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The effect of stress concentration on the bending behavior of a ZrCuNiAl bulk metallic glass
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
The effect of stress concentration on the bending behavior of a ZrCuNiAl bulk metallic glass Zhiliang Ninga,b,⁎, Yongjiang Huanga,b,⁎, Zhe Shenc, Haicao Suna,b, Weizhong Liangd, Jianfei Suna,b a
School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China National Key Laboratory of Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, PR China c Shenyang Engine Research Institute, Aero Engine Corporation of China, Shenyang 110000, PR China d School of Materials Science and Engineering, Heilongjiang University of Science and Technology, Harbin 150027, PR China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Bulk metallic glasses Stress concentration Bending Fracture
The bending behaviors of a Zr55Cu30Ni5Al10 bulk metallic glass (BMG) samples with different notch radii are studied. The artificial notch will introduce stress concentration within the BMG sample during bending. That means, smaller notch radius leads to greater stress concentration around the notch area, and thus results in earlier failure and smoother fracture surface. Then, the sample with smaller notch radius possesses smaller fracture toughness. The relationship between the stress concentration and deformation feature has been discussed in terms of grease model.
1. Introduction
sample geometry dependence of bending ductility of BMG plates; thin plate usually exhibits ductility while thicker plate with the same chemical composition shows brittle feature under identical loading condition. Liu and Wang [28] demonstrated the shear band evolution under bending in a super-plastic Zr-based BMG. During service, BMG components are often suffered to a multi-axial complex stress state induced by artificial defects, such as holes, and notches [29–32]. As a BMG material with an artificial defect is loaded, a great stress concentration usually takes place near the defect. As a result, the stress distribution is inhomogeneous over the whole cross-section, which could exert a crucial role on the deformation of the BMG materials. Until now few research has been focused on the bending behaviors of BMGs after the introduce of stress concentration. In the present work, Zr55Cu30Ni5Al10 (at. %) alloy was selected as the model material due to its excellent glass forming ability. Notches with different radii, as stress concentrators, were introduced into the BMG samples. The effect of stress concentration induced by notch on the bending behaviors of the Zr-based BMG was studied. The fracture morphologies of the failed samples were examined after bending deformation. It is expected that the results obtained can provide a better understanding the bending deformation mechanism of BMGs, and thus extend their applications in complex multi-axial stress states.
During the last decades, bulk metallic glasses (BMGs), also termed as bulk amorphous alloys, have triggered intensive attention from materials science researchers due to their importance in both fundamental science and industrial uses [1–5]. However, at a temperature far below the glass transition temperature, the plastic deformation of BMGs usually localizes within few narrow shear bands of ~20 nm thick, which causes catastrophic failure and a lack of plasticity [6–8]. Some monolithic metallic glasses exhibit great plastic deformation capacity upon compressive loading [9,10] whereas almost all BMGs show disappointed tensile plasticity [11]. Such a brittle feature hinders seriously any practical applications of BMGs. Therefore, to understand the intrinsic deformation mechanism and thus to improve the ductility of BMGs have recently become one of the most important issues in BMGs research community [12–16]. As a kind of high-performance materials for engineering applications, knowledge regarding how BMGs behave under bending conditions is critical [17–21]. Therefore, the bending behaviors of BMGs deserve further attention. When a BMG alloy sample subjected to bending condition, the inherent stress gradient induced by multi-axial stress would favor the formation of multiple shear bands. This has aroused considerable research interests [22–24]. Zhang et al. [25] studied the multiplication of shear bands aided by free volume under three-point bending of a BMG. Conner et al. [26,27] examined the
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Corresponding authors. E-mail addresses: [email protected] (Z. Ning), [email protected] (Y. Huang).
http://dx.doi.org/10.1016/j.jnoncrysol.2017.04.005 Received 5 January 2017; Received in revised form 15 February 2017; Accepted 11 April 2017 0022-3093/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Ning, Z., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.04.005
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Table 1 The maximum load, F, the maximum displacement, Dmax, stress concentration factor, average dimple height, h, and fracture toughness of the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii, ρ. Notch radius, ρ (mm)
Maximum displacement, Dmax (mm)
Maximum load, F(N)
Stress concentration factor, Kt
Dimple height, h (μm)
Fracture toughness, Pa·m1/2
0.2 0.3 0.5 1.0
0.3712 0.4465 0.4869 0.5531
868.42 959.86 1099.81 1226.78
2.808 2.319 1.823 1.315
5.56 6.38 6.54 7.09
38.42 43.27 46.88 51.56
2. Experimental procedures Ingots with a nominal chemical composition of Zr55Cu30Ni5Al10 were produced by arc-melting a mixture of the starting pure Zr, Cu, Ni, and Al elements, each with 99.5 wt% purity or better, under a Tigettered argon atmosphere. Prior to the preparation of the master ingots, pure Ti was melted enough to absorb the oxygen within the chamber, which is harmful to glass formation. To ensure a chemical homogeneity, each ingot was remelted at least four times with electromagnetic stir. Then as-cast BMG samples with a 3 × 30 × 75 mm3 dimension were prepared by drop casting the remelted alloys into a copper mold. The amorphous nature of the ascast samples was confirmed by X-ray diffraction (XRD) with Cu Kα radiation. Three-point bending samples with a 3 × 5 × 30 mm3 dimension were electrical discharge machined from the as-cast BMG alloy samples, and the top and the bottom surfaces of the samples were then carefully grinded and polished. Notches with a radius of 0.2 mm, 0.3 mm, 0.5 mm, or 1.0 mm were cut at one edge in the middle of the samples. Notch length is 2.5 mm. The outer appearance of the bending samples is shown in Fig. 1a. Bending tests were conducted on a computer-controlled Instron 5500R type machine at a displacement rate of 0.3 mm/min. The span was set to be 24 mm. During bending tests, the load-deflection curves were recorded continuously. After testing, fracture surfaces of all failed samples were examined in a scanning electron microscope, SEM (FEI Helios Nanolab600i) or a 3-D laser scanning confocal microscope (Phenom Pro X). In addition, a finite-element method (FEM) with ABAQUS software was adopted to simulate the stress distributions of the studied Zr-based BMG samples with different notch radii upon bending condition.
Fig. 1. (a) The outer appearance (from top to bottom shows the sample with a notch radius of 0.2, 0.3, 0.5, 1.0 mm, respectively) and (b) XRD patterns of three-point bending Zr55Cu30Ni5Al10 (at. %) bulk metallic glass samples.
3. Results and discussion Fig. 1b shows the XRD pattern obtained from the as-cast quaternary ZrCuNiAl alloy sample. It can be seen from Fig. 1b that the pattern of cast samples consists of only a series of broad diffraction maxima, without any detectable sharp Bragg peaks corresponding to crystalline phase. This confirms that the as-cast plate-shaped sample is amorphous in nature. Fig. 2 presents the representative load-deflection curves obtained from the room temperature bending tests of the studied Zr-based BMG alloy samples with different notch radii. As can be seen, for the studied Zr-based BMG alloy, the bending samples exhibit a similar elastic feature prior to failure, i.e., without any macroscopic plastic displacement. This indicates a typical brittle deformation feature for the studied BMG during bending. The maximum load, F and the maximum displacement, Dmax is 868.42 N and 0.3712 mm, 959.86 N and Fig. 2. The bending load-reflection curves of the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii (Color online).
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Fig. 3. The stress field distribution near the notch during three-point bending deformation of the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm (Color online).
Fig. 4. SEM micrographs of the whole fracture surface in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm.
were used. It can be seen from Fig. 3 that the stress distributions in the notched Zr-based BMG samples are highly complex due to the existence of artificial notches during bending tests. The area near the notch tip exhibits a maximum stress, whereas, the area away from the notch has smaller stress. This suggests that U-shaped notch causes high stress level around the notch, indicating a stress concentration. It can be also noticed that smaller notch radius causes a higher maximum stress near the notch tip, demonstrating a greater stress concentration. The stress concentration factor, Kt, is defined as the ratio of the
0.4465 mm, 1099.81 N and 0.4869 mm, and 1226.78 N and 0.5531 mm, for the bending sample with notch radius ρ of 0.2 mm, 0.3 mm, 0.5 mm, and 1.0 mm, respectively, as listed in Table 1. These above results suggest that the smaller notch radius will result in earlier brittle failure during bending test, considering that the loading conditions are identical for all Zr-based BMG alloy samples. The numerical simulation results of the stress distributions for Zrbased BMG samples under a load of 100 N are displayed in Fig. 3a–d, in which an elastic modulus of 94.8 GPa and a Poisson's ratio of 0.366
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Fig. 5. SEM micrographs of the fracture surface near the notch area in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm.
maximum stress, σmax, to the nominal stress that would exist in the materials if the stress distribution keeps uniform, σnom; that is [33],
Kt =
σmax σnom
the smooth region is a region main consisting of vein-like patterns, marked by II in Fig. 5, similar with those of typical compressive fractured surfaces for BMGs, caused by the subsequent catastrophic failure. Here, we call it as transition region. Such vein-like pattern in the fractured surface of BMGs indicate ductile fracture feature, which can be ascribed to a substantial rise in temperature associated with the conversion of the stored elastic energy to local heat during final deformation stage [35]. These vein-like patterns on the fractography also clearly reveal a pure shear fracture process of a BMG. The liquid droplets, demonstrating a local great temperature rise [36–38], can be also observed in this region, as seen in Fig. 6. Lewandowski and Greer [39] experimentally estimated the local temperature rise based on a fusible coating and suggested that there exists a remarkable temperature rise of a few thousand Kelvin for a few nanoseconds within a shear band. These vein-like pattern and liquid droplet features observed on the fractured surface of the failed samples indicate that the bending deformation process is characterized by the shear band nucleation and fast propagation, which cause a catastrophic fracture. Interestingly, numerous radiate cores with different diameters can be also detected in the transition region of the fractured surface. A typical core is highlighted in Fig. 6e. Zhang et al. [11] suggested that, during tensile test, the veins radiate from cores and propagate towards the outside, causing the formation of a radiating core feature in the fractured surface. Zhang et al. [11] attributed this core feature to normal tension stress in the initial stage of fracture. Therefore, the transition region experiences a complex stress state of shear stress and normal stress. During the final stage of bending deformation, rapid fracture region forms in the fractured surface, see Fig. 7. Numerous dense and fine dimples dominate the rapid fracture region of the fractured samples with different notch radii. As the notch radius increases, the rapid fracture region becomes more and more uneven. Fig. 8 shows 3-D laser scanning confocal microscope images of the fractured samples. Fig. 8 inset presents the corresponding surface
(1)
Upon the Mode I bending conditions, the maximum stress concentration occurs near the tip of the notches, where σnom can be calculated by,
σnom =
3FS 2B (w − a )2
(2)
where w is the width of the sample, a is the notch length, F is the maximum load, S is the span, and B is the thickness of the sample. Substituting the simulated σmax values and the results calculated based on Eq. (2) into Eq. (1) yields the corresponding stress concentration factor for the BMG samples with different notch radii. The calculated Kt values are also listed in Table 1. As seen, for the studied Zr-based BMG, Kt increases from 1.315 to 2.808 as the notch radius ρ decreases from 1.0 mm to 0.2 mm. Fractography is an excellent methodology to understand the deformation behaviors of a material. Fig. 4 shows the whole fractured surface morphologies of the failed samples. The whole fractured surface of the BMG samples after bending deformation can be roughly divided into three regions. A smooth region can be found near the artificial notch for the all bending samples, as seen in Fig. 5 marked by I. This smooth region was caused by shear sliding [34]. Here, we call it as crack propagation region. The width of the smooth region is equal to the critical shear offset, an efficient parameter directly indicating the stable shear deformation ability [34]. The shear offsets of the samples with notch radius ρ of 0.2 mm, 0.3 mm, 0.5 mm, and 1.0 mm, is ~ 130 μm [Fig.5a], 235 μm [Fig.5b], 420 μm [Fig.5c], and 480 μm [Fig.5d], respectively. This mean that the sliding along shear bands is also an important bending deformation mechanism of BMGs. Close to
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Fig. 6. SEM micrographs of the rapid propagation region of the fracture surface in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; d) ρ = 1.0 mm; and e) the radiating patterns and liquid droplets (Color online).
and has numerous fine dimples. For the bending samples with other radii, the fractured surfaces exhibit the same features with 0.2 mm one [Fig. 8b–8d]. It can be also seen from Fig. 8 that, as the notch radius increases, the roughness of all the three regions in the fractured surface gradually increases. To establish the relationship between the fracture toughness and the 3-D fractured surface of the bent BMG samples, the fracture process has been quantitatively interpreted based on a “grease” model which was proposed by Takayama and Maddin [40]. Based on this model, as the glass in the fracture process zone can be considered as a viscous fluid due to great local heating associated with plastic deformation in the vicinity of the crack tip, a fluid meniscus will form in the crack tip [41]. Local stress causes a negative pressure inside the fracture process zone. The balance between the negative pressure and the surface tension of the viscous fluid would lead to the formation of a curved fluid surface, called a fluid meniscus [41]. Thus, the crack propagation can be
profile across the fractured surface. The color evolution from red to blue means the profile evolution from high to low. In order to quantitatively analyze the effect of notch radius on the bending behaviors of the studied Zr-based BMG alloy samples, the line profiles across the three regions, i.e., the crack propagation region, transition region, and rapid fracture region, are taken from the fracture surfaces, and shown in the inset of Fig. 8. It can be seen from Fig. 8 that the fracture features of three regions, especially the vein height, are different with each other. Taking the sample with a notch radius of 0.2 mm for example [Fig. 8a], its rapid fracture region consists of periodic peaks and valleys, and there is a large drop between peaks and valleys. The whole rapid fracture region shows a very rough feature. Besides the valleys with a relatively shallower depth, the transition region possesses some meniscus dimple-like features, and is a little smoother than the crack propagation region. Crack propagation region is smoother than both the transition zone and the rapid fracture region,
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Fig. 7. SEM micrographs of the final fracture region of the fracture surface in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm;and d) ρ = 1.0 mm.
assumed to be a fluid flowing in a channel with a height of H. The shear dilatation of the viscous fluid would cause in the formation of numerous voids in the plastic deformation zone. As the cracks further propagate, the voids in the plastic deformation zone were merged with the main crack. Finally, numerous dimples with a height of h form in the fractured surface. Therefore, the channel height, H can be approximately estimated to be twice the vein height, h. According to the fluid meniscus instability, the relationship between the crack tip opening displacement (CTOD) and the critical stress intensity factor, i.e., fracture toughness, can be established as follows [41],
the artificial notch. This reveals that enhanced notch radius could lead to an improved fracture toughness of the glassy solids, as shown in Table 1. Therefore, the BMG sample with a larger notch radius fails sluggishly, and exhibits a higher maximum displacement and load, than that with a smaller notch radius, as shown in Fig. 2. Higher fracture toughness will result in a wider crack propagation region [Fig. 5], and higher roughness of the fracture surface for the sample with a smaller notch radius [Fig. 7, Fig. 8 and Table 1].
4. Summary
Kc =
CTODmσy E
(3) The effect of stress concentration induced by notch in the sample center on the deformation behaviors of a ZrCuNiAl bulk metallic glass has been studied at room temperature under bending loading. The notch radius of the bending sample exerts a crucial role on the deformation behaviors of the studied BMG. As the notch radius increases, both the maximum load and the maximum displacement prior to final failure increase. The fractured surface can be roughly divided into three regions, i.e., the crack propagation region, transition region, and rapid fracture region. The increase in the notch radius causes the gradual increase in the roughness of all the three regions in the fractured surface. Based on “grease” model, the relationship between the fracture toughness and the 3-D fracture surface of the bent BMG samples is quantitatively established. As the notch radius increases, the Kc value increases as well. Higher notch radius decreases the opening stress levels near the notch area, and promotes the plastic strain accumulation ahead of the notch, thereby causing higher fracture toughness of the studied BMG sample.
where m is a dimensionless constant depending on the material properties and the stress states, σyis the yield stress, and E is Young's modulus. The average vein height, h, is measured to be 5.56, 6.38, 6.54, and 7.09 μm for the bending sample with a notch radius of 0.2, 0.3, 0.5, and 1.0 mm, respectively, yielding Kc value of 38.42, 43.27, 46.88, and 51.56 MPa·m1/2 after substituting them into Eq. (3), as summarized in Table 1. Clearly, as the notch radius of the bending sample increases, the Kc value increases as well. From the above results, for the bending deformation of a BMG, a larger notch radius will result in a sluggish fracture, and higher fracture toughness. Next, this phenomenon will be interpreted based on the stress field around the notch. An increase in the notch radius leads to an increase in the plastic zone size ahead of the notch and causes this zone to rotate forward. Higher notch radius also results in a dramatic decrease in opening stress ahead of the artificial notch. Hydrostatic stress at all angles around the notch would reduce. Meanwhile, it also gives rise to a great increase in the plastic strain accumulation ahead of
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Fig. 8. Three dimensional (3-D) laser scanning confocal microscope images of the fracture surfaces in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm; The inset shows the corresponding surface profile. The column from left to right represents the rapid fracture region, transition region, and crack propagation region, respectively (Color online).
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
The effect of stress concentration on the bending behavior of a ZrCuNiAl bulk metallic glass Zhiliang Ninga,b,⁎, Yongjiang Huanga,b,⁎, Zhe Shenc, Haicao Suna,b, Weizhong Liangd, Jianfei Suna,b a
School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China National Key Laboratory of Precision Hot Processing of Metals, Harbin Institute of Technology, Harbin 150001, PR China c Shenyang Engine Research Institute, Aero Engine Corporation of China, Shenyang 110000, PR China d School of Materials Science and Engineering, Heilongjiang University of Science and Technology, Harbin 150027, PR China b
A R T I C L E I N F O
A B S T R A C T
Keywords: Bulk metallic glasses Stress concentration Bending Fracture
The bending behaviors of a Zr55Cu30Ni5Al10 bulk metallic glass (BMG) samples with different notch radii are studied. The artificial notch will introduce stress concentration within the BMG sample during bending. That means, smaller notch radius leads to greater stress concentration around the notch area, and thus results in earlier failure and smoother fracture surface. Then, the sample with smaller notch radius possesses smaller fracture toughness. The relationship between the stress concentration and deformation feature has been discussed in terms of grease model.
1. Introduction
sample geometry dependence of bending ductility of BMG plates; thin plate usually exhibits ductility while thicker plate with the same chemical composition shows brittle feature under identical loading condition. Liu and Wang [28] demonstrated the shear band evolution under bending in a super-plastic Zr-based BMG. During service, BMG components are often suffered to a multi-axial complex stress state induced by artificial defects, such as holes, and notches [29–32]. As a BMG material with an artificial defect is loaded, a great stress concentration usually takes place near the defect. As a result, the stress distribution is inhomogeneous over the whole cross-section, which could exert a crucial role on the deformation of the BMG materials. Until now few research has been focused on the bending behaviors of BMGs after the introduce of stress concentration. In the present work, Zr55Cu30Ni5Al10 (at. %) alloy was selected as the model material due to its excellent glass forming ability. Notches with different radii, as stress concentrators, were introduced into the BMG samples. The effect of stress concentration induced by notch on the bending behaviors of the Zr-based BMG was studied. The fracture morphologies of the failed samples were examined after bending deformation. It is expected that the results obtained can provide a better understanding the bending deformation mechanism of BMGs, and thus extend their applications in complex multi-axial stress states.
During the last decades, bulk metallic glasses (BMGs), also termed as bulk amorphous alloys, have triggered intensive attention from materials science researchers due to their importance in both fundamental science and industrial uses [1–5]. However, at a temperature far below the glass transition temperature, the plastic deformation of BMGs usually localizes within few narrow shear bands of ~20 nm thick, which causes catastrophic failure and a lack of plasticity [6–8]. Some monolithic metallic glasses exhibit great plastic deformation capacity upon compressive loading [9,10] whereas almost all BMGs show disappointed tensile plasticity [11]. Such a brittle feature hinders seriously any practical applications of BMGs. Therefore, to understand the intrinsic deformation mechanism and thus to improve the ductility of BMGs have recently become one of the most important issues in BMGs research community [12–16]. As a kind of high-performance materials for engineering applications, knowledge regarding how BMGs behave under bending conditions is critical [17–21]. Therefore, the bending behaviors of BMGs deserve further attention. When a BMG alloy sample subjected to bending condition, the inherent stress gradient induced by multi-axial stress would favor the formation of multiple shear bands. This has aroused considerable research interests [22–24]. Zhang et al. [25] studied the multiplication of shear bands aided by free volume under three-point bending of a BMG. Conner et al. [26,27] examined the
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Corresponding authors. E-mail addresses: [email protected] (Z. Ning), [email protected] (Y. Huang).
http://dx.doi.org/10.1016/j.jnoncrysol.2017.04.005 Received 5 January 2017; Received in revised form 15 February 2017; Accepted 11 April 2017 0022-3093/ © 2017 Elsevier B.V. All rights reserved.
Please cite this article as: Ning, Z., Journal of Non-Crystalline Solids (2017), http://dx.doi.org/10.1016/j.jnoncrysol.2017.04.005
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Table 1 The maximum load, F, the maximum displacement, Dmax, stress concentration factor, average dimple height, h, and fracture toughness of the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii, ρ. Notch radius, ρ (mm)
Maximum displacement, Dmax (mm)
Maximum load, F(N)
Stress concentration factor, Kt
Dimple height, h (μm)
Fracture toughness, Pa·m1/2
0.2 0.3 0.5 1.0
0.3712 0.4465 0.4869 0.5531
868.42 959.86 1099.81 1226.78
2.808 2.319 1.823 1.315
5.56 6.38 6.54 7.09
38.42 43.27 46.88 51.56
2. Experimental procedures Ingots with a nominal chemical composition of Zr55Cu30Ni5Al10 were produced by arc-melting a mixture of the starting pure Zr, Cu, Ni, and Al elements, each with 99.5 wt% purity or better, under a Tigettered argon atmosphere. Prior to the preparation of the master ingots, pure Ti was melted enough to absorb the oxygen within the chamber, which is harmful to glass formation. To ensure a chemical homogeneity, each ingot was remelted at least four times with electromagnetic stir. Then as-cast BMG samples with a 3 × 30 × 75 mm3 dimension were prepared by drop casting the remelted alloys into a copper mold. The amorphous nature of the ascast samples was confirmed by X-ray diffraction (XRD) with Cu Kα radiation. Three-point bending samples with a 3 × 5 × 30 mm3 dimension were electrical discharge machined from the as-cast BMG alloy samples, and the top and the bottom surfaces of the samples were then carefully grinded and polished. Notches with a radius of 0.2 mm, 0.3 mm, 0.5 mm, or 1.0 mm were cut at one edge in the middle of the samples. Notch length is 2.5 mm. The outer appearance of the bending samples is shown in Fig. 1a. Bending tests were conducted on a computer-controlled Instron 5500R type machine at a displacement rate of 0.3 mm/min. The span was set to be 24 mm. During bending tests, the load-deflection curves were recorded continuously. After testing, fracture surfaces of all failed samples were examined in a scanning electron microscope, SEM (FEI Helios Nanolab600i) or a 3-D laser scanning confocal microscope (Phenom Pro X). In addition, a finite-element method (FEM) with ABAQUS software was adopted to simulate the stress distributions of the studied Zr-based BMG samples with different notch radii upon bending condition.
Fig. 1. (a) The outer appearance (from top to bottom shows the sample with a notch radius of 0.2, 0.3, 0.5, 1.0 mm, respectively) and (b) XRD patterns of three-point bending Zr55Cu30Ni5Al10 (at. %) bulk metallic glass samples.
3. Results and discussion Fig. 1b shows the XRD pattern obtained from the as-cast quaternary ZrCuNiAl alloy sample. It can be seen from Fig. 1b that the pattern of cast samples consists of only a series of broad diffraction maxima, without any detectable sharp Bragg peaks corresponding to crystalline phase. This confirms that the as-cast plate-shaped sample is amorphous in nature. Fig. 2 presents the representative load-deflection curves obtained from the room temperature bending tests of the studied Zr-based BMG alloy samples with different notch radii. As can be seen, for the studied Zr-based BMG alloy, the bending samples exhibit a similar elastic feature prior to failure, i.e., without any macroscopic plastic displacement. This indicates a typical brittle deformation feature for the studied BMG during bending. The maximum load, F and the maximum displacement, Dmax is 868.42 N and 0.3712 mm, 959.86 N and Fig. 2. The bending load-reflection curves of the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii (Color online).
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Fig. 3. The stress field distribution near the notch during three-point bending deformation of the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm (Color online).
Fig. 4. SEM micrographs of the whole fracture surface in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm.
were used. It can be seen from Fig. 3 that the stress distributions in the notched Zr-based BMG samples are highly complex due to the existence of artificial notches during bending tests. The area near the notch tip exhibits a maximum stress, whereas, the area away from the notch has smaller stress. This suggests that U-shaped notch causes high stress level around the notch, indicating a stress concentration. It can be also noticed that smaller notch radius causes a higher maximum stress near the notch tip, demonstrating a greater stress concentration. The stress concentration factor, Kt, is defined as the ratio of the
0.4465 mm, 1099.81 N and 0.4869 mm, and 1226.78 N and 0.5531 mm, for the bending sample with notch radius ρ of 0.2 mm, 0.3 mm, 0.5 mm, and 1.0 mm, respectively, as listed in Table 1. These above results suggest that the smaller notch radius will result in earlier brittle failure during bending test, considering that the loading conditions are identical for all Zr-based BMG alloy samples. The numerical simulation results of the stress distributions for Zrbased BMG samples under a load of 100 N are displayed in Fig. 3a–d, in which an elastic modulus of 94.8 GPa and a Poisson's ratio of 0.366
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Fig. 5. SEM micrographs of the fracture surface near the notch area in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm.
maximum stress, σmax, to the nominal stress that would exist in the materials if the stress distribution keeps uniform, σnom; that is [33],
Kt =
σmax σnom
the smooth region is a region main consisting of vein-like patterns, marked by II in Fig. 5, similar with those of typical compressive fractured surfaces for BMGs, caused by the subsequent catastrophic failure. Here, we call it as transition region. Such vein-like pattern in the fractured surface of BMGs indicate ductile fracture feature, which can be ascribed to a substantial rise in temperature associated with the conversion of the stored elastic energy to local heat during final deformation stage [35]. These vein-like patterns on the fractography also clearly reveal a pure shear fracture process of a BMG. The liquid droplets, demonstrating a local great temperature rise [36–38], can be also observed in this region, as seen in Fig. 6. Lewandowski and Greer [39] experimentally estimated the local temperature rise based on a fusible coating and suggested that there exists a remarkable temperature rise of a few thousand Kelvin for a few nanoseconds within a shear band. These vein-like pattern and liquid droplet features observed on the fractured surface of the failed samples indicate that the bending deformation process is characterized by the shear band nucleation and fast propagation, which cause a catastrophic fracture. Interestingly, numerous radiate cores with different diameters can be also detected in the transition region of the fractured surface. A typical core is highlighted in Fig. 6e. Zhang et al. [11] suggested that, during tensile test, the veins radiate from cores and propagate towards the outside, causing the formation of a radiating core feature in the fractured surface. Zhang et al. [11] attributed this core feature to normal tension stress in the initial stage of fracture. Therefore, the transition region experiences a complex stress state of shear stress and normal stress. During the final stage of bending deformation, rapid fracture region forms in the fractured surface, see Fig. 7. Numerous dense and fine dimples dominate the rapid fracture region of the fractured samples with different notch radii. As the notch radius increases, the rapid fracture region becomes more and more uneven. Fig. 8 shows 3-D laser scanning confocal microscope images of the fractured samples. Fig. 8 inset presents the corresponding surface
(1)
Upon the Mode I bending conditions, the maximum stress concentration occurs near the tip of the notches, where σnom can be calculated by,
σnom =
3FS 2B (w − a )2
(2)
where w is the width of the sample, a is the notch length, F is the maximum load, S is the span, and B is the thickness of the sample. Substituting the simulated σmax values and the results calculated based on Eq. (2) into Eq. (1) yields the corresponding stress concentration factor for the BMG samples with different notch radii. The calculated Kt values are also listed in Table 1. As seen, for the studied Zr-based BMG, Kt increases from 1.315 to 2.808 as the notch radius ρ decreases from 1.0 mm to 0.2 mm. Fractography is an excellent methodology to understand the deformation behaviors of a material. Fig. 4 shows the whole fractured surface morphologies of the failed samples. The whole fractured surface of the BMG samples after bending deformation can be roughly divided into three regions. A smooth region can be found near the artificial notch for the all bending samples, as seen in Fig. 5 marked by I. This smooth region was caused by shear sliding [34]. Here, we call it as crack propagation region. The width of the smooth region is equal to the critical shear offset, an efficient parameter directly indicating the stable shear deformation ability [34]. The shear offsets of the samples with notch radius ρ of 0.2 mm, 0.3 mm, 0.5 mm, and 1.0 mm, is ~ 130 μm [Fig.5a], 235 μm [Fig.5b], 420 μm [Fig.5c], and 480 μm [Fig.5d], respectively. This mean that the sliding along shear bands is also an important bending deformation mechanism of BMGs. Close to
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Fig. 6. SEM micrographs of the rapid propagation region of the fracture surface in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; d) ρ = 1.0 mm; and e) the radiating patterns and liquid droplets (Color online).
and has numerous fine dimples. For the bending samples with other radii, the fractured surfaces exhibit the same features with 0.2 mm one [Fig. 8b–8d]. It can be also seen from Fig. 8 that, as the notch radius increases, the roughness of all the three regions in the fractured surface gradually increases. To establish the relationship between the fracture toughness and the 3-D fractured surface of the bent BMG samples, the fracture process has been quantitatively interpreted based on a “grease” model which was proposed by Takayama and Maddin [40]. Based on this model, as the glass in the fracture process zone can be considered as a viscous fluid due to great local heating associated with plastic deformation in the vicinity of the crack tip, a fluid meniscus will form in the crack tip [41]. Local stress causes a negative pressure inside the fracture process zone. The balance between the negative pressure and the surface tension of the viscous fluid would lead to the formation of a curved fluid surface, called a fluid meniscus [41]. Thus, the crack propagation can be
profile across the fractured surface. The color evolution from red to blue means the profile evolution from high to low. In order to quantitatively analyze the effect of notch radius on the bending behaviors of the studied Zr-based BMG alloy samples, the line profiles across the three regions, i.e., the crack propagation region, transition region, and rapid fracture region, are taken from the fracture surfaces, and shown in the inset of Fig. 8. It can be seen from Fig. 8 that the fracture features of three regions, especially the vein height, are different with each other. Taking the sample with a notch radius of 0.2 mm for example [Fig. 8a], its rapid fracture region consists of periodic peaks and valleys, and there is a large drop between peaks and valleys. The whole rapid fracture region shows a very rough feature. Besides the valleys with a relatively shallower depth, the transition region possesses some meniscus dimple-like features, and is a little smoother than the crack propagation region. Crack propagation region is smoother than both the transition zone and the rapid fracture region,
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Fig. 7. SEM micrographs of the final fracture region of the fracture surface in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm;and d) ρ = 1.0 mm.
assumed to be a fluid flowing in a channel with a height of H. The shear dilatation of the viscous fluid would cause in the formation of numerous voids in the plastic deformation zone. As the cracks further propagate, the voids in the plastic deformation zone were merged with the main crack. Finally, numerous dimples with a height of h form in the fractured surface. Therefore, the channel height, H can be approximately estimated to be twice the vein height, h. According to the fluid meniscus instability, the relationship between the crack tip opening displacement (CTOD) and the critical stress intensity factor, i.e., fracture toughness, can be established as follows [41],
the artificial notch. This reveals that enhanced notch radius could lead to an improved fracture toughness of the glassy solids, as shown in Table 1. Therefore, the BMG sample with a larger notch radius fails sluggishly, and exhibits a higher maximum displacement and load, than that with a smaller notch radius, as shown in Fig. 2. Higher fracture toughness will result in a wider crack propagation region [Fig. 5], and higher roughness of the fracture surface for the sample with a smaller notch radius [Fig. 7, Fig. 8 and Table 1].
4. Summary
Kc =
CTODmσy E
(3) The effect of stress concentration induced by notch in the sample center on the deformation behaviors of a ZrCuNiAl bulk metallic glass has been studied at room temperature under bending loading. The notch radius of the bending sample exerts a crucial role on the deformation behaviors of the studied BMG. As the notch radius increases, both the maximum load and the maximum displacement prior to final failure increase. The fractured surface can be roughly divided into three regions, i.e., the crack propagation region, transition region, and rapid fracture region. The increase in the notch radius causes the gradual increase in the roughness of all the three regions in the fractured surface. Based on “grease” model, the relationship between the fracture toughness and the 3-D fracture surface of the bent BMG samples is quantitatively established. As the notch radius increases, the Kc value increases as well. Higher notch radius decreases the opening stress levels near the notch area, and promotes the plastic strain accumulation ahead of the notch, thereby causing higher fracture toughness of the studied BMG sample.
where m is a dimensionless constant depending on the material properties and the stress states, σyis the yield stress, and E is Young's modulus. The average vein height, h, is measured to be 5.56, 6.38, 6.54, and 7.09 μm for the bending sample with a notch radius of 0.2, 0.3, 0.5, and 1.0 mm, respectively, yielding Kc value of 38.42, 43.27, 46.88, and 51.56 MPa·m1/2 after substituting them into Eq. (3), as summarized in Table 1. Clearly, as the notch radius of the bending sample increases, the Kc value increases as well. From the above results, for the bending deformation of a BMG, a larger notch radius will result in a sluggish fracture, and higher fracture toughness. Next, this phenomenon will be interpreted based on the stress field around the notch. An increase in the notch radius leads to an increase in the plastic zone size ahead of the notch and causes this zone to rotate forward. Higher notch radius also results in a dramatic decrease in opening stress ahead of the artificial notch. Hydrostatic stress at all angles around the notch would reduce. Meanwhile, it also gives rise to a great increase in the plastic strain accumulation ahead of
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Fig. 8. Three dimensional (3-D) laser scanning confocal microscope images of the fracture surfaces in the Zr55Cu30Ni5Al10 bulk metallic glass samples with different notch radii after three-point bending deformation tests: a) ρ = 0.2 mm; b) ρ = 0.3 mm; c) ρ = 0.5 mm; and d) ρ = 1.0 mm; The inset shows the corresponding surface profile. The column from left to right represents the rapid fracture region, transition region, and crack propagation region, respectively (Color online).
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