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Compressive fracture characteristics of Ni42Cu5Ti19Zr22.5Al8Si3.5 bulk metallic glass
Materials Science and Engineering A 497 (2008) 378–382
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Compressive fracture characteristics of Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 bulk metallic glass W.Z. Liang a,c , J. Shen b,∗ , J.F. Sun b , L.Z. Wu d , P.K. Liaw e a
Postdoctoral Research Station on Mechanics, Harbin Institute of Technology, 150001, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c School of Materials Science and Engineering, Heilongjiang Institute of Science and Technology, Harbin 150027, China d Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, China e Department of Materials Science and Engineering, University of Tennesee, Knoxville, TN 37996-2200, USA b
a r t i c l e
i n f o
Article history: Received 2 April 2008 Received in revised form 15 July 2008 Accepted 15 July 2008 Keywords: Bulk metallic glasses Fracture mode Mechanical properties
a b s t r a c t The uniaxial compressive fracture behavior of Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 bulk metallic glass (BMG) was investigated. It was found that the 2 mm rod exhibited a high fracture strength of 2851 MPa and plastic strain of 0.5%, while the 3 mm sample showed a fracture strength of 2724 MPa and nearly zero plastic strain. The property difference in the two samples was explained due to different structure caused by different cooling rates in glass formation. The compressive fracture surfaces of the deformed samples consisted of a flat shear zone and a coarse zone. The compressive fracture angles between the stress axis and the fracture plane changed from <45 to 90◦ as the fracture proceeded, suggesting that the compression fracture mechanism of the alloy might be understood in terms of the ellipse criterion. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The research on mechanical behavior of BMGs has become a hot topic due to their increasing glass-forming ability and excellent mechanical properties, such as high strength and elastic strain limit. Despite considerable theoretical and experimental investigations, large discrepancy still exists in understanding the deformation and fracture mechanisms of BMGs [1,2]. The plastic flow of BMGs only occurs within shear bands by a highly localized manner owing to lack of dislocations and grains [3–5]. It was reported recently that the as-cast Cu50 Zr50 BMGs sustained a compressive plastic strain of more than 50% at room temperature due to containing a dispersion of embedded nanocrystals, which was explained by the suppression of shear softening through nanocrystal coalescence [6] Lewandowski et al. [7] pointed out that the intrinsic plasticity or brittleness of metallic glasses correlated with the ratio of the elastic shear modulus to the bulk modulus B. When the ratio /B exceeds a critical value 0.41–0.43, the metallic glasses are brittle. On the fracture mechanism of BMGs, Zhang et al. [8] proposed an ellipse criterion adapted for describing the tensile fracture behavior, which unified the classical failure criteria, such as maximum normal stress and Mohr–Coulomb criterion. It was reported that the Mohr–Coulomb criterion could reasonably explain the slight
∗ Corresponding author. Tel.: +86 451 86418317; fax: +86 451 86415776. E-mail address: [email protected] (J. Shen). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.07.040
deviation of BMGs’ compressive fracture angles from the maximum shear planes owing to normal compressive stress [9,10]. However, it was well known that the Mohr–Coulomb criterion could not interpret why a BMG rod failed along a plane perpendicular to the stress axis. In this paper, the unique fracture morphology features of Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG with diameters of 2 and 3 mm were analyzed. It was thought that different degree amorphous structure affected the plastic flow. The ellipse criterion, being suitable for tensile fracture, still could be used for explaining the change of compressive fracture angles from <45 to 90◦ during the fracture process of a BMG sample.
2. Experimental Button ingots of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 alloy were fabricated by arc melting of mixtures of the composing elements (99.9% purity) in a Ti-gettered argon atmosphere. BMG rods with diameters of 2 and 3 mm were synthesized by casting the melt into a copper mould in a purified argon atmosphere. The structure was characterized by X-ray diffraction (XRD) with Cu K␣ radiation ( = 1.5405 Å) using a D/MAX-RB diffractometer. Thermal analysis was carried out by a Pyris-1 differential scanning calorimetry (DSC) at a heating rate of 0.33 K/s. Compression tests were performed on the cylindrical rods of 2 mm in diameter and 4 mm in length, and 3 mm in diameter and 6 mm in length by using an INSTRON5569 testing machine at room temperature with a strain rate of
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3 × 10−4 s−1 . Fractured specimens were observed in an FEI Sirion high-resolution scanning electron microscope (HRSEM) operated at 20 kV with a resolution of 1.5 nm. Nanoindentation experiments were conducted using an XP nanoindenter in load-control mode with a load of 10 mN at a loading rate of 0.025 mN/s. 3. Results 3.1. Effect of cooling rate on amorphous structure Due to the differences in the enthalpy of crystallization (Hx ), the glass transition temperature (Tg ) and the crystallization temperature (Tx ), the structure differences in the rods with diameters of 2 and 3 mm may be evidenced by the DSC curves, as shown in Fig. 1. The values of Hx , Tg and Tx of the 2 mm rod are −41.1 J/g, 795 K and 855 K, respectively, while those values for the 3 mm rod are −39.7 J/g, 784 K and 852 K, respectively. Tg of the 2 mm rod is distinctly higher than that of 3 mm sample, indicating that the 2 mm rod has much more free volume. The slightly lower Hx suggests that there are a small amount of nano-sized crystals in the 3 mm rod assuming that the 2 mm sample is fully amorphous. X-ray diffraction experiments were carried out to confirm the amorphous structure degrees of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 alloys. As shown in the XRD patterns (the inset in Fig. 1), no appreciable crystallization diffraction peaks are observed on the main broad maxima for the 2 mm alloys indicative of an amorphous structure, while a faint crystallization peak is detected for the 3 mm sample (pointed by arrow). This implies the structure difference between 2 and 3 mm rods due to their different cooling rates in solidification. 3.2. Compressive mechanical properties at room temperature and fracture features The nominal compressive stress–strain curves of the 2 and 3 mm samples are shown in Fig. 2. The 2 mm rod exhibits a fracture strength of 2851 MPa and plastic strain of 0.5%, while the 3 mm sample displays a strength of 2724 MPa and no any measurable plasticity. It can be seen that the strength and plasticity of the amorphous alloy with the same chemical composition strongly rely on their structures, which are determined by the cooling rates of the samples experienced during the solidification process.
Fig. 1. The DSC curves and XRD patterns (inset) of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG with different diameters: (a) 3 mm and (b) 2 mm.
Fig. 2. The stress–strain curves of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG with different diameters: (a) 2 mm and (b) 3 mm.
Figs. 3 and 4 show the SEM micrographs of the compression fracture surfaces of 2 and 3 mm rods, respectively. Fig. 3a clearly exhibits a typical flat shear zone (A) followed by a hackle zone (B) on the fracture surface, and some long shear bands on the side surface (pointed by arrows). The shear fracture angle between the shear plane and the stress axes is about 43.8◦ (inset in Fig. 3a). The similar compressive fracture features were observed in Nibased and Cu-based BMGs [11–14]. However, the hackle zone B has rarely been mentioned in detail before [15]. Fig. 3b shows the characteristic vein pattern produced by the initiation and propagation of local shear bands upon fracture [16], and some resolidified droplets caused by the localized melting during the final fracture [17]. Fig. 3c displays the rough fracture surface (zone B) with flower-like patterns, the cores of which are indicated by arrows. Fig. 4a shows a similar flat shear zone A and rough zone B on the fracture surface of the 3 mm sample. However, the proportion of the shear zone in the 3 mm sample is smaller than that in 2 mm sample. The angle between shear plane and stress axis is about 41.8◦ (inset in Fig. 4a), and a few shorter shear bands form on the side surface of the 3 mm sample. More recently some researches demonstrated that the closer to 45◦ the shear fracture angle, the higher the plastic strain would be [6,18]. Our observations confirm this relationship between fracture angle and plasticity. The unique fish-bone type vein patterns are observed in shear zone A and the more fully developed flower-like patterns are clearly exhibited in rough zone B, as shown in Fig. 4b and c, respectively. Small areas of the rough fracture surfaces, as indicated by circles in Figs. 3c and 4c, were further observed with HRSEM to investigate the deformation and fracture behaviors of the studied alloy. A typical dimple structure at 100–400 nm scale was found in the 2 mm sample, while the 100–200 nm dimple structure was observed for the 3 mm alloy, as shown in Fig. 5a and b, respectively. This kind of similar dimple structure was also reported in Zr-based BMGs under tensile condition but at different size scales [19]. These results indicate that the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG exhibits plastic flow in local shear bands. The associated microvoids also give the evidence of high local plasticity arising from instabilities in the shear band of lowered viscosity [1]. It can be seen from the shape of the dimples that the local plasticity of the 2 mm rod is larger than that of 3 mm rod. However, the minor local plasticity has no distinct effect on the global compressive plasticity.
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Fig. 4. The compressive fracture features of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG rod with a diameter of 3 mm: (a) the fracture feature with shear zone A and coarse zone B, inset shows the shear fracture angle; (b) zone A at larger magnification; (c) zone B at larger magnification. Fig. 3. The compressive fracture features of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG rod with a diameter of 2 mm: (a) the fracture feature with shear zone A and coarse zone B, inset shows the shear fracture angle; (b) zone A at larger magnification; (c) zone B at larger magnification.
4. Discussion 4.1. Compressive property difference in 2 and 3 mm rods The microstructure difference in the BMG samples with different size has been confirmed by DSC results and XRD patterns. Two samples exhibit different fracture strength and plastic strain, as shown in their stress–strain curves. These results indicate that the plasticity and strength of the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG depend on its amorphous structure. The appreciable plastic strain in the 2 mm as-cast alloy might be explained by shear transition model. According to shear transition model proposed by Argon [20], the plastic deformation rate at room temperature, , ˙ might
be expressed by: ˙ = ˙ G exp
−G∗ kT
(1)
where ˙ G is the pre-exponential constant, G* the activation free enthalpy, k Boltzmann’s constant, and T temperature. Due to a higher cooling rate, the 2 mm BMG alloy contains a larger amount of free volume compared with the 3 mm alloy. The more excess free volume may result in smaller free energy barrier for shear transformation and the activation free enthalpy G* for the plastic flow [20]. In view of the Eq. (1), relative large plastic deformation would occur in the 2 mm rod. Dense characteristic vein patterns and plentiful resolidified droplets were observed on the failure surface of the 2 mm rod, indicating that the glass viscosity within the shear bands had greatly decreased [21]. The serrated stress–strain curve of the 2 mm rod representing 0.5% plastic strain with many small load drops corresponded to the activation of individual shear bands [22]. The macroscopic shear bands propagating over the whole sample surface essentially indicates the improved plastic deformation of the 2 mm sample.
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Fig. 6. The nanoindentation load–displacement curves of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG with different diameters: (a) 2 mm and (b) 3 mm.
Fig. 5. The amplified image of the circled site (a) in Fig. 3c and (b) in Fig. 4c.
To further reveal the effect of the microstructure on the fracture behavior of the BMG alloy, nanoindentation experiments were carried out on the 2 and 3 mm rods in a load-control mode. The nanoindentation load–displacement curves are shown in Fig. 6. The discrete displacement bursts on the loading portion of the load–displacement curve are more distinctly visible for the 2 mm sample compared to those for the 3 mm sample, indicating larger
micro-plastic deformation occurring in the former sample. This behavior is analogous to the serrated flow observed in compression tests of the present alloy, each serration corresponds to the operation of a single shear band that quickly accommodates the applied strain, which is determined by atomic structure depending on the different cooling rates in solidification process [22,23]. The true amount of plastic displacement of the 2 mm rod that is revealed by the residual depth after unloading of the nanoindent [22], is distinctly smaller than that of the 3 mm sample. 4.2. Compression fracture mechanism The shear fracture angles of the 2 and 3 mm BMG rods are 43.8 and 41.8◦ , respectively. This indicates that the fracture planes deviate from the maximum shear stress plane (45◦ ). Following the shear fracture, the Ni-based BMG fractured along the maximum normal stress plane (90◦ ). In other words, the pure shear fracture mode
Fig. 7. Schematic illustration of the formation of tensile stress in compression: (a) crack propagating approximately along the maximum shear direction (45◦ ); (b) tensile stress and moment formation due to loading direction deviation from the center axis of the sample; (c) final fracture. The counter-clockwise bending moment as indicated represents the bending moment of the upper part of the specimen.
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did not prevail over the whole fracture process. This suggests that Mohr–Coulomb criterion cannot explain the BMG’s fracture behavior. Deviation of the fracture plane away from the maximum shear plane shows that fracture and deformation of BMGs have a dependency on the normal stress acting on the shear plane [24]. Our observations clearly show that tensile stress is indeed present in the material even under the compressive loading, as verified by the presence of core-like structure on the fracture surface, typical of a tensile stress induced fracture [9,10]. Fig. 7 schematically shows how the stress state changes as the fracture process proceeds. At the initial stage of fracture under compressive loading, cracking starts from the surface of the specimen, the fracture occurs in a pure shear mode. The compressive loading, , can be disassembled as the normal stress, c , exerting on the fracture plane, and the shear stress, c , driving the crack to propagate along the fracture plane (see Fig. 7a, where denotes the angle between the shear stress and the compressive loading direction). As the main crack propagates, the crack-induced gap between the upper part and the lower part of the specimen yields the building-up of tensile stress and moment, M, ahead of the crack tip, and the local stress state changes accordingly (see Fig. 7b). As the energy input upon loading accumulates, the main crack becomes unstable due to the rapid increase in cracking velocity, leading to microbranching and final failure (see Fig. 7c). The radiating veins with round cores exist on the fracture surfaces (Figs. 3c and 4c), suggesting that the normal tensile stress induces the nucleation of the cores and the shear stress drives the propagation of the radiating veins [9,10]. Due to the changes in the roles of shear stress and normal stress and the fracture angles in fracture process, it can be assumed that the ellipse criterion [8] is more suitable to describe the failure behavior of the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG. Accordingly, we can have: 2 02
+
2 02
≥1
(2)
where 0 is the critical normal fracture stress, 0 is the critical shear fracture stress, is the normal fracture stress, and is the shear fracture stress. When the ratio ˛ = 0 / 0 → 0, the fracture angle should be quite close to 45◦ , which represents shear fracture mode, agreeing with Tresca criterion. However, when the ratio ˛ = 0 /0 ≥ √ 2/2, the fracture angle equals 90◦ , i.e., the compressive fracture occurs along the plane perpendicular to the compressive axis. This implies that compressive fracture accords with the maximum normal stress criterion. So, we can conclude that the failure mode of the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG can be reasonably understood in the frame of the ellipse criterion.
5. Conclusions Due to difference in the structure, the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG rods with diameters of 2 and 3 mm exhibit different fracture strength and plasticity upon compression. The higher the cooling rate for glass formation, the more free volumes trapped in the glassy alloy and the larger the plasticity of the material would be. The compressive fracture surfaces consists of a smooth shear zone and a coarse zone, accompanying the fracture angles changing from <45 to 90◦ , suggesting that the compressive fracture might satisfy the ellipse criterion. The formation of microvoids in the fracture process is believed resulting from the presence of tensile stress on the fracture planes. Acknowledgments This work was supported by the National Natural Science Foundation of China under grant Nos. 50771040 and 10732010 (J. Shen) and the Foundation of China Postdoctor (20070420871), the Foundation of Heilongjiang Province Postdoctor (AUGA41001081) and the Education Bureau of Heilongjiang Province, under Project No.11531316 and HIST(07-57). (W.Z. Liang). References [1] X.K. Xi, D.Q. Zhao, M.X. Pan, W.H. Wang, Y. Wu, J.J. Lewandowski, Phys. Rev. Lett. 94 (2005) 125510. [2] J.-P. Guin, S.M. Wiederhorn, Phys. Rev. Lett. 29 (2004) 215502. [3] F. Spaepen, Acta Metall. 25 (1977) 407. [4] E. Pekarskaya, C.P. Kim, W.L. Johnson, J. Mater. Res. 16 (2001) 2513. [5] B. Yang, M.L. Morrison, P.K. Liaw, R.A. Buchanan, G.Y. Wang, C.T. Liu, Appl. Phys. Lett. 86 (2005) 141904. [6] A. Inoue, W. Zhang, T. Tsurui, A.R. Yavaris, A.L. Greer, Phil. Mag. Lett. 85 (2005) 221. [7] J.J. Lewandowski, W.H. Wang, A.L. Greer, Phil. Mag. Lett. 85 (2005) 77. [8] Z.F. Zhang, J. Eckert, Phys. Rev. Lett. 94 (2005) 094301. [9] Z.F. Zhang, J. Eckert, L. Schultz, Acta Mater. 51 (2003) 1167. [10] Z.F. Zhang, G. He, J. Eckert, L. Schultz, Phys. Rev. Lett. 91 (2003) 045505. [11] S.J. Pang, T. Zhang, K. Asami, A. Inoue, Mater. Sci. Eng. A 375–377 (2004) 368. [12] W. Zhang, A. Inoue, Scripta Mater. 48 (2003) 641. [13] A. Inoue, W. Zhang, T. Zhang, K. Kurosaka, Acta Mater. 49 (2001) 2645. [14] J.K. Lee, D.H. Bae, S. Yi, W.T. Kim, D.H. Kim, J. Non-Cryst Solids 333 (2004) 212. [15] J. Shen, W.Z. Liang, J.F. Sun, Appl. Phys. Lett. 86 (2006) 141904. [16] N. Nagendra, U. Ramamurty, T.T. Goh, Y. Li, Acta Mater. 48 (2000) 2603. [17] W.J. Wright, R.B. Schwarz, W.D. Nix, Mater. Sci. Eng. A 319–321 (2001) 229. [18] Z.F. Zhang, G. He, H. Zhang, J. Eckert, Scripta Mater. 52 (2005) 945. [19] J. Saida, A. Deny, H. Setyawan, H. Kato, A. Inoue, Appl. Phys. Lett. 87 (2005) 151907. [20] A.S. Agron, Acta Metall. 27 (1979) 47. [21] K.A. Flores, R.H. Dauskardt, Intermetallics 12 (2004) 1025. [22] T.G. Nieh, C. Schuh, J. Wadsworth, Y. Li, Intermetallics 10 (2002) 1177. [23] C.A. Schuh, T.G. Nieh, Acta Mater. 51 (2003) 87. [24] P. Lowhapandu, S.L. Montgomery, J.J. Lewandowki, Scripta Mater. 41 (1999)19.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Compressive fracture characteristics of Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 bulk metallic glass W.Z. Liang a,c , J. Shen b,∗ , J.F. Sun b , L.Z. Wu d , P.K. Liaw e a
Postdoctoral Research Station on Mechanics, Harbin Institute of Technology, 150001, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c School of Materials Science and Engineering, Heilongjiang Institute of Science and Technology, Harbin 150027, China d Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, China e Department of Materials Science and Engineering, University of Tennesee, Knoxville, TN 37996-2200, USA b
a r t i c l e
i n f o
Article history: Received 2 April 2008 Received in revised form 15 July 2008 Accepted 15 July 2008 Keywords: Bulk metallic glasses Fracture mode Mechanical properties
a b s t r a c t The uniaxial compressive fracture behavior of Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 bulk metallic glass (BMG) was investigated. It was found that the 2 mm rod exhibited a high fracture strength of 2851 MPa and plastic strain of 0.5%, while the 3 mm sample showed a fracture strength of 2724 MPa and nearly zero plastic strain. The property difference in the two samples was explained due to different structure caused by different cooling rates in glass formation. The compressive fracture surfaces of the deformed samples consisted of a flat shear zone and a coarse zone. The compressive fracture angles between the stress axis and the fracture plane changed from <45 to 90◦ as the fracture proceeded, suggesting that the compression fracture mechanism of the alloy might be understood in terms of the ellipse criterion. © 2008 Elsevier B.V. All rights reserved.
1. Introduction The research on mechanical behavior of BMGs has become a hot topic due to their increasing glass-forming ability and excellent mechanical properties, such as high strength and elastic strain limit. Despite considerable theoretical and experimental investigations, large discrepancy still exists in understanding the deformation and fracture mechanisms of BMGs [1,2]. The plastic flow of BMGs only occurs within shear bands by a highly localized manner owing to lack of dislocations and grains [3–5]. It was reported recently that the as-cast Cu50 Zr50 BMGs sustained a compressive plastic strain of more than 50% at room temperature due to containing a dispersion of embedded nanocrystals, which was explained by the suppression of shear softening through nanocrystal coalescence [6] Lewandowski et al. [7] pointed out that the intrinsic plasticity or brittleness of metallic glasses correlated with the ratio of the elastic shear modulus to the bulk modulus B. When the ratio /B exceeds a critical value 0.41–0.43, the metallic glasses are brittle. On the fracture mechanism of BMGs, Zhang et al. [8] proposed an ellipse criterion adapted for describing the tensile fracture behavior, which unified the classical failure criteria, such as maximum normal stress and Mohr–Coulomb criterion. It was reported that the Mohr–Coulomb criterion could reasonably explain the slight
∗ Corresponding author. Tel.: +86 451 86418317; fax: +86 451 86415776. E-mail address: [email protected] (J. Shen). 0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.07.040
deviation of BMGs’ compressive fracture angles from the maximum shear planes owing to normal compressive stress [9,10]. However, it was well known that the Mohr–Coulomb criterion could not interpret why a BMG rod failed along a plane perpendicular to the stress axis. In this paper, the unique fracture morphology features of Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG with diameters of 2 and 3 mm were analyzed. It was thought that different degree amorphous structure affected the plastic flow. The ellipse criterion, being suitable for tensile fracture, still could be used for explaining the change of compressive fracture angles from <45 to 90◦ during the fracture process of a BMG sample.
2. Experimental Button ingots of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 alloy were fabricated by arc melting of mixtures of the composing elements (99.9% purity) in a Ti-gettered argon atmosphere. BMG rods with diameters of 2 and 3 mm were synthesized by casting the melt into a copper mould in a purified argon atmosphere. The structure was characterized by X-ray diffraction (XRD) with Cu K␣ radiation ( = 1.5405 Å) using a D/MAX-RB diffractometer. Thermal analysis was carried out by a Pyris-1 differential scanning calorimetry (DSC) at a heating rate of 0.33 K/s. Compression tests were performed on the cylindrical rods of 2 mm in diameter and 4 mm in length, and 3 mm in diameter and 6 mm in length by using an INSTRON5569 testing machine at room temperature with a strain rate of
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3 × 10−4 s−1 . Fractured specimens were observed in an FEI Sirion high-resolution scanning electron microscope (HRSEM) operated at 20 kV with a resolution of 1.5 nm. Nanoindentation experiments were conducted using an XP nanoindenter in load-control mode with a load of 10 mN at a loading rate of 0.025 mN/s. 3. Results 3.1. Effect of cooling rate on amorphous structure Due to the differences in the enthalpy of crystallization (Hx ), the glass transition temperature (Tg ) and the crystallization temperature (Tx ), the structure differences in the rods with diameters of 2 and 3 mm may be evidenced by the DSC curves, as shown in Fig. 1. The values of Hx , Tg and Tx of the 2 mm rod are −41.1 J/g, 795 K and 855 K, respectively, while those values for the 3 mm rod are −39.7 J/g, 784 K and 852 K, respectively. Tg of the 2 mm rod is distinctly higher than that of 3 mm sample, indicating that the 2 mm rod has much more free volume. The slightly lower Hx suggests that there are a small amount of nano-sized crystals in the 3 mm rod assuming that the 2 mm sample is fully amorphous. X-ray diffraction experiments were carried out to confirm the amorphous structure degrees of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 alloys. As shown in the XRD patterns (the inset in Fig. 1), no appreciable crystallization diffraction peaks are observed on the main broad maxima for the 2 mm alloys indicative of an amorphous structure, while a faint crystallization peak is detected for the 3 mm sample (pointed by arrow). This implies the structure difference between 2 and 3 mm rods due to their different cooling rates in solidification. 3.2. Compressive mechanical properties at room temperature and fracture features The nominal compressive stress–strain curves of the 2 and 3 mm samples are shown in Fig. 2. The 2 mm rod exhibits a fracture strength of 2851 MPa and plastic strain of 0.5%, while the 3 mm sample displays a strength of 2724 MPa and no any measurable plasticity. It can be seen that the strength and plasticity of the amorphous alloy with the same chemical composition strongly rely on their structures, which are determined by the cooling rates of the samples experienced during the solidification process.
Fig. 1. The DSC curves and XRD patterns (inset) of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG with different diameters: (a) 3 mm and (b) 2 mm.
Fig. 2. The stress–strain curves of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG with different diameters: (a) 2 mm and (b) 3 mm.
Figs. 3 and 4 show the SEM micrographs of the compression fracture surfaces of 2 and 3 mm rods, respectively. Fig. 3a clearly exhibits a typical flat shear zone (A) followed by a hackle zone (B) on the fracture surface, and some long shear bands on the side surface (pointed by arrows). The shear fracture angle between the shear plane and the stress axes is about 43.8◦ (inset in Fig. 3a). The similar compressive fracture features were observed in Nibased and Cu-based BMGs [11–14]. However, the hackle zone B has rarely been mentioned in detail before [15]. Fig. 3b shows the characteristic vein pattern produced by the initiation and propagation of local shear bands upon fracture [16], and some resolidified droplets caused by the localized melting during the final fracture [17]. Fig. 3c displays the rough fracture surface (zone B) with flower-like patterns, the cores of which are indicated by arrows. Fig. 4a shows a similar flat shear zone A and rough zone B on the fracture surface of the 3 mm sample. However, the proportion of the shear zone in the 3 mm sample is smaller than that in 2 mm sample. The angle between shear plane and stress axis is about 41.8◦ (inset in Fig. 4a), and a few shorter shear bands form on the side surface of the 3 mm sample. More recently some researches demonstrated that the closer to 45◦ the shear fracture angle, the higher the plastic strain would be [6,18]. Our observations confirm this relationship between fracture angle and plasticity. The unique fish-bone type vein patterns are observed in shear zone A and the more fully developed flower-like patterns are clearly exhibited in rough zone B, as shown in Fig. 4b and c, respectively. Small areas of the rough fracture surfaces, as indicated by circles in Figs. 3c and 4c, were further observed with HRSEM to investigate the deformation and fracture behaviors of the studied alloy. A typical dimple structure at 100–400 nm scale was found in the 2 mm sample, while the 100–200 nm dimple structure was observed for the 3 mm alloy, as shown in Fig. 5a and b, respectively. This kind of similar dimple structure was also reported in Zr-based BMGs under tensile condition but at different size scales [19]. These results indicate that the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG exhibits plastic flow in local shear bands. The associated microvoids also give the evidence of high local plasticity arising from instabilities in the shear band of lowered viscosity [1]. It can be seen from the shape of the dimples that the local plasticity of the 2 mm rod is larger than that of 3 mm rod. However, the minor local plasticity has no distinct effect on the global compressive plasticity.
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Fig. 4. The compressive fracture features of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG rod with a diameter of 3 mm: (a) the fracture feature with shear zone A and coarse zone B, inset shows the shear fracture angle; (b) zone A at larger magnification; (c) zone B at larger magnification. Fig. 3. The compressive fracture features of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG rod with a diameter of 2 mm: (a) the fracture feature with shear zone A and coarse zone B, inset shows the shear fracture angle; (b) zone A at larger magnification; (c) zone B at larger magnification.
4. Discussion 4.1. Compressive property difference in 2 and 3 mm rods The microstructure difference in the BMG samples with different size has been confirmed by DSC results and XRD patterns. Two samples exhibit different fracture strength and plastic strain, as shown in their stress–strain curves. These results indicate that the plasticity and strength of the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG depend on its amorphous structure. The appreciable plastic strain in the 2 mm as-cast alloy might be explained by shear transition model. According to shear transition model proposed by Argon [20], the plastic deformation rate at room temperature, , ˙ might
be expressed by: ˙ = ˙ G exp
−G∗ kT
(1)
where ˙ G is the pre-exponential constant, G* the activation free enthalpy, k Boltzmann’s constant, and T temperature. Due to a higher cooling rate, the 2 mm BMG alloy contains a larger amount of free volume compared with the 3 mm alloy. The more excess free volume may result in smaller free energy barrier for shear transformation and the activation free enthalpy G* for the plastic flow [20]. In view of the Eq. (1), relative large plastic deformation would occur in the 2 mm rod. Dense characteristic vein patterns and plentiful resolidified droplets were observed on the failure surface of the 2 mm rod, indicating that the glass viscosity within the shear bands had greatly decreased [21]. The serrated stress–strain curve of the 2 mm rod representing 0.5% plastic strain with many small load drops corresponded to the activation of individual shear bands [22]. The macroscopic shear bands propagating over the whole sample surface essentially indicates the improved plastic deformation of the 2 mm sample.
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Fig. 6. The nanoindentation load–displacement curves of the Ni42 Ti19 Zr22.5 Al8 Cu5 Si3.5 BMG with different diameters: (a) 2 mm and (b) 3 mm.
Fig. 5. The amplified image of the circled site (a) in Fig. 3c and (b) in Fig. 4c.
To further reveal the effect of the microstructure on the fracture behavior of the BMG alloy, nanoindentation experiments were carried out on the 2 and 3 mm rods in a load-control mode. The nanoindentation load–displacement curves are shown in Fig. 6. The discrete displacement bursts on the loading portion of the load–displacement curve are more distinctly visible for the 2 mm sample compared to those for the 3 mm sample, indicating larger
micro-plastic deformation occurring in the former sample. This behavior is analogous to the serrated flow observed in compression tests of the present alloy, each serration corresponds to the operation of a single shear band that quickly accommodates the applied strain, which is determined by atomic structure depending on the different cooling rates in solidification process [22,23]. The true amount of plastic displacement of the 2 mm rod that is revealed by the residual depth after unloading of the nanoindent [22], is distinctly smaller than that of the 3 mm sample. 4.2. Compression fracture mechanism The shear fracture angles of the 2 and 3 mm BMG rods are 43.8 and 41.8◦ , respectively. This indicates that the fracture planes deviate from the maximum shear stress plane (45◦ ). Following the shear fracture, the Ni-based BMG fractured along the maximum normal stress plane (90◦ ). In other words, the pure shear fracture mode
Fig. 7. Schematic illustration of the formation of tensile stress in compression: (a) crack propagating approximately along the maximum shear direction (45◦ ); (b) tensile stress and moment formation due to loading direction deviation from the center axis of the sample; (c) final fracture. The counter-clockwise bending moment as indicated represents the bending moment of the upper part of the specimen.
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did not prevail over the whole fracture process. This suggests that Mohr–Coulomb criterion cannot explain the BMG’s fracture behavior. Deviation of the fracture plane away from the maximum shear plane shows that fracture and deformation of BMGs have a dependency on the normal stress acting on the shear plane [24]. Our observations clearly show that tensile stress is indeed present in the material even under the compressive loading, as verified by the presence of core-like structure on the fracture surface, typical of a tensile stress induced fracture [9,10]. Fig. 7 schematically shows how the stress state changes as the fracture process proceeds. At the initial stage of fracture under compressive loading, cracking starts from the surface of the specimen, the fracture occurs in a pure shear mode. The compressive loading, , can be disassembled as the normal stress, c , exerting on the fracture plane, and the shear stress, c , driving the crack to propagate along the fracture plane (see Fig. 7a, where denotes the angle between the shear stress and the compressive loading direction). As the main crack propagates, the crack-induced gap between the upper part and the lower part of the specimen yields the building-up of tensile stress and moment, M, ahead of the crack tip, and the local stress state changes accordingly (see Fig. 7b). As the energy input upon loading accumulates, the main crack becomes unstable due to the rapid increase in cracking velocity, leading to microbranching and final failure (see Fig. 7c). The radiating veins with round cores exist on the fracture surfaces (Figs. 3c and 4c), suggesting that the normal tensile stress induces the nucleation of the cores and the shear stress drives the propagation of the radiating veins [9,10]. Due to the changes in the roles of shear stress and normal stress and the fracture angles in fracture process, it can be assumed that the ellipse criterion [8] is more suitable to describe the failure behavior of the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG. Accordingly, we can have: 2 02
+
2 02
≥1
(2)
where 0 is the critical normal fracture stress, 0 is the critical shear fracture stress, is the normal fracture stress, and is the shear fracture stress. When the ratio ˛ = 0 / 0 → 0, the fracture angle should be quite close to 45◦ , which represents shear fracture mode, agreeing with Tresca criterion. However, when the ratio ˛ = 0 /0 ≥ √ 2/2, the fracture angle equals 90◦ , i.e., the compressive fracture occurs along the plane perpendicular to the compressive axis. This implies that compressive fracture accords with the maximum normal stress criterion. So, we can conclude that the failure mode of the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG can be reasonably understood in the frame of the ellipse criterion.
5. Conclusions Due to difference in the structure, the Ni42 Cu5 Ti19 Zr22.5 Al8 Si3.5 BMG rods with diameters of 2 and 3 mm exhibit different fracture strength and plasticity upon compression. The higher the cooling rate for glass formation, the more free volumes trapped in the glassy alloy and the larger the plasticity of the material would be. The compressive fracture surfaces consists of a smooth shear zone and a coarse zone, accompanying the fracture angles changing from <45 to 90◦ , suggesting that the compressive fracture might satisfy the ellipse criterion. The formation of microvoids in the fracture process is believed resulting from the presence of tensile stress on the fracture planes. Acknowledgments This work was supported by the National Natural Science Foundation of China under grant Nos. 50771040 and 10732010 (J. Shen) and the Foundation of China Postdoctor (20070420871), the Foundation of Heilongjiang Province Postdoctor (AUGA41001081) and the Education Bureau of Heilongjiang Province, under Project No.11531316 and HIST(07-57). (W.Z. Liang). References [1] X.K. Xi, D.Q. Zhao, M.X. Pan, W.H. Wang, Y. Wu, J.J. Lewandowski, Phys. Rev. Lett. 94 (2005) 125510. [2] J.-P. Guin, S.M. Wiederhorn, Phys. Rev. Lett. 29 (2004) 215502. [3] F. Spaepen, Acta Metall. 25 (1977) 407. [4] E. Pekarskaya, C.P. Kim, W.L. Johnson, J. Mater. Res. 16 (2001) 2513. [5] B. Yang, M.L. Morrison, P.K. Liaw, R.A. Buchanan, G.Y. Wang, C.T. Liu, Appl. Phys. Lett. 86 (2005) 141904. [6] A. Inoue, W. Zhang, T. Tsurui, A.R. Yavaris, A.L. Greer, Phil. Mag. Lett. 85 (2005) 221. [7] J.J. Lewandowski, W.H. Wang, A.L. Greer, Phil. Mag. Lett. 85 (2005) 77. [8] Z.F. Zhang, J. Eckert, Phys. Rev. Lett. 94 (2005) 094301. [9] Z.F. Zhang, J. Eckert, L. Schultz, Acta Mater. 51 (2003) 1167. [10] Z.F. Zhang, G. He, J. Eckert, L. Schultz, Phys. Rev. Lett. 91 (2003) 045505. [11] S.J. Pang, T. Zhang, K. Asami, A. Inoue, Mater. Sci. Eng. A 375–377 (2004) 368. [12] W. Zhang, A. Inoue, Scripta Mater. 48 (2003) 641. [13] A. Inoue, W. Zhang, T. Zhang, K. Kurosaka, Acta Mater. 49 (2001) 2645. [14] J.K. Lee, D.H. Bae, S. Yi, W.T. Kim, D.H. Kim, J. Non-Cryst Solids 333 (2004) 212. [15] J. Shen, W.Z. Liang, J.F. Sun, Appl. Phys. Lett. 86 (2006) 141904. [16] N. Nagendra, U. Ramamurty, T.T. Goh, Y. Li, Acta Mater. 48 (2000) 2603. [17] W.J. Wright, R.B. Schwarz, W.D. Nix, Mater. Sci. Eng. A 319–321 (2001) 229. [18] Z.F. Zhang, G. He, H. Zhang, J. Eckert, Scripta Mater. 52 (2005) 945. [19] J. Saida, A. Deny, H. Setyawan, H. Kato, A. Inoue, Appl. Phys. Lett. 87 (2005) 151907. [20] A.S. Agron, Acta Metall. 27 (1979) 47. [21] K.A. Flores, R.H. Dauskardt, Intermetallics 12 (2004) 1025. [22] T.G. Nieh, C. Schuh, J. Wadsworth, Y. Li, Intermetallics 10 (2002) 1177. [23] C.A. Schuh, T.G. Nieh, Acta Mater. 51 (2003) 87. [24] P. Lowhapandu, S.L. Montgomery, J.J. Lewandowki, Scripta Mater. 41 (1999)19.