Scattering mechanical performances of brittle La- and Mg-based BMGs are found in the present study. Upon dynamic loading, there exist largely scattered fracture strengths even if the strain rates are under the same order, and the BMG systems are the same. The negative strain rate dependence for La- and Mg-based BMGs is obtained, i.e., a decreased fracture strength is dominating from quasi-static to dynamic compression. At cryogenic temperatures, distinguishingly low fracture strengths are available for these two brittle BMGs, and decreased tolerance to accommodate strains makes BMGs more and more brittle. It is concluded that the scattering mechanical performances of brittle BMGs should be carefully evaluated before actual applications.
I. INTRODUCTION
In relatively short period bulk metallic glasses (BMGs) have emerged as a new class of metallic materials with excellent physical and mechanical properties envisaged promising for functional and structural applications.1–3 Compared to conventional metallic materials, BMGs exhibit attractive mechanical properties such as high strength and large elastic limit. However the applications of this kind of materials are still hindered by its poor room-temperature ductility and brittle fracture behavior. The research aiming at understanding its poor ductility suggests at room temperature, BMGs usually deform inhomogeneously, and the plastic strain is highly localized in so-called shear bands.4 To address the plasticity issue of BMGs, a so-called in-situ dendrite-reinforced metallic glass matrix composites (MGMCs) has been established by several groups. For examples, ductile dendrite-reinforced metallic glass composites have been fabricated with a dramatic enhancement of the toughness and agreeable preservation of the high strengths.5 Besides, some intrinsically ductile BMGs have been recently designed,6–9 and Lewandowski et al.6 found a universal correlation between the fracture energy, G, and the elastic modulus ratio, μ/B, i.e. metallic glasses with μ/B > 0.41 – 0.43 are brittle and the larger Poisson’s ratio, the more ductile BMGs are. Based on this guidance, Liu et al.8 designed a series of Zr-based BMGs, which exhibit superior plastic behaviors at room temperature.
It is well-known that La- and Mg-based10–12 BMGs generally possess low Poisson’s ratio. Lewandowski et al.6 have reported that the critical Poisson’s ratio of 0.34 determined the toughness and brittleness in various BMGs. For example, the brittle Mg-based BMGs displayed a notch fracture toughness KC of about 2.0 MPam0.5, which approaches the ideal brittle behavior associated with silicate glasses, while the KC of larger than 60 MPam0.5 have been reported for ductile Zr-based BMGs.10 In addition, Wang et al.12 speculated that the rare-earth based BMGs, including La-based BMGs, would have a Poisson’s ratio less than 0.34. Therefore, the ‘brittle’ BMGs are defining those having low Poisson’s ratios, exhibiting poor plasticity at room temperature. Brittle materials generally have energy instability upon loading.13,14 It is acknowledged that the mechanical behavior of BMGs is closely related to the surrounding conditions, including loading rates, loading modes, and temperatures, etc.15 Thus, it is of considerable interest to investigate the effect of surrounding conditions on mechanical behavior of brittle BMGs. In this study, the evaluation on the mechanical properties of both two brittle La- and Mg-based BMGs is conducted, and corresponding failure mechanisms are explored.
II. EXPERIMENTAL
Ingots of alloys with a nominal composition of (La0.7Ce0.3)65Al10Co25 were prepared by arc melting a mixture of pure Co (99.9 wt.%), Al(99.99 wt.%), La and Ce (>99.5 wt.%) in a high-purity argon atmosphere. For the rod-shaped sample (10 mm in diameter), the ingot was remelted in a quartz tube using an induction heating coil in a high-purity argon atmosphere, and then injected into a copper mold through a nozzle using a high-purity argon atmosphere at 0.2 atm pressure to produce glassy rods. The composition had a critical diameter of 25 mm to form complete amorphous structure.16
The Cu – Ag – Dy pre-alloys were prepared by arc melting Cu (99.99%), Ag (99.9%) and Dy (99.99%) under a Ti-gettered argon atmosphere in a water-cooled copper crucible. The pre-alloys were remelted with Mg (99.9%) to form master alloys with nominal chemical composition of Mg56.5Cu27Ag5Dy11.5 by induction melting in a graphite crucible. From the master alloys, cylindrical rods with diameters of 10 mm were fabricated using tilt casting under an argon atmosphere.17
The synchrotron X-ray experiments were carried out at the beamline, 11ID-C, of the Advanced Photon Source (APS), Argonne National Laboratory (ANL), USA. The monochromatic synchrotron high-energy X-ray beam with an energy of 115 KeV penetrated the specimens, and the transmission-diffraction patterns were collected by a two-dimensional (2D) detector. Cylindrical specimens, with an aspect ratio (height / diameter) of about 2, were sliced from rods and, subsequently, well polished for the two ends. The uniaxial-compressive tests at 298 K and 77 K were performed on the cylindrical specimens using a MTS testing machine with a strain rate of 2 ×10−4 s−1. Dynamic loading experiment was conducted at room temperature using a split Hopkinson pressure bar (SHPB) apparatus with a momentum trap and the detailed process was described elsewhere.18 Cylindrical samples with an aspect ratio of 1: 1, were prepared for dynamic testing. The fracture and lateral surfaces of the deformed samples were investigated by scanning-electron microscopy (SEM) to identify the fracture mechanisms.
III. RESULTS AND DISCUSSION
Figure 1(a) shows the synchrotron high-energy X-ray profile of the (La0.7Ce0.3)65Al10Co25 BMG, together with its corresponding diffraction pattern, as presented in the inset of Figure 1(a). Both indicate a typical amorphous structure for the present La-based BMGs, and no partial crystallization included. Figure 1(b) shows the synchrotron high-energy X-ray profile of the Mg56.5Cu27Ag5Dy11.5 BMG. In contrast, some small diffraction peaks can be observed with an unsmooth diffraction background, indicating nano-crystalline precipitated within the glass matrix. However, its corresponding diffraction pattern, as shown in the inset of Figure 1(b), demonstrates an amorphous structure for the Mg-based BMGs. Synthetically, it is reasonable to deduce that very few nano-crystalline precipitate are present in the sample.
Figure 2(a) shows the compressive engineering stress-strain curve of (La0.7Ce0.3)65Al10Co25 BMG with a strain rate of 2 ×10−4 s−1 at room temperature. A fracture strength of 660 MPa, and no plasticity are available, which is comparable to the quasi-static loading result of other La-based BMGs reported previously19–21. Figure 2(b) shows the compressive engineering stress-strain curve of (La0.7Ce0.3)65Al10Co25 BMG with a strain rate range from 1.0 ×103 to 1.5 ×103 s−1 at room temperature. It can be seen that unstable fracture exists with facture strengths from 250 to 550 MPa at the strain rate with the order of 103 s−1, and analogous phenomena can be found for La62Al14Cu12Ni12 BMGs.21 The fracture strengths from 200 to 400 MPa are obtained for La62Al14Cu12Ni12 BMGs upon dynamic loading.21 For BMGs with large sizes, it is inevitable to find impurity and / or defects on the glass matrix, which would increase fracture instability. Figure 2(c) exhibits the deformation curve at a cryogenic temperature with a strain rate of 2 ×10−4 s−1. The fracture strength is only 150 MPa, greatly decreased in contrast to the room-temperature fracture strength.
The mechanical behaviors of Mg-based BMGs resemble those of La-based BMGs. Figure 2(d) shows the compressive engineering stress-strain curve of Mg56.5Cu27Ag5Dy11.5 BMG with a strain rate of 2 ×10−4 s−1 at room temperature. The fracture strength is 515 MPa with no plasticity, and lower than that of Mg-Cu-(Y, Nd) BMGs11 and in-situ Mg–Cu–Y–Zn and ex-situ Mo particle / Mg58Cu28.5Gd11Ag2.5 BMG composites.22,23 Figure 2(e) exhibits the compressive engineering stress-strain curve of Mg56.5Cu27Ag5Dy11.5 BMG with a strain rate range from 5.0 ×102 to 1.2 ×103 s−1 at room temperature. The obtained fracture strengths range from 280 to 550 MPa, behaving scattered. It should be noted that so far the dynamic loading to brittle Mg-based BMGs has yet to be reported. The large scattered data upon dynamic loading may be attributed to the casting defects.24 As the diameter of cylindrical sample increases, apparent fracture strength is reduced by 25% from ∼950 MPa at 1-mm down to ∼710 MPa at 10-mm sample, which is associated with the population and size of as-cast porosity in the BMG rods as indicated by X-ray computed tomography (CT).24 Figure 2(f) presents the deformation curve at cryogenic temperature with a strain rate of 2 ×10−4 s−1. The obtained fracture strength value at this low temperature is 140 MPa. For brittle BMGs such as the Mg65Cu20Ag5Gd10, split fracture is usually found.25 Before the macroscopic yielding, small pieces split can be observed from the samples, accompanied by the serrated flow in the elastic loading part, as indicated by arrows in Figures 2(c) and 2(f). As shown in Figure 2(f), the localized split fracture is present only under very low pressure of 10 MPa. It should be noted that usually the strength of BMGs at cryogenic temperature is higher than that at room temperature. But for the current two kinds of brittle BMGs, a decreased strength is obtained at cryogenic temperature. It is known that the size of the plastic zone ahead of crack, r, can be estimated by the following formula:
where Kc is the fracture toughness, and σy is the yielding strength. From Eq. (1), since the Kc of Mg- and La-based BMGs is greatly smaller than that of Zr- and Ti-based BMGs by two powers of ten,10 the corresponding small plastic zones for brittle Mg- and La-based BMGs results. As we know, at low temperatures, the bonding at atomic level tends to be stiffer. Thus, upon the loading, a much smaller size of plastic zones would prevail at low temperature, which facilitates the extension of cracks, resulting in a premier failure.
In fact, enhanced compressive plasticity at cryogenic temperatures has been observed in some Zr-based BMGs.4 Interestingly, at 77 K, the serrations in the stress-strain curve actually disappeared. Based on the calculation of the temperature rise within the shear bands and the heat conduction in the heat-affected zones (HAZs), the disappearance of serrations can be attributed to both the instantly high temperature rise and the rapid heat conduction.4 The disappearance of serrations usually indicates that a slow shear banding dominates upon low-temperature compression. As a result, an enhanced plasticity is achieved. This could also explain why an increased plasticity is obtained for ductile Zr-based BMGs with high Poisson’s ratio when lowing the surrounding temperature. For the present brittle La- and Mg-based BMGs with low Poisson’s ratio, although slow shear banding occurs when the temperature is decreased, the dominating affecting factor is the decreased size of plastic zones which facilitates the extension of cracks. Upon yielding even within elastic deformation, once shearing happens, rapid evolution from shear bands to crack is very hard to stop. Consequently, decreased plasticity is going to be accompanied by decreased strength, in accordance to the results shown in Figure 2.
Regardless of La- or Mg-based BMGs, the fracture strength upon dynamic loading exhibits obviously decreased, compared to that upon quasi-static loading. Effect of strain rate on response of La-, and Mg-based BMG suggests a negative strain rate dependence. Liu et al. speculated this negative rate sensitivity was attributed to the occurrence of non-uniformity of stress, as well as stress concentrations induced at high strain rates.21 For ‘ductile’ BMGs, such as Zr-based BMGs, a negative strain-rate dependence is also found.26–28 Stable fracture usually dominates, behaving close fracture strength for ductile Zr-based BMGs.26,29 But for brittle La- and Mg-based BMGs, a large dipartition for the fracture strength is available. Spaepen30 has suggested the following softening mechanism during inhomogeneous deformation of metallic glass: if there is to be a lowering of viscosity in shear bands, there must be an increase of the free volume.
where is the shear strain rate, χ is a factor associated with the amount of the flow units, α is a constant between 1 and 1/2, V* is the effective hard-sphere size of atoms, Vf is the average free volume of an atom, ΔGm is the thermal activation energy, R is the gas constant, T is the absolute temperature, and Ω is the molar atomic volume. The value of λ is in the range of 0-1. From Eq. (2), it is simply deduced that the higher shear strain rate, , may lead to more creation of free volumes, Vf, which facilitates the propagation of shear bands. As a result, a decreased fracture strength prevails with the increasing of the strain rate.
For the calculation of predicated fracture strength of BMGs, Li et al.31 have found that the normalized strength (σ/E) shows a linear relationship with the normalized temperature (T/Tg), and an equation can be established as:
where σ is the strength of BMGs, E is Young’s modulus, T is the testing temperature, Tg is the glass-transition temperature, and a and b are constants. According to elastic modulus (E) inheritance in metallic glasses,32 the present La-based BMG has an E of ∼ 37 GPa. And the glass transition temperature is 437 K.16 For the present Mg-based BMGs, the E is ∼ 45 GPa, and the glass transition temperature is 434 K.17 Based on Eq. (2), the fracture strengths at room temperature and cryogenic temperature are 668 and 867 MPa for La-based BMGs, and 810 and 1054 MPa for Mg-based BMGs. The predicated fracture strength for both La- and Mg-based BMGs seriously deviates from the experimental results. Specially, it is totally not meaningful to predict the low-temperature strength using Eq. (2). For these brittle BMGs, any perturbation by stress concentration would lead to rapid crack propagation, since La- and Mg-based BMGs have smaller plastic zones in contrast to ductile BMGs. At 77 K, not only does the thermodynamic mobility of atoms, such as the frequency of atomic vibrations, decrease, but also the bonds between the atoms become stiffer.31 Decreased tolerance to accommodate strains makes BMGs more and more brittle at cryogenic temperature. Besides, the existence of nano-crystalline makes the present Mg-based BMGs prone to split fracture due to the localized stress concentration.
In order to give detailed analysis on the fracture of brittle BMGs under different conditions, the investigation of fractographes is essential. Figure 3(a) shows the morphology of the La-based BMGs after low-temperature (77 K) deformation. It can be seen both ruffle region (A) and smooth region (B). Individual ruffle region is displayed in Figure 3(b), and the spacing between ridges is about 20 μm. The enlarged ruffle part is shown in Figure 3(c). Some ridges crack into pieces, as indicated by black arrows. In addition, outcrops of crack ridges can be observed, as indicated by white arrows. High magnification of the smooth region is shown in Figure 3(d). Nanoscale periodic stripes are dispersed in this region, and the spacing between strips is about 61 nm. Analogous periodic strips can be found on the fracture surface of many kinds of BMGs, including Mg-, Fe-, Tb-, La-, Zr-, and Ni-based BMGs.10,33 Here, the ridge spacing (w) found on the fracture surface was used to estimate the fracture toughness (Kc) in BMGs.10
where σy is the fracture strength. According to Eq. (3), Kc = 0.16 MPa m0.5, close to that of silicon.
In contrast, the fractographes of Mg-based BMGs at cryogenic temperature are shown in Figure 4. The samples are cracked into pieces. Some macroscopic cracks can be found on the fractures, as indicated by the arrow in Figure 4(a). The localized fracture surface is displayed in Figure 4(b). The radiating ruffles are prevailing, and some ridges split from others, similar to the result in Figure 3(b), as indicated by the arrow in Figure 4(b). Besides, periodic stripes are not found from the fracture surface of Mg-based BMGs at low temperatures.
Figure 5 presents the fractographes of Mg-based BMGs after dynamic loading at room temperature. Power-like particles are obtained after high-speed dynamic compression, as shown in Figure 5(a). Some flakes can be seen due to the pressure, as indicated by arrows. High-magnification of particles is displayed in Figure 5(b), and shearing occurs on polyhedral fracture surfaces. Ruffles with a spacing of ∼10 μm are found on the fracture surfaces, as shown in Figure 5(c). Instead of typical vein patterns,34 close inspection suggests periodic stripes on the smooth part of fracture surfaces with a spacing of 46 nm, as shown in Figure 5(d). Based on Eq. (3), Kc = 0.51 MPa m0.5 upon dynamic loading, which is distinguishingly lower than that of other Mg-based BMGs.10
Due to the high pressure on the particles, leading to the formation of flakes, it is necessary to investigate the crystallization of flakes. Figure 6 shows the synchrotron high-energy X-ray profile of the Mg56.5Cu27Ag5Dy11.5 BMG after dynamic compression, together with its corresponding diffraction pattern, as shown in the inset of Figure 6. The curve resembles that before deformation, which demonstrates an amorphous structure for the Mg-based BMGs undergoing dynamic loading, and no crystallization happens.
In conclusion, the mechanical properties of two brittle BMGs under different conditions are investigated. Scattering mechanical performances are found. Upon dynamic loading, largely scattered fracture strengths are gained even if the strain rate is under the same order and the BMG system is the same. A negative strain rate dependence for La- and Mg-based BMGs is obtained, i.e., a decreased fracture strength is dominating upon dynamic compression. At cryogenic temperatures, distinguishingly low fracture strength is available for these two brittle BMGs, and decreased tolerance to accommodate strains makes BMGs more and more brittle. The present studies demonstrate that the mechanical properties of brittle BMGs are greatly affected by the surrounding, and the scattering mechanical performance should be evaluated before actual applications.
Acknowledgment
The authors thank for Dr. Peter K. Liaw’ help on the synchrotron experiments. J.W.Q. would like to acknowledge the financial support of National Natural Science Foundation of China (No.51101110 and No.51371122), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Human Resources and Social Security of China, and the Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi (2013). H.J.Y. would like to acknowledge the financial support from the National Natural Science Foundation of China (No. 51341006 and No. 51401141), State Key Lab of Advanced Metals and Materials (No. 2013-Z03), the Youth Science Foundation of Shanxi Province, China (No. 2014021017-3), and the financial support from Key Laboratory of Cryogenics, TIPC, CAS (Grant No. CRYO201306). Z.H.W. would like to acknowledge the National Natural Science Foundation of China (Grant No. 11390362). R.L. would like to acknowledge the Natural Science Foundation of China (Grant No. 51131002) and Program for New Century Excellent Talents in University (NCET).