni10.12Al10 bulk metallic glasses with an aspect ratio of 1[14]. Liu et al. performed compression tests on Zr55Al10Ni5Cu30 metallic glass samples with different aspect ratios from 2 to 4, and the sample with an aspect ratio of 2.5 showed the best plasticity[12]. Sha et al. investigated the effect of aspect ratio on plasticity for Cu50Zr50 metallic glass during a tensile deformation process[16]. However, most of these works mentioned above only concerned the effect of aspect ratio on the plasticity of metallic glasses. The effect of aspect ratio on the density and distribution of shear bands for metallic glasses endured inhomogeneous plastic deformation has not been systematically studied so far. Since the density and distribution of shear bands have a significant effect on the properties of metallic glasses, it is undoubtedly of interest to study how aspect ratio affects the evolution of shear bands for metallic glasses endured inhomogeneous deformation. In the present work, the effect of aspect ratio on the distribution of shear bands and the evolution of shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured uniaxial compression deformation was investigated. It is found that the shear band density increases monotonically with increasing aspect ratio. For the sample with an aspect ratio of 2.25 and endured 80% compressive plastic deformation, a minimal shear band spacing with an average value of 0.478 μm is achieved, and the fractions of the shear
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bands with spacings below 100 and 50 nm are about 12.84% and 6.76%, respectively. 2. Experimental Master alloy ingots with a composition of Zr61.7Al8Ni13Cu17Sn0.3 were prepared by arc-melting the mixtures of pure Zr (99.99%), Al (99.99%), Ni (99.99%), Cu (99.99%), and Sn (99.99%) in a Ti-gettered argon atmosphere. The master alloy ingots were re-melted six times to ensure the compositional homogeneity and subsequently suctioncasted into a copper mold with a size of 2 mm × 2 mm × 70 mm. The as-cast metallic glass samples were cut into different heights of 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, and 4.5 mm, and hence samples with different aspect ratios in the range of 0.25–2.25 were obtained. Before compression deformation, the samples with different aspect ratios were polished mechanically to make the upper and lower plane parallel. The uniaxial compression deformation was conducted at room temperature using a WDW-100D testing machine at a strain rate of 1.0 × 10−2 s−1. The amorphous nature of the as-cast and deformed samples was examined by a Rigaku D/max-2400 X-ray diffractometer (XRD) using CuKα radiation (wavelength of 0.154187 nm). The morphology of shear bands on the deformed samples was analyzed by scanning electron microscopy (SEM) using a Hitachi S-4800 field emission scanning electron microscope. Transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM) observations, and selected area electron diffraction (SAED) analysis were performed on the as-cast and deformed samples using an FEI Tecnai G2 F30 electron microscope operating at a voltage of 300 kV. The process of statistics on the shear bands in this work is as follows: (1) 20 SEM images at the magnification of 50 000 were selected at random for each sample. (2) The center of each SEM image is regarded as the center of a circle and the circle is drawn on the image (the radius of the circle equals to the half of the distance between the upper and the lower sides of the SEM image). (3) Four diameter line segments separating the circle equally are drawn. (4) The intersection number between the diameter line segments and the shear bands is counted. (5) If we use n to represent the whole intersection number between the diameter line segments and the shear band in the corresponding 20 SEM images, d to represent the diameter of the circle, ρ the statistical shear band density, the shear band density of each sample, ρ = n/(20 × 4d). The average shear band spacing in this work equals 1/ρ.
3. Results and Discussion Fig. 1(a) shows the XRD patterns of the as-cast sample and the deformed samples with different aspect ratios. A distinct diffraction halo at about 2θ = 38° without diffraction peaks corresponding to crystalline phases can be observed for the as-cast sample, indicating that the as-cast sample is amorphous. To further confirm the amorphous nature of the as-cast sample, HRTEM analysis was conducted and the corresponding HRTEM image, as well as the SAED pattern, is shown in Fig. 1(b). A homogeneous contrast without obvious lattice fringes can be found in the corresponding HRTEM image. In addition, the SAED pattern shown in the inset of Fig. 1(b) consists of a broad diffraction halo and a faint large one, which are typical for amorphous materials. Therefore, the as-cast Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass is completely amorphous. To examine whether crystallization occurred in the deformed samples, the deformed samples with different aspect ratios of 0.25– 2.25 were analyzed by XRD. The XRD patterns for these samples endured 80% compressive plastic deformation at a strain rate of 1.0 × 10−2 s−1 are shown in Fig. 1(a). Similar to that for the as-cast sample, the XRD patterns for these deformed samples also exhibit only a broad diffraction halo of around 2θ of 38°, indicating that the deformed samples are amorphous. In addition, the bright field TEM image for the 80% deformed sample with an aspect ratio of 2.25 is shown in Fig. 1(c). No other strong contrast than the bright “bandlike” regions can be observed in this image. Obviously, these bright regions should be shear bands as they were usually observed with a bright contrast in the bright field TEM images due to the lower atomic density in these regions[17]. The corresponding SAED pattern in the inset of Fig. 1(c) consists of one broad diffraction halo and a faint larger one without obvious diffraction spots, which are indicative of amorphous nature. Therefore, only shear bands form and no crystallization occurs in the 80% deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass sample with an aspect ratio of 2.25. Fig. 2 shows the side-viewed SEM images of the deformed samples with aspect ratios of 0.25–2.25. Intersected and branched shear bands can be observed on the surfaces of these deformed samples. When the aspect ratio increases from 0.25 to 0.75 (Fig. 2(a–c)), it can be found that parallel shear bands mainly exist, and a few intersected and branched shear bands can be observed along the parallel shear bands. At the same time, fine shear bands begin to appear when the aspect ratio is 0.75. With increasing aspect ratio from 1.00 to 1.50 (Fig. 2(d–f)), intersected and branched shear
Fig. 1. (a) XRD patterns of the as-cast Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass and the deformed samples with a strain of 80% deformed at strain rate of 1.0 × 10−2 s−1 with aspect ratios of 0.25–2.25; (b) HRTEM micrograph and the SAED pattern of the as-cast Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass; and (c) TEM (an SAED pattern in the inset) of the 80% deformed sample with an aspect ratio of 2.25.
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Fig. 2. SEM images for the deformed Zr61.7Al8Ni13Cu17Sn0.3 metallic glass samples endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1 with aspect ratios of 0.25 (a), 0.50 (b), 0.75 (c), 1.00 (d), 1.25 (e), 1.50 (f), 1.75 (g), 2.00 (h), and 2.25 (i).
bands gradually increase and the number of fine shear bands continues to grow. It seems that the shear band density increases for these samples compared with that for the sample with low aspect ratios of 0.25 to 0.75. When the aspect ratio increases further (from 1.75 to 2.25) as shown in Fig. 2(g–i), more intersected, branched and fine shear bands can be observed. Especially for the sample with the maximum aspect ratio of 2.25, a high density of intersected, branched and fine shear bands with a minimal spacing forms after 80% compressive plastic deformation (Fig. 2(i)). Hence, the shear band density increases further for these deformed samples with larger aspect ratios. Therefore, a large number of shear bands form on the side surface of these deformed samples with different aspect ratios, and fine shear bands increase with increasing aspect ratio. To further investigate the variation of shear band evolution with increasing aspect ratio for the 80% deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass, statistics was performed on shear band spacing for these deformed samples with different aspect ratios. Fig. 3 presents the statistical distribution of shear band spacing in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with aspect ratios
of 0.25, 1.00, 1.50, and 2.25. It can be observed that the spacings of most shear bands are between 1.1 and 1.2 μm for the sample with the aspect ratio of 0.25 (Fig. 3(a)). For the sample with the aspect ratio of 1.00 (Fig. 3(b)), the spacings of most shear bands are reduced to the range between 0.6 and 0.8 μm. When the aspect ratio increases to 1.50 (Fig. 3(c)), the spacings of most shear bands are reduced to a range of 0.5–0.6 μm. For the sample with the largest aspect ratio of 2.25 (Fig. 3(d)), the spacings of most shear bands are in the range of 0.3–0.4 μm. The statistical results shown here are consistent with the corresponding SEM observations shown in Fig. 2, and both of them indicate that with increasing aspect ratio the average shear band spacing decreases for the deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glasses. Fig. 4 shows the variation of the shear band density and average shear band spacing with increasing aspect ratio for the 80% deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples. For the sample with an aspect ratio of 0.25, the average shear band spacing is 1.388 μm and the corresponding shear band density is 0.720 μm−1. When the aspect ratio increases from 0.25 to 1.00, the average shear
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Fig. 3. Statistical distribution of shear band spacing in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1 with aspect ratios of 0.25 (a), 1.00 (b), 1.50 (c), and 2.25 (d).
band spacing decreases from 1.388 to 0.787 μm. Meanwhile, the average shear band spacing decreases from 0.787 to 0.761 μm with increasing aspect ratio from 1.00 to 1.50. The average shear band spacing decreases obviously from 0.761 to 0.478 μm when the aspect ratio increases from 1.50 to 2.25. Accordingly, the variation of the shear band density increases. As compared to the shear band density of 0.720 μm−1 for the sample with an aspect ratio of 0.25, the shear band density increases monotonously to 2.092 μm−1 for the sample with an aspect ratio of 2.25. In one word, the average shear band spacing decreases from 1.388 to 0.478 μm and the corresponding shear band density increases from 0.720 to 2.092 μm−1 with aspect ratio increasing from 0.25 to 2.25. For the sample with an aspect
ratio of 2.25, the average shear band spacing is as small as 0.478 μm and the shear band density is as high as 2.092 μm−1. The variation trend of the shear band density, as well as the corresponding average shear band spacing for the samples endured smaller deformation strains such as 7% and 45% (not shown here), is similar to that for the samples endured a deformation strain of 80%. Hence, the shear band density increases and the corresponding average shear band spacing decreases with increasing aspect ratio for Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass. Fig. 5 shows the fractions of shear bands with spacings below 100 and 50 nm in all shear bands for the Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with different aspect ratios. As the aspect ratio
Fig. 4. Variation trend for the effect of aspect ratio on the average shear band spacing and shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1.
Fig. 5. Ratio distribution of shear bands with spacings below 100 and 50 nm in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass endured a strain of 80% at a strain rate of 1.0 × 10−2 s−1 with different aspect ratios.
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increases from 0.25 to 0.50, no shear band with spacings below 100 nm can be found. For the sample with an aspect ratio of 0.75, the fraction of shear bands with spacings below 100 nm is 1.35%. As the aspect ratio increases from 1.25 to 2.00, the fraction of shear bands with spacings below 100 nm is larger than that for the sample with an aspect ratio of 0.75 and increases with increasing aspect ratio. For the sample with the largest aspect ratio of 2.25, the fraction of shear bands with spacings below 100 nm accounts for about 12.84%, which is maximal in all these samples with different aspect ratios. Furthermore, the variation trend in the fraction of shear bands with spacings below 50 nm with increasing aspect ratio is similar to that in the fraction of shear bands with spacings below 100 nm. For the sample with an aspect ratio of 2.25, the fraction of shear bands with spacings below 50 nm accounts for about 6.76%, which is also maximal in all the samples with different aspect ratios. Therefore, as the aspect ratio increases, the fractions of shear bands with spacings below 100 and 50 nm both increase. Based on the experimental results described above, it can be considered that the evolution of shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glasses is strongly affected by aspect ratio. According to the shear band phase (SBP) model proposed by Liu et al., the initiation and propagation of shear bands may be treated as a quasi-phase transition process[12]. When a new phase (shear bands) forms, the transition results in an increase in volume free energy (the difference in free energy per unit volume between the SBP and glassy matrix) and produces new interfaces between the SBP and glassy matrix, giving rise to an interfacial free energy[18]. It is known that the driving force for SBP transition process is the stored elastic energy in samples[19,20]. Therefore, the driving force for the SBP transition is the stored elastic energy ΔGE, while the resistance is the increasing volume free energy ΔGV and the interfacial free energy ΔGI. If the driving force overcomes the resistance, the SBP transition is theoretically favored[21–25]. Here, we take a metallic glass bar with a square cross section as an example, and the dimension of this metallic glass bar is d02 × L0 (d0 is the side length of the square cross section and L0 is the height of a bar). Because all the samples failure occurs via a single shear band, according to the results proposed by Sha et al.[16], the change in the elastic energy ΔGE of the sample upon forming a shear band with the aspect ratio of λ can be obtained:
ΔG E = Ed 02ε 0kl −
Ed 0l 2k 2 2λ
(1)
where E is the Young’s modulus of the sample, d0 is the side length of the sample, ε0 is the critical strain, at which a shear band forms, and k is a positive constant[12], l is the length of a formed shear band, and λ is the aspect ratio of the sample. According to Eq. (1), because E, d0, ε0, and l are independent of the aspect ratio of metallic glass samples[16], the stored elastic energy ΔGE will be larger when the aspect ratio is larger[16]. From this respect, the elastic energy may be an important factor affecting the shear band density as well as shear band spacing, as proposed by Chen et al.[26]. According to the results presented by Liu et al., the increase in the volume free energy after the formation of a shear band can be expressed as
ΔG V = g 0V max
ΔG I = σ S max
where σ is the interfacial free energy per unit interface area, and Smax represents the total area of the upper and lower interfacial areas between the SBP and MG phases, as well as the interfacial area at shear band tip[12]. Theoretically, for a formed shear band, Vmax in Eq. (2) and Smax in Eq. (3) are both constant, so ΔGV and ΔGI are constant, too. According to what was mentioned above, the driving force for the initiation and propagation of shear bands will be larger when the aspect ratio is larger[16], and the resistance (the increase in the volume free energy and the newly generated interfacial free energy induced by forming a shear band) is constant. Therefore, with increasing aspect ratio, the change of the total energy ΔG = ΔGE + ΔGV + ΔGI increases. This means that the stored energy in the sample is increased. This energy is the driving force to form another shear band. On this basis, the driving force for the formation of new shear bands is higher for a metallic glass sample with a larger aspect ratio. Therefore, it becomes easier for more shear bands to initiate and propagate as the aspect ratio increases. According to the above analysis, a higher aspect ratio is favorable for forming greater amount of shear bands. This is consistent with our results. Namely, Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass sample with a higher aspect ratio exhibits a higher density of shear bands after uniaxial compressive deformation.
4. Conclusion It is found that the distribution of the shear bands and the evolution of shear band density in Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass strongly depend on the aspect ratio during the compressive deformation. For the deformed Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass, the shear band density increases with increasing aspect ratio. A minimal shear band spacing with an average spacing of 0.478 μm was achieved for the sample with an aspect ratio of 2.25. In addition, the fractions of shear bands with spacings below 100 and 50 nm are about 12.84% and 6.76%, respectively, for the sample with an aspect ratio of 2.25. The driving force for the initiation and propagation of shear bands will be larger if the aspect ratio is larger. Obviously, the driving force for the formation of new shear bands is higher for the sample with a larger aspect ratio. This can probably explain why the Zr61.7Al8Ni13Cu17Sn0.3 bulk metallic glass samples with a higher aspect ratio exhibit a higher density of shear bands after uniaxial compression deformation.
Acknowledgments This work was supported by the National Natural Science Foundation of China (Nos. 51071079, 51272098, and 51301080).
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(2) [7]
where g0 is the increase in the volume free energy per unit volume, and Vmax is the total volume of forming a SBP zone[12]. Moreover, the newly generated interfacial free energy after the formation of a shear band can be given by (3)
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Please cite this article in press as: Wenli Ma, Yuanli Xu, Bo Shi, Jiangong Li, Effect of Aspect Ratio on the Evolution of Shear Bands in Zr61.7Al8Ni13Cu17Sn0.3 Bulk Metallic Glass, Journal of Materials Science & Technology (2015), doi: 10.1016/j.jmst.2015.12.020