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Bulk metallic glasses: “Defects” determines performance
Materials Science & Engineering A 675 (2016) 379–385
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Bulk metallic glasses: “Defects” determines performance C. Zhang a, J.C. Qiao a,b,n, J.M. Pelletier b, Y. Yao a,nn a b
School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, Xi’an 710072, China Université de Lyon, MATEIS, UMR CNRS5510, Bat. B. Pascal, INSA-Lyon, F-69621 Villeurbanne Cedex, France
art ic l e i nf o
a b s t r a c t
Article history: Received 29 June 2016 Received in revised form 18 August 2016 Accepted 19 August 2016
In the current work, the size effect to plasticity of the Zr50Cu40 þ xAl10 x (x¼ 0, and 2) bulk metallic glasses has been investigated experimentally. It is found that macroscopic plasticity are affected by different of leading factors. The mean stress drop of serrated flow is positively related to the number of weak regions. With greater number of weak regions, more pronounced stress drop occurs in the serrated flow process. The experimental results suggested that fewer number of weak regions lead to larger dimple patterns area. Besides, the average spacing of primary shear bands is associated with the weak regions and the position where shear bands terminate. & 2016 Elsevier B.V. All rights reserved.
Keywords: Metallic glass Plasticity Shear bands Micromechanics Defects
1. Introduction As an advanced material, bulk metallic glasses show good functional properties, such as high elastic strength and hardness, good fracture toughness and corrosion resistance [1–3]. Although there are some particular metallic glasses exhibit good plastic deformation ability [4–8], most of the bulk metallic glasses turn to be brittle fractured with negligible plastic strain under compression and without non-elastic deformation under tension [9]. In the compression test, if specific metallic glasses show good plastic deformation, usually nucleation and propagation of the shear bands would be observed all over the surface of sample, rather than severe fractures instantaneously. It is essential to investigate the compressive plasticity in metallic glasses and the formation of multiple shear bands on the surface could be the main factor [4– 8,10]. The mechanical behavior of metallic glasses is sensitive to the chemical composition, specimen size, strain rate and processing treatment [11–16]. With the same components, the size effect to mechanical properties can be divided into two categories: (1) intrinsic size effect attributed to the microstructural development of the metallic glass and different cooling rates in the process of glass n Corresponding author at: School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, Xi’an 710072, China. nn Corresponding author. Tel.: þ 86 29 88431015. E-mail addresses: [email protected] (J.C. Qiao), [email protected], [email protected] (Y. Yao).
http://dx.doi.org/10.1016/j.msea.2016.08.082 0921-5093/& 2016 Elsevier B.V. All rights reserved.
forming [13,16]; (2) extrinsic size effect, which is the size effect of engineering disciplines, i.e. the sample size decreases after original manufacturing process [17]. Yang et al. pointed out that metallic glasses display different plasticity behaviors with excessive heating, and a trend of low temperature-rise was revealed in metallic glass with remarkable plasticity [18]. It is well accept that the frozen-in “defects” [19], namely the origin of structural relaxation, is the source of macroscopic plasticity. The “defects” has been described as free volume [20,21], shear transformation zones [22], liquid-like core [23], and weakly bonded regions [24]. Smaller is softer, i.e. a small bulk metallic glass with a faster cooling rate during solidification contains more free volume, nucleates shear bands easily, and enhances plasticity under compression [25]. However, few researches have been performed on both size effect and chemical composition to the mechanical properties of metallic glasses, while the size and composition could affect plasticity of metallic glasses profoundly. Therefore, it is essential to understand mutual effects of size effect and material on the plastic deformation of metallic glasses. In the current work, size effect on the plastic strain of Zr50Cu40 þ xAl10 x (x ¼ 0, and 2) bulk metallic glass is investigated. The quasi-static compression experiments were performed at room temperature. It is noted that macroscopic plasticity is affected by different leading factors. The correlation among the mean stress drop in serrated flow, average spacing of primary shear bands, fractured surface and weakly bonded regions are studied.
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2. Experiments The Zr50Cu40 þ xAl10 x (x ¼0, 2) (at%) bulk metallic glass were selected as representative alloys, which were prepared in Tigathered high purity Ar atmosphere. The purity of mixing elemental metals is above 99.9% and the ingot was re-melted 5–6 times to ensure its homogeneity macroscopically. Cylindrical alloys with diameter of 2 mm and 3 mm were made from coppermold casting. The amorphous nature of as-cast specimens was confirmed by X-ray diffraction (XRD, Philips PW3830) using the monochromatic Cu-Kα radiation. The glass transition and crystallization behaviors were examined by differential scanning calorimetry (TA Instruments DSC Q1000) under high purity dry nitrogen flow, and the heating rate is 20 K min 1. The glass transition temperature (Tg), onset temperature of crystallization (Tx), and sum of the crystallization enthalpy of Zr50Cu40 þ xAl10 x metallic glass are calculated. The height and diameter of each metallic glass samples are 6:3; 5:3; 4:3; 3:3; 4:2; 3.33:2; 2.67:2; 2:2(mm), respectively. The test specimens were cut by a low speed precision cutting machine, and both ends were polished carefully to ensure parallelism and dustless [26]. The height error of each sample is less than 0.05 mm. Uniaxial compression experiments were conducted using electronic universal tester (Instron 5567). In the process of test, the values of time, displacement, and load were recorded at a frequency of 33.33 Hz. The experiments were performed under a constant strain rate of 1 10 4 s 1 at room temperature, at least three specimens were tested under the same experimental condition. After the mechanical tests, the morphology of shear bands and fracture surfaces were investigated by a high-resolution scanning electronic microscope (FEI Nova NanoSEM 450) to reveal the deformation features.
3. Results As shown in Fig. 1, XRD patterns reveal that there exists single broad diffraction peak and no peak corresponding to the crystalline phase, which represents fully amorphous structure. Fig. 2 shows the DSC curves of Zr50Cu42Al8 and Zr50Cu40Al10 metallic glass with diameter of 2 mm and 3 mm at a heating rate of 20 K min 1, respectively. All the DSC traces exhibit single endothermic event, which is characteristic of glass transition. It followed by an exothermic reaction corresponding to a crystallization peak of the supercooled liquid. From Fig. 2, Tg and Tx of metallic glass can be obtained, and the specific data is given in Table 1. Fig. 3 shows typical stress-strain curves of the
Fig. 2. DSC curves at a heating rate of 20 K min 1. See Table 1 in detail.
Table 1 DSC data: the glass transition temperature (Tg), onset temperature of crystallization (Tx), and sum of the crystallization enthalpy of Zr50Cu40 þ xAl10 x metallic glass with diameter of 2 mm and 3 mm. Zr50Cu40Al10
Zr50Cu42Al8
Diameter (mm)
2
3
2
3
Tg (K) Tx (K) ΔH (J/g) Weak regions per unit volume (b0) Fracture surface The number of dimple pattern in Fig. 4 Mean area of dimple pattern (a0)
699 774 3.35 1.1 S1 86 1
699 773 3.04 1 S2 399 2.21
692 767 12.61 4.15 S3 Unfractured
696 769 6.28 2.07 S4 32 2.69
Zr50Cu40 þ xAl10 x(x ¼0, 2) metallic glass with different sizes under a constant strain rate of 1 10 4 s 1. These curves are divided into four groups. The first group in Fig. 3(a) contains Zr50Cu40Al10 metallic glass, the height is from 3 mm to 6 mm with a diameter of 3 mm. The second group in Fig. 3(b) contains Zr50Cu42Al8 metallic glass, the height is from 3 mm to 6 mm with a diameter of 3 mm. The third group in Fig. 3(c) contains Zr50Cu40Al10 metallic glass, the height is from 2 mm to 4 mm with a diameter of 2 mm. The forth group in Fig. 3(d) contains Zr50Cu42Al8 metallic glass, the height is from 2 mm to 4 mm with a diameter of 2 mm. The compressive properties of metallic glass rods with different diameters and heights are listed in Table 2. The yield strength sy, fracture strength sf, and plastic strain εp are given. For each condition, there are about 2.2% elastic strain zones followed by the yield stage, as shown in the stress strain curve. However, different plastic deformation stages from long to short are observed. The deformation characteristics are reflected by the morphology of shear bands. From the SEM observation, a large number of shear bands exist on the specimen surface of samples with a large plasticity [27], as shown in Fig. 4.
4. Discussion 4.1. Serrated flow analysis
Fig. 1. XRD patterns of Zr50Cu40 þ xAl10 x(x¼ 0, and 2) metallic glass with different diameters.
For the sake of simple description, all the samples with aspect ratio of 1 are defined as S1 to S4, as shown in Fig. 3(a) and (d). From the typical stress-strain curve, the unstable–metastable plastic deformation are marked is S2 and S3. There appears a distinct stress valley with the strain of 18%, and the stress increases monotonically again, which is in good agreement with previous experimental results (20–25%) [17].
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Fig. 3. Stress-strain curves under the strain rate of 1 10 4 s 1 at room temperature: (a) for the Zr50Cu40Al10 metallic glass with diameter of 2 mm and height of 2, 2.67, 3.33, 4 mm, respectively; (b) for the Zr50Cu40Al10 metallic glass with diameter of 3 mm and height of 3, 4, 5, 6 mm, respectively; (c) and (d) the Zr50Cu42Al8 metallic glass.
Table 2 The yield strength sy, fracture strength sf, and plastic strain εp, the shear fracture angle θf, initial shear angle of the primary shear bands θ0, and the average spacing of primary shear bands S for the metallic glasses samples with different heights and diameters. Zr50Cu40Al10 H: D θf (deg) 2:2 40.3 2.67:2 40.9 3.33:2 40.6 4:2 40.5 3:3 42.5 4:3 40.5 5:3 40.4 6:3 40.3 Zr50Cu42Al8 2:2 42.4 2.67:2 40.5 3.33:2 39.7 4:2 41.4 3:3 35.4 4:3 39.7 5:3 39.1 6:3 41
θ0 (deg)
sy (MPa)
sf (MPa)
εp (%)
40.26 40.85 40.55 40.49 38.89 40.47 40.03 40.22
1925 1729 1890 1892
1827 1801 1887 1871 2243 1925 1901 1910
0.16 0.19 0.20 0.06 13.63 0.14 1.50 0.32
34.32 40.34 39.54 41.15 35.28 39.60 39.00 40.80
1922 1849 1929 1817 1777 1843 1840 1860
Unfractured 1881 1935 1878 1867 1908 1907 1908
30.10 0.65 0.66 0.98 0.61 0.42 0.44 0.81
S (μm)
250,88
199
As shown in Fig. 5, serrated flow is manifested as repeat cycles of an elastic loading and a sudden stress drop in the stress-time curve [28]. In the elastic loading stage, the shear bands stop to nucleate and propagate. The corresponding energy is gradually stored in the machine-sample system, accompanied by a slow increase of the stress. Once a shear band is activated or propagated, there is an elastic energy release corresponding to a sharp stress drop [29,30]. In the plastic deformation regime, S2 exhibits obvious serrated flow behavior until it breaks. However, S3 shows serrated flow only at the beginning of plastic strain, and the serration disappears
after a stress valley, as shown in Fig. 5(a) and (b). Statistics analysis is performed to understand the serrated flow behavior. Fig. 5(c) and (d) show variation of the stress drop magnitude ΔsS with the deformation time, which is extracted from stress-time curve with a strain rate of 1 10 4 s 1 (Fig. 5(a) and (b)). The statistics analysis of stress drop magnitude is counted from the beginning of plastic deformation to the stress valley. In general, the tendency of stress drop increases with the deformation time. However, it incorporates the effect of energy accumulation, release of machine-sample system and increase of the specimen cross-section area. The results could not reflect the dynamic nature of serrated flow behavior. Thus, a normalized stress drop magnitude is adopted in the current research. A relationship Δσ¯S = f ( t ) can be obtained by regression of the stress drop ΔsS and time t. The stress drop can be normalized by [31,32]:
ΔσN = Δσs /⎡⎣ f ( t )/f ( t0)⎤⎦
(1)
where f(t) and f(t0) are linear fitting of the stress drop magnitude at the deformation time t and the start deformation time t0, respectively. The scatter function removes the influence of the system and cross section area. The normalized stress drop magnitude ΔsN versus the deformation time t are shown in Fig. 5(e) and (f), which give the relationship between the normalized stress drop and statistic distribution for S2 and S3, respectively. Different from a self-organized critical behavior, which is characterized by the power-law distribution without a characterized serration size [33,34], the histogram displays a peak-shape distribution with a normalized stress drop corresponding to chaotic behavior of shear band dynamics. For the histogram distribution with a characterized size, as shown in Fig. 5(g) and (h), the mean value of ΔsN are 12.38 MPa and 34.91 MPa for S2 and S3, respectively. By arithmetic operations, the mean stress drop magnitude of S3 is around 3 times of S2.
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Fig. 4. SEM images of the samples surfaces or fracture surfaces: (a) S2; (b) the fracture angle of S2; (c) S3; (d) angle of the crack of S3; (e) S1; (f) S2; (g) S4. All the arrows point to the primary shear bands.
4.2. Morphology analysis
sin θ0 =
As shown in Fig. 4 and Table 2, all the fracture angles are smaller than 45°, which indicates that the deformation mechanism follows the Mohr-Coulomb criterion. It is known that the bulk metallic glasses fracture in a pure shear mode under compression formally [35]. The primary shear band angle θ0 is different from the compressive shear fracture angle θf, which is caused by a rotation mechanism of the primary shear bands due to compressive plasticity [36]. It is generally accepted that the sample volume V and length lSB of the primary shear band remain constant before and after compression. Hence, the following relationship can be obtained:
As shown in Table 2, with the increases of diameter, the value of θ0 decreases slightly at the same aspect ratio. The heat content of shear band is proportional to the shear offset [37–39], thus
⎛ d ⎞2 ⎛ d ⎞2 V = π⋅⎜ 0 ⎟ ⋅l0 = π⋅⎜ ⎟ ⋅l ⎝ 2⎠ ⎝ 2⎠
(2)
lSB = 2d0/sin θ0=2d/sin θf
(3)
where, l0 and l are the sample length before and after deformation; d0 and d are the sample diameter before and after deformation, respectively. In the compression experiments, it can be written as follow:
εp = ( l0 − l)/l0
(4)
From Eqs. (2) and (3), the sample length can be eliminated out from Eq. (4), then the relationship between θ0 and θf can be obtained:
1
1 − εp sin θf
H = 2 σyδ , where sy is the yield stress and
(5)
δ is the shear offset
proportional to the sample size [40]. More heat in the shear bands leads to stronger shear softening, which results in lower macroscopic plasticity. The observed mechanical behaviors of Zr50Cu42Al8 metallic glass are in good agreement with the theory. On the other hand, there are abundant shear bands on the surface of the larger macroscopic plastic sample. As shown in Fig. 4, the primary shear bands of S3 are close to each other, and the direction is consistent with the fracture surface. However, the shear bands of S2 hold different directions (arrowed in Fig. 4). The average space and direction of the primary shear bands, as well as density of the secondary shear bands are correlated to the thermal effects, which involves both glass formation and the compression process. The mean area of the dimple patterns are studied to characterize the fracture surface. In the field of a microscope, the relative size of the dimple patterns can be reflected through the field number. As shown in Fig. 4(e)–(g), there are 86, 39, 32 vein patterns in the same field at the fracture surface of S1, S3, and S4, respectively. Statistical calculations are provided in the Supplementary material. It assumes that the mean dimple patterns area of S1 is a0. Thus, the values of S3 and S4 are 2.21a0 and 2.69a0, respectively.
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Fig. 5. (a) and (b) are the typical stress-time curve of S2 and S3, respectively; (c) and (e) the extracted stress drop magnitude versus the deformation time of S2 and S3; (d) and (f) the normalized stress drop magnitude versus the deformation time of S2 and S3, respectively; (g) and (h) the number count distribution histogram for the normalized stress drop of S2 and S3. Note: the statistics of the stress drop magnitude of S3 is from beginning of the plastic deformation to the stress valley.
4.3. Thermal analysis The DSC thermogram of the samples with diameter of 2 mm and 3 mm are presented in Fig. 2. All the samples exhibit an
endothermic process corresponding to glass transition, followed by an obvious exothermic event related to crystallization in the supercooled liquid region. The plastic flow of metallic glasses is associated with “defects”
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[19]. The “defects” has been described in terms of free volume [20,21], shear transformation zones [22], liquid-like core [23], and weakly bonded regions [24]. For convenience, the concept of weakly bonded regions is adopted in this research. Numerous researches have been performed by using DSC to characterize the change of “defects”, which is strongly associated with structural relaxation in amorphous materials [25,40,41]. In the DSC curve, an exothermic process at temperature slightly below Tg is corresponding to annihilation of “defects” or structural relaxation [25]. Besides, the change in “defects” is proportional to the heat released during relaxation [42]:
(ΔH )fυ = β′Δvf
(6)
where β′ is a constant, (ΔH )fυ represents the enthalpy change, and Δvf is the change of “defects” per unit volume. According to Eq. (6), a semi-quantitative difference in weak regions can be obtained. Here, the weak regions per unit volume for Zr50Cu40Al10 metallic glass with diameter of 3 mm is defined to be b0. The relaxation exothermic enthalpy ΔH0 (corresponding to the exothermic peak) was calculated by integrating the heat flow near the glass transition. Substitute the values of ΔH0 (see Table 1 and the inset of Fig. 2 for details) into Eq. (6), the weak regions per unit volume are calculated to be 1.10b0, 2.07b0 and 4.15b0 for Zr50Cu40Al10 metallic glass with diameter of 2 mm, Zr50Cu42Al8 metallic glass with diameter of 3 mm and 2 mm, respectively. It suggests that smaller sample contains more weak regions per unit volume than the larger one (shown in Table 1). It should be noted that the weak regions of Zr50Cu40Al10 metallic glass with diameter of 2 mm and 3 mm are close to each other, and the gap is very small, around 10%, which implies that the fracture angle of Zr50Cu40Al10 metallic glass could not be determined by the theory previously discussed. At the same aspect ratio, different plasticity of Zr50Cu42Al8
metallic glass were caused by the diameter of samples, which will result in the difference in weak region. Different plasticity of Zr50Cu40Al10 metallic glass, however, is the result of the diameter of samples containing the same weak region. In other words, the different size of weak region and diameter result in the former, whereas the latter phenomenon induced by only one factor, a simple sense size effect. 4.4. Coupling among serrated flow, morphology, and thermal analysis Generally smaller ratio of length to diameter lead to larger plasticity, which is caused by the interface effect between ends of specimen and the testing machine. According to the analytical result, S2 has stronger plasticity than that of S1 at the same aspect ratio, because it is difficult for the shear bands to run through the sample with similar weak regions. Compared to S2, the plastic deformation of S3 is affected by not only the smaller diameter, but also the weak regions. Fig. 6 shows a schematic diagram of the Zr50Cu40 þ xAl10 x (x ¼0, and 2) metallic glass with different sizes under compression. The area of dimple patterns in fracture surface and direction of shear bands are given. It is noted that the leading factors are not consistent with each other. With more weak regions, the secondary shear band can be activated easily. Therefore, there are abundant secondary shear bands on the surface of S3, and the directions of primary shear bands are similar to the fracture surface. Besides, the average spacing of the primary shear bands is relatively narrow (199 mm). Contrasted with S3, there are many primary shear bands but fewer secondary shear bands on the surface of S2, which is with respect to less weak regions, and the average spacing of primary shear bands is wider (250 mm). Different form the secondary shear bands, the direction of primary shear bands are either parallel or perpendicular to the
Fig. 6. Schematic diagram of the Zr50Cu40 þ xAl10 x (x¼ 0, and 2) metallic glass with different sizes under compression process.
C. Zhang et al. / Materials Science & Engineering A 675 (2016) 379–385
fracture surface. The detailed information is given in Table 2, Figs. 4 and 6. It should be noted that spacing of the primary shear bands of S2 can be divided into 3 parts. The write and yellow arrows point out different primary shear bands directions. The red and write arrows are separated by a green arrow, and the average spacing of the primary shear bands shown in red arrow is narrower (85 mm), which is caused by the position of primary shear bands’ terminal point. Here the ends of primary shear bands pointed by red arrow are on the surface of samples, others pointed by white arrow are on the interface between the sample and testing machine, as shown in Table 2 and Fig. 4. Based on the experimental observations, stress drop of the serrated flow in S3 is about 3 times of S2. At the same time, the thermal analysis shows that the free volume of S2 is 4 times of S1. It is well-known that macroscopic behavior reflects microscopic view of characteristic. In the current study, it shows that stress drop of the serrated flow is positive relation to weak regions. Furthermore, there is strong connection between the average areas of dimple patterns and weak regions. In general, greater number of weak regions leads to smaller area once activated. In addition, fewer number of weak regions causes greater dimple patterns area, as shown in Fig. 6 This also can explain why the weak regions of 1 mm samples is much greater than that of 6 mm, and the former has smaller dimple patterns area in the previous literature [25]. Generally the number of weak regions decides the average dimple patterns area size.
385
Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.msea.2016.08.082.
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5. Conclusions
[18] [19]
From the experimental analysis, it is found that smaller length to diameter ratio brings larger macroscopic plasticity. Macroscopic plasticity is affected by the leading factors, including the diameter for Zr50Cu40Al10 metallic glass, and weak regions for Zr50Cu42Al8 metallic glass. The stress drop of the serrated flow shows positive relation to the number of weak regions. With more weak regions, bigger stress drop is observed in the serrated flow process. In addition, the average spacing of the primary shear bands is strongly associated with weak regions and the position where shear bands ends. Fewer number of weak regions leads to larger dimple patterns area once activated. In other words, the mean area of dimple patterns grows negatively associated with the number of weak regions or relaxation exothermic enthalpy.
[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
Acknowledgments
[32] [33]
This work was supported by the National Natural Science Foundation of China (Nos. 51401192, 51611130120 and 11572249), the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University, the Fundamental Research Funds for the Central Universities (No. 3102015ZY027 and 3102015BJ (II) JGZ019), the Aeronautical Science Foundation of China (2015ZF53072), the Shanghai Aerospace Science and Technology Innovation Fund (SAST2016047), the Natural Science Foundation of Shaanxi Province (No.2016JM5009) and the Aerospace Technology Foundation (N2014KC0068).
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Bulk metallic glasses: “Defects” determines performance C. Zhang a, J.C. Qiao a,b,n, J.M. Pelletier b, Y. Yao a,nn a b
School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, Xi’an 710072, China Université de Lyon, MATEIS, UMR CNRS5510, Bat. B. Pascal, INSA-Lyon, F-69621 Villeurbanne Cedex, France
art ic l e i nf o
a b s t r a c t
Article history: Received 29 June 2016 Received in revised form 18 August 2016 Accepted 19 August 2016
In the current work, the size effect to plasticity of the Zr50Cu40 þ xAl10 x (x¼ 0, and 2) bulk metallic glasses has been investigated experimentally. It is found that macroscopic plasticity are affected by different of leading factors. The mean stress drop of serrated flow is positively related to the number of weak regions. With greater number of weak regions, more pronounced stress drop occurs in the serrated flow process. The experimental results suggested that fewer number of weak regions lead to larger dimple patterns area. Besides, the average spacing of primary shear bands is associated with the weak regions and the position where shear bands terminate. & 2016 Elsevier B.V. All rights reserved.
Keywords: Metallic glass Plasticity Shear bands Micromechanics Defects
1. Introduction As an advanced material, bulk metallic glasses show good functional properties, such as high elastic strength and hardness, good fracture toughness and corrosion resistance [1–3]. Although there are some particular metallic glasses exhibit good plastic deformation ability [4–8], most of the bulk metallic glasses turn to be brittle fractured with negligible plastic strain under compression and without non-elastic deformation under tension [9]. In the compression test, if specific metallic glasses show good plastic deformation, usually nucleation and propagation of the shear bands would be observed all over the surface of sample, rather than severe fractures instantaneously. It is essential to investigate the compressive plasticity in metallic glasses and the formation of multiple shear bands on the surface could be the main factor [4– 8,10]. The mechanical behavior of metallic glasses is sensitive to the chemical composition, specimen size, strain rate and processing treatment [11–16]. With the same components, the size effect to mechanical properties can be divided into two categories: (1) intrinsic size effect attributed to the microstructural development of the metallic glass and different cooling rates in the process of glass n Corresponding author at: School of Mechanics and Civil & Architecture, Northwestern Polytechnical University, Xi’an 710072, China. nn Corresponding author. Tel.: þ 86 29 88431015. E-mail addresses: [email protected] (J.C. Qiao), [email protected], [email protected] (Y. Yao).
http://dx.doi.org/10.1016/j.msea.2016.08.082 0921-5093/& 2016 Elsevier B.V. All rights reserved.
forming [13,16]; (2) extrinsic size effect, which is the size effect of engineering disciplines, i.e. the sample size decreases after original manufacturing process [17]. Yang et al. pointed out that metallic glasses display different plasticity behaviors with excessive heating, and a trend of low temperature-rise was revealed in metallic glass with remarkable plasticity [18]. It is well accept that the frozen-in “defects” [19], namely the origin of structural relaxation, is the source of macroscopic plasticity. The “defects” has been described as free volume [20,21], shear transformation zones [22], liquid-like core [23], and weakly bonded regions [24]. Smaller is softer, i.e. a small bulk metallic glass with a faster cooling rate during solidification contains more free volume, nucleates shear bands easily, and enhances plasticity under compression [25]. However, few researches have been performed on both size effect and chemical composition to the mechanical properties of metallic glasses, while the size and composition could affect plasticity of metallic glasses profoundly. Therefore, it is essential to understand mutual effects of size effect and material on the plastic deformation of metallic glasses. In the current work, size effect on the plastic strain of Zr50Cu40 þ xAl10 x (x ¼ 0, and 2) bulk metallic glass is investigated. The quasi-static compression experiments were performed at room temperature. It is noted that macroscopic plasticity is affected by different leading factors. The correlation among the mean stress drop in serrated flow, average spacing of primary shear bands, fractured surface and weakly bonded regions are studied.
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2. Experiments The Zr50Cu40 þ xAl10 x (x ¼0, 2) (at%) bulk metallic glass were selected as representative alloys, which were prepared in Tigathered high purity Ar atmosphere. The purity of mixing elemental metals is above 99.9% and the ingot was re-melted 5–6 times to ensure its homogeneity macroscopically. Cylindrical alloys with diameter of 2 mm and 3 mm were made from coppermold casting. The amorphous nature of as-cast specimens was confirmed by X-ray diffraction (XRD, Philips PW3830) using the monochromatic Cu-Kα radiation. The glass transition and crystallization behaviors were examined by differential scanning calorimetry (TA Instruments DSC Q1000) under high purity dry nitrogen flow, and the heating rate is 20 K min 1. The glass transition temperature (Tg), onset temperature of crystallization (Tx), and sum of the crystallization enthalpy of Zr50Cu40 þ xAl10 x metallic glass are calculated. The height and diameter of each metallic glass samples are 6:3; 5:3; 4:3; 3:3; 4:2; 3.33:2; 2.67:2; 2:2(mm), respectively. The test specimens were cut by a low speed precision cutting machine, and both ends were polished carefully to ensure parallelism and dustless [26]. The height error of each sample is less than 0.05 mm. Uniaxial compression experiments were conducted using electronic universal tester (Instron 5567). In the process of test, the values of time, displacement, and load were recorded at a frequency of 33.33 Hz. The experiments were performed under a constant strain rate of 1 10 4 s 1 at room temperature, at least three specimens were tested under the same experimental condition. After the mechanical tests, the morphology of shear bands and fracture surfaces were investigated by a high-resolution scanning electronic microscope (FEI Nova NanoSEM 450) to reveal the deformation features.
3. Results As shown in Fig. 1, XRD patterns reveal that there exists single broad diffraction peak and no peak corresponding to the crystalline phase, which represents fully amorphous structure. Fig. 2 shows the DSC curves of Zr50Cu42Al8 and Zr50Cu40Al10 metallic glass with diameter of 2 mm and 3 mm at a heating rate of 20 K min 1, respectively. All the DSC traces exhibit single endothermic event, which is characteristic of glass transition. It followed by an exothermic reaction corresponding to a crystallization peak of the supercooled liquid. From Fig. 2, Tg and Tx of metallic glass can be obtained, and the specific data is given in Table 1. Fig. 3 shows typical stress-strain curves of the
Fig. 2. DSC curves at a heating rate of 20 K min 1. See Table 1 in detail.
Table 1 DSC data: the glass transition temperature (Tg), onset temperature of crystallization (Tx), and sum of the crystallization enthalpy of Zr50Cu40 þ xAl10 x metallic glass with diameter of 2 mm and 3 mm. Zr50Cu40Al10
Zr50Cu42Al8
Diameter (mm)
2
3
2
3
Tg (K) Tx (K) ΔH (J/g) Weak regions per unit volume (b0) Fracture surface The number of dimple pattern in Fig. 4 Mean area of dimple pattern (a0)
699 774 3.35 1.1 S1 86 1
699 773 3.04 1 S2 399 2.21
692 767 12.61 4.15 S3 Unfractured
696 769 6.28 2.07 S4 32 2.69
Zr50Cu40 þ xAl10 x(x ¼0, 2) metallic glass with different sizes under a constant strain rate of 1 10 4 s 1. These curves are divided into four groups. The first group in Fig. 3(a) contains Zr50Cu40Al10 metallic glass, the height is from 3 mm to 6 mm with a diameter of 3 mm. The second group in Fig. 3(b) contains Zr50Cu42Al8 metallic glass, the height is from 3 mm to 6 mm with a diameter of 3 mm. The third group in Fig. 3(c) contains Zr50Cu40Al10 metallic glass, the height is from 2 mm to 4 mm with a diameter of 2 mm. The forth group in Fig. 3(d) contains Zr50Cu42Al8 metallic glass, the height is from 2 mm to 4 mm with a diameter of 2 mm. The compressive properties of metallic glass rods with different diameters and heights are listed in Table 2. The yield strength sy, fracture strength sf, and plastic strain εp are given. For each condition, there are about 2.2% elastic strain zones followed by the yield stage, as shown in the stress strain curve. However, different plastic deformation stages from long to short are observed. The deformation characteristics are reflected by the morphology of shear bands. From the SEM observation, a large number of shear bands exist on the specimen surface of samples with a large plasticity [27], as shown in Fig. 4.
4. Discussion 4.1. Serrated flow analysis
Fig. 1. XRD patterns of Zr50Cu40 þ xAl10 x(x¼ 0, and 2) metallic glass with different diameters.
For the sake of simple description, all the samples with aspect ratio of 1 are defined as S1 to S4, as shown in Fig. 3(a) and (d). From the typical stress-strain curve, the unstable–metastable plastic deformation are marked is S2 and S3. There appears a distinct stress valley with the strain of 18%, and the stress increases monotonically again, which is in good agreement with previous experimental results (20–25%) [17].
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Fig. 3. Stress-strain curves under the strain rate of 1 10 4 s 1 at room temperature: (a) for the Zr50Cu40Al10 metallic glass with diameter of 2 mm and height of 2, 2.67, 3.33, 4 mm, respectively; (b) for the Zr50Cu40Al10 metallic glass with diameter of 3 mm and height of 3, 4, 5, 6 mm, respectively; (c) and (d) the Zr50Cu42Al8 metallic glass.
Table 2 The yield strength sy, fracture strength sf, and plastic strain εp, the shear fracture angle θf, initial shear angle of the primary shear bands θ0, and the average spacing of primary shear bands S for the metallic glasses samples with different heights and diameters. Zr50Cu40Al10 H: D θf (deg) 2:2 40.3 2.67:2 40.9 3.33:2 40.6 4:2 40.5 3:3 42.5 4:3 40.5 5:3 40.4 6:3 40.3 Zr50Cu42Al8 2:2 42.4 2.67:2 40.5 3.33:2 39.7 4:2 41.4 3:3 35.4 4:3 39.7 5:3 39.1 6:3 41
θ0 (deg)
sy (MPa)
sf (MPa)
εp (%)
40.26 40.85 40.55 40.49 38.89 40.47 40.03 40.22
1925 1729 1890 1892
1827 1801 1887 1871 2243 1925 1901 1910
0.16 0.19 0.20 0.06 13.63 0.14 1.50 0.32
34.32 40.34 39.54 41.15 35.28 39.60 39.00 40.80
1922 1849 1929 1817 1777 1843 1840 1860
Unfractured 1881 1935 1878 1867 1908 1907 1908
30.10 0.65 0.66 0.98 0.61 0.42 0.44 0.81
S (μm)
250,88
199
As shown in Fig. 5, serrated flow is manifested as repeat cycles of an elastic loading and a sudden stress drop in the stress-time curve [28]. In the elastic loading stage, the shear bands stop to nucleate and propagate. The corresponding energy is gradually stored in the machine-sample system, accompanied by a slow increase of the stress. Once a shear band is activated or propagated, there is an elastic energy release corresponding to a sharp stress drop [29,30]. In the plastic deformation regime, S2 exhibits obvious serrated flow behavior until it breaks. However, S3 shows serrated flow only at the beginning of plastic strain, and the serration disappears
after a stress valley, as shown in Fig. 5(a) and (b). Statistics analysis is performed to understand the serrated flow behavior. Fig. 5(c) and (d) show variation of the stress drop magnitude ΔsS with the deformation time, which is extracted from stress-time curve with a strain rate of 1 10 4 s 1 (Fig. 5(a) and (b)). The statistics analysis of stress drop magnitude is counted from the beginning of plastic deformation to the stress valley. In general, the tendency of stress drop increases with the deformation time. However, it incorporates the effect of energy accumulation, release of machine-sample system and increase of the specimen cross-section area. The results could not reflect the dynamic nature of serrated flow behavior. Thus, a normalized stress drop magnitude is adopted in the current research. A relationship Δσ¯S = f ( t ) can be obtained by regression of the stress drop ΔsS and time t. The stress drop can be normalized by [31,32]:
ΔσN = Δσs /⎡⎣ f ( t )/f ( t0)⎤⎦
(1)
where f(t) and f(t0) are linear fitting of the stress drop magnitude at the deformation time t and the start deformation time t0, respectively. The scatter function removes the influence of the system and cross section area. The normalized stress drop magnitude ΔsN versus the deformation time t are shown in Fig. 5(e) and (f), which give the relationship between the normalized stress drop and statistic distribution for S2 and S3, respectively. Different from a self-organized critical behavior, which is characterized by the power-law distribution without a characterized serration size [33,34], the histogram displays a peak-shape distribution with a normalized stress drop corresponding to chaotic behavior of shear band dynamics. For the histogram distribution with a characterized size, as shown in Fig. 5(g) and (h), the mean value of ΔsN are 12.38 MPa and 34.91 MPa for S2 and S3, respectively. By arithmetic operations, the mean stress drop magnitude of S3 is around 3 times of S2.
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Fig. 4. SEM images of the samples surfaces or fracture surfaces: (a) S2; (b) the fracture angle of S2; (c) S3; (d) angle of the crack of S3; (e) S1; (f) S2; (g) S4. All the arrows point to the primary shear bands.
4.2. Morphology analysis
sin θ0 =
As shown in Fig. 4 and Table 2, all the fracture angles are smaller than 45°, which indicates that the deformation mechanism follows the Mohr-Coulomb criterion. It is known that the bulk metallic glasses fracture in a pure shear mode under compression formally [35]. The primary shear band angle θ0 is different from the compressive shear fracture angle θf, which is caused by a rotation mechanism of the primary shear bands due to compressive plasticity [36]. It is generally accepted that the sample volume V and length lSB of the primary shear band remain constant before and after compression. Hence, the following relationship can be obtained:
As shown in Table 2, with the increases of diameter, the value of θ0 decreases slightly at the same aspect ratio. The heat content of shear band is proportional to the shear offset [37–39], thus
⎛ d ⎞2 ⎛ d ⎞2 V = π⋅⎜ 0 ⎟ ⋅l0 = π⋅⎜ ⎟ ⋅l ⎝ 2⎠ ⎝ 2⎠
(2)
lSB = 2d0/sin θ0=2d/sin θf
(3)
where, l0 and l are the sample length before and after deformation; d0 and d are the sample diameter before and after deformation, respectively. In the compression experiments, it can be written as follow:
εp = ( l0 − l)/l0
(4)
From Eqs. (2) and (3), the sample length can be eliminated out from Eq. (4), then the relationship between θ0 and θf can be obtained:
1
1 − εp sin θf
H = 2 σyδ , where sy is the yield stress and
(5)
δ is the shear offset
proportional to the sample size [40]. More heat in the shear bands leads to stronger shear softening, which results in lower macroscopic plasticity. The observed mechanical behaviors of Zr50Cu42Al8 metallic glass are in good agreement with the theory. On the other hand, there are abundant shear bands on the surface of the larger macroscopic plastic sample. As shown in Fig. 4, the primary shear bands of S3 are close to each other, and the direction is consistent with the fracture surface. However, the shear bands of S2 hold different directions (arrowed in Fig. 4). The average space and direction of the primary shear bands, as well as density of the secondary shear bands are correlated to the thermal effects, which involves both glass formation and the compression process. The mean area of the dimple patterns are studied to characterize the fracture surface. In the field of a microscope, the relative size of the dimple patterns can be reflected through the field number. As shown in Fig. 4(e)–(g), there are 86, 39, 32 vein patterns in the same field at the fracture surface of S1, S3, and S4, respectively. Statistical calculations are provided in the Supplementary material. It assumes that the mean dimple patterns area of S1 is a0. Thus, the values of S3 and S4 are 2.21a0 and 2.69a0, respectively.
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Fig. 5. (a) and (b) are the typical stress-time curve of S2 and S3, respectively; (c) and (e) the extracted stress drop magnitude versus the deformation time of S2 and S3; (d) and (f) the normalized stress drop magnitude versus the deformation time of S2 and S3, respectively; (g) and (h) the number count distribution histogram for the normalized stress drop of S2 and S3. Note: the statistics of the stress drop magnitude of S3 is from beginning of the plastic deformation to the stress valley.
4.3. Thermal analysis The DSC thermogram of the samples with diameter of 2 mm and 3 mm are presented in Fig. 2. All the samples exhibit an
endothermic process corresponding to glass transition, followed by an obvious exothermic event related to crystallization in the supercooled liquid region. The plastic flow of metallic glasses is associated with “defects”
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[19]. The “defects” has been described in terms of free volume [20,21], shear transformation zones [22], liquid-like core [23], and weakly bonded regions [24]. For convenience, the concept of weakly bonded regions is adopted in this research. Numerous researches have been performed by using DSC to characterize the change of “defects”, which is strongly associated with structural relaxation in amorphous materials [25,40,41]. In the DSC curve, an exothermic process at temperature slightly below Tg is corresponding to annihilation of “defects” or structural relaxation [25]. Besides, the change in “defects” is proportional to the heat released during relaxation [42]:
(ΔH )fυ = β′Δvf
(6)
where β′ is a constant, (ΔH )fυ represents the enthalpy change, and Δvf is the change of “defects” per unit volume. According to Eq. (6), a semi-quantitative difference in weak regions can be obtained. Here, the weak regions per unit volume for Zr50Cu40Al10 metallic glass with diameter of 3 mm is defined to be b0. The relaxation exothermic enthalpy ΔH0 (corresponding to the exothermic peak) was calculated by integrating the heat flow near the glass transition. Substitute the values of ΔH0 (see Table 1 and the inset of Fig. 2 for details) into Eq. (6), the weak regions per unit volume are calculated to be 1.10b0, 2.07b0 and 4.15b0 for Zr50Cu40Al10 metallic glass with diameter of 2 mm, Zr50Cu42Al8 metallic glass with diameter of 3 mm and 2 mm, respectively. It suggests that smaller sample contains more weak regions per unit volume than the larger one (shown in Table 1). It should be noted that the weak regions of Zr50Cu40Al10 metallic glass with diameter of 2 mm and 3 mm are close to each other, and the gap is very small, around 10%, which implies that the fracture angle of Zr50Cu40Al10 metallic glass could not be determined by the theory previously discussed. At the same aspect ratio, different plasticity of Zr50Cu42Al8
metallic glass were caused by the diameter of samples, which will result in the difference in weak region. Different plasticity of Zr50Cu40Al10 metallic glass, however, is the result of the diameter of samples containing the same weak region. In other words, the different size of weak region and diameter result in the former, whereas the latter phenomenon induced by only one factor, a simple sense size effect. 4.4. Coupling among serrated flow, morphology, and thermal analysis Generally smaller ratio of length to diameter lead to larger plasticity, which is caused by the interface effect between ends of specimen and the testing machine. According to the analytical result, S2 has stronger plasticity than that of S1 at the same aspect ratio, because it is difficult for the shear bands to run through the sample with similar weak regions. Compared to S2, the plastic deformation of S3 is affected by not only the smaller diameter, but also the weak regions. Fig. 6 shows a schematic diagram of the Zr50Cu40 þ xAl10 x (x ¼0, and 2) metallic glass with different sizes under compression. The area of dimple patterns in fracture surface and direction of shear bands are given. It is noted that the leading factors are not consistent with each other. With more weak regions, the secondary shear band can be activated easily. Therefore, there are abundant secondary shear bands on the surface of S3, and the directions of primary shear bands are similar to the fracture surface. Besides, the average spacing of the primary shear bands is relatively narrow (199 mm). Contrasted with S3, there are many primary shear bands but fewer secondary shear bands on the surface of S2, which is with respect to less weak regions, and the average spacing of primary shear bands is wider (250 mm). Different form the secondary shear bands, the direction of primary shear bands are either parallel or perpendicular to the
Fig. 6. Schematic diagram of the Zr50Cu40 þ xAl10 x (x¼ 0, and 2) metallic glass with different sizes under compression process.
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fracture surface. The detailed information is given in Table 2, Figs. 4 and 6. It should be noted that spacing of the primary shear bands of S2 can be divided into 3 parts. The write and yellow arrows point out different primary shear bands directions. The red and write arrows are separated by a green arrow, and the average spacing of the primary shear bands shown in red arrow is narrower (85 mm), which is caused by the position of primary shear bands’ terminal point. Here the ends of primary shear bands pointed by red arrow are on the surface of samples, others pointed by white arrow are on the interface between the sample and testing machine, as shown in Table 2 and Fig. 4. Based on the experimental observations, stress drop of the serrated flow in S3 is about 3 times of S2. At the same time, the thermal analysis shows that the free volume of S2 is 4 times of S1. It is well-known that macroscopic behavior reflects microscopic view of characteristic. In the current study, it shows that stress drop of the serrated flow is positive relation to weak regions. Furthermore, there is strong connection between the average areas of dimple patterns and weak regions. In general, greater number of weak regions leads to smaller area once activated. In addition, fewer number of weak regions causes greater dimple patterns area, as shown in Fig. 6 This also can explain why the weak regions of 1 mm samples is much greater than that of 6 mm, and the former has smaller dimple patterns area in the previous literature [25]. Generally the number of weak regions decides the average dimple patterns area size.
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Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.msea.2016.08.082.
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5. Conclusions
[18] [19]
From the experimental analysis, it is found that smaller length to diameter ratio brings larger macroscopic plasticity. Macroscopic plasticity is affected by the leading factors, including the diameter for Zr50Cu40Al10 metallic glass, and weak regions for Zr50Cu42Al8 metallic glass. The stress drop of the serrated flow shows positive relation to the number of weak regions. With more weak regions, bigger stress drop is observed in the serrated flow process. In addition, the average spacing of the primary shear bands is strongly associated with weak regions and the position where shear bands ends. Fewer number of weak regions leads to larger dimple patterns area once activated. In other words, the mean area of dimple patterns grows negatively associated with the number of weak regions or relaxation exothermic enthalpy.
[20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
Acknowledgments
[32] [33]
This work was supported by the National Natural Science Foundation of China (Nos. 51401192, 51611130120 and 11572249), the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University, the Fundamental Research Funds for the Central Universities (No. 3102015ZY027 and 3102015BJ (II) JGZ019), the Aeronautical Science Foundation of China (2015ZF53072), the Shanghai Aerospace Science and Technology Innovation Fund (SAST2016047), the Natural Science Foundation of Shaanxi Province (No.2016JM5009) and the Aerospace Technology Foundation (N2014KC0068).
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