Toughness, extrinsic effects and Poisson’s ratio of bulk metallic glasses

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Acta Materialia 60 (2012) 4800–4809 www.elsevier.com/locate/actamat

Toughness, extrinsic effects and Poisson’s ratio of bulk metallic glasses S.V. Madge a,b,⇑, D.V. Louzguine-Luzgin b, J.J. Lewandowski c, A.L. Greer b,d a National Metallurgical Laboratory, Jamshedpur 831 007, India WPI-AIMR, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan c Department of Materials Science & Engineering, Case Western Reserve University, Cleveland, OH 41106, USA d Department of Materials Science & Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK b

Received 17 April 2012; accepted 16 May 2012 Available online 28 June 2012

Abstract A range of bulk metallic glasses has been cast and their mode II fracture toughness has been estimated from the length scale of shear band vein patterns on fracture surfaces. As-cast rare-earth and Mg-based bulk metallic glasses invariably consist of oxide particles dispersed in a glassy matrix and the apparent brittleness of these alloys is partly extrinsic in nature, caused by these inclusions. The intrinsic toughness of these glasses is higher than previous reports suggest. An attempt has been made to correlate the toughness of a variety of glassy alloys, including La- and Mg-based systems, with their Poisson’s ratio (m). The findings show that mode II toughness increases with m, though gradually, instead of an abrupt transition occurring at a critical value of m. Certain glassy alloys are profoundly brittle, irrespective of m, and this seems to be related to alloy chemistry. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Bulk metallic glasses; Toughness; Poisson’s ratio; Extrinsic effects; Oxygen embrittlement

1. Introduction Bulk metallic glasses (BMGs) possess certain attractive properties, like a higher strength and lower modulus than crystalline alloys. The room temperature deformation in most BMGs tends to be highly localized into narrow regions called shear bands and, as a result, the macroscopic plasticity in tensile tests is often very low [1]. Yet the plastic strain inside a shear band is enormous and indeed, some BMGs can have high fracture toughness. The glassy alloys based on Zr, Cu, or Pd/Pt are typically tough, whereas those based on metals like Mg, Fe or rare earths can be brittle, with a reported notch toughness Kc  2 MPa m1/2, almost as low as silicate glasses [2]. The fracture surfaces of BMGs show characteristic shear band vein patterns and interestingly, Xi et al. [2] have reported a correlation between the length scale of such patterns and the fracture ⇑ Corresponding author at: National Metallurgical Laboratory, Jamshedpur 831 007, India. Tel.: +91 9471137687. E-mail address: [email protected] (S.V. Madge).

toughness, consistent with more recent reports showing similar observations on a Ti-BMG [3] as well as different viscosity materials [4]. Essentially, the vein patterns reflect the process zone size in a glass and typically, the tougher BMGs exhibit vein patterns of the order of a few tens of micrometres, while the brittle BMGs apparently have nanometre-sized patterns. The toughness of metallic glasses was shown to depend quite sensitively on elastic properties, i.e. the Poisson’s ratio (m), or equivalently, the ratio of the shear modulus (l) to the bulk modulus (B). Toughness/ plasticity in BMGs is favoured by a higher m or a lower l/B and in fact, the toughness was reported to sharply reduce below a critical Poisson’s ratio of 0.31–0.32 [5–7]. The Mg-based glasses, for instance, lie below this critical value. Wear resistance is a material property that depends on both hardness and toughness and thus can be an indicator of brittleness. Fig. 1 reproduces the wear data for a variety of materials, i.e. pure metals, alloys and ceramics, all measured using a three-body abrasive wear tester, by Greer and co-workers at Cambridge [8,9]. Data for each class of

1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.05.025

S.V. Madge et al. / Acta Materialia 60 (2012) 4800–4809

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2. Experimental procedures Co

tool steels

pure metals

alumina

hardened alloys

Ag

ceramics

Zr-BMG Pd-BMG Mg-BMG hardened Al alloy La-BMG

Al

Ge

Si

soda-lime glass

Fig. 1. Abrasive wear resistance data for a variety of materials – pure metals, alloys and ceramics. Within each class of material, the wear resistance scales linearly with hardness. All BMGs, even the brittle systems, lie in the category of hardened alloys instead of ceramics [8].

materials fall on a single line, and it is seen that, for a given hardness, metallic alloys are more wear-resistant than ceramics. This is because metals are usually tougher than ceramics and the wear mechanism does not involve brittle fracture, leading to a lower wear rate [9]. The wear resistance of BMGs scales linearly with the hardness and, moreover, both the tough (Zr-, Pd-based) as well as brittle BMGs (rare earth and Mg-based) firmly lie in the category of hardened alloys, which is puzzling, taking into account the reported low toughness of La- and Mg-based systems. A reduction in wear resistance with decreasing toughness was demonstrated for a Cu50Hf41.5Al8.5 glass [10] and the data corroborate the idea that a material with a fracture toughness less than 10 MPa m1/2 (e.g. Mg-based BMGs) will have a low wear resistance. Hence, it is reasonable to expect that the extreme brittleness of these systems would translate into a much lower wear resistance (perhaps the data should be in the category of ceramics), in contrast to the experimental observations in Fig. 1. One objective of this work was thus to probe the mechanical behaviour of the brittle La- and Mg-based BMGs – is their toughness really as low as ceramic glasses? In the current work, toughness has been estimated from the scale of vein patterns on fracture surfaces and it is found that glasses like those based on La or Mg possess a higher toughness than previously thought. Their apparent brittleness arises from extrinsic effects like oxide inclusions, which act as crack nucleation sites. Taking into account the higher intrinsic toughness of Mg- and Labased glasses, an attempt has been made to correlate the toughness data of a variety of BMGs with Poisson’s ratio (m), a parameter previously reported to crucially affect the toughness of metallic glasses [5–7]. The data are in agreement with the idea of a higher m favouring toughness, but the transition from the tough to the less-tough glasses appears to be gradual when tested under the present conditions, instead of an abrupt one occurring at a critical Poisson’s ratio.

The BMG compositions synthesized in the present work are: La55Al25Co5Cu10Ni5, Mg65Cu25Tb10, Mg65Cu25Gd10, Mg65Ni20Nd15, Au49Ag5.5Pd2.3Cu26.9Si16.3, Ce60Al20Cu10Ni10, Cu60Zr20Ti10Hf10 and Fe48Cr15Mo14C15B6Er2 (all compositions are in at.%). Alloys have been prepared from metals with a purity >99.9 wt.%, by the standard techniques of arc or induction melting under an Ar atmosphere, followed by Cu mould injection casting into 2 mm or 3 mm diameter rods. Samples for compression testing were cut from the as-cast rods, and polished using a specially designed fixture to ensure that the ends remained parallel to each other and perpendicular to the specimen axis. Compression testing was done using a Shimadzu universal testing machine using tungsten carbide spacers, on samples having an aspect ratio of 2:1, at an engineering strain rate of 5  104 s1. At least three and up to five specimens per alloy were tested. The fractured specimens were examined using a Hitachi high-resolution scanning electron microscope (SEM), and at least 50 measurements were made to arrive at an average length scale of shear band vein patterns. Energy-dispersive X-ray analysis (EDX) was used to verify alloy compositions and importantly, to identify oxide inclusions in some of the glassy samples. The oxygen content in some of the glasses was measured by the He carrier gas infrared absorption technique. The fracture toughness has been estimated using the method introduced by Xi et al. [2]. The scale of vein patterns (w) on the fracture surface of a glass is related to the fracture toughness (Kc) and the yield strength (ry) through 2

w ¼ 0:025ðK c =ry Þ

ð1Þ

3. Results and discussion In assessing the fracture toughness of BMGs from the scale of shear band vein patterns (using Eq. (1)), it is important to know whether the measured toughness is KIc or KIIc. Xi et al. had used three-point bending of notched specimens, whereas the present work uses compression testing. Independent fracture toughness measurements [11] on a Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) BMG have shown KIc and KIIc to be 16 MPa m1/2 and 75 MPa m1/2 respectively. Xi et al. report a Kc of 86 MPa m1/2 for Vit 1, showing that the notch toughness is very close to the KIIc toughness. The notch toughness strongly depends on the notch root radius, as nicely demonstrated in Ref. [12], and it is only the fatigue pre-cracked specimens that can yield a Kc value that is close to KIc. For blunter notches, numerous shear bands emanate from the notch root, and the measured toughness has a significant mode II component. Previous reports indicate that mixed

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mode I/II loading enormously increases the toughness of Zr-based BMGs [13]. In contrast to notch toughness testing in Ref. [2], the present work uses uniaxial compression. The compressive fracture surfaces also show shear band vein patterns, but it is vital to know whether the KIIc values estimated therefrom are still similar. This has been verified with two BMG compositions of known notch toughness. For the Cu60Zr20Ti10Hf10 BMG, the reported notch toughness is 67 MPa m1/2 [2,14,15]. Fig. 2 shows the typical vein patterns on the compressive fracture surface of this glass and the average size of the patterns is 16 lm. The observed compressive yield strength of 2100 MPa yields a KIIc of 54 MPa m1/2, close to the 67 MPa m1/2 reported in Refs. [2,14,15]. Likewise, the notch toughness of a Cu49Hf42Al9 glass is reported to be 65 ± 10 MPa m1/2 [14], very similar to 76 MPa m1/2 estimated using compression testing [16]. Thus, the KIIc estimates from compression testing closely approximate the notch toughness data and are accurate enough to permit a reliable comparison between different BMG compositions. Fig. 3a shows a specimen of a La55Al25Co5Cu10Ni5 bulk glass, which has fractured through shear. Shear band vein patterns of 20 lm are seen on the fracture surface (Fig. 3b). As seen in Fig. 3c, some samples also fail through a combination of shear (area marked I) and smooth areas representing brittle fracture (area II). In fact, area II bears a morphological similarity to conchoidal fracture in glassy minerals. Area I shows micrometre-scale vein patterns, and area II shows nanoscale features on the 100 nm–1 lm scale (Fig. 3d), typically associated with fracture in brittle BMGs [2]. Also visible are white, La-oxide particles. In fact, a polished cross-section of the alloy shows La-oxide particles dispersed in the glassy matrix (Fig. 3e). Importantly, the interface between the oxides and the glass is weak, evidenced through the interfacial cracks. Brittle phases dispersed in a glassy matrix can dramatically embrittle even the more “tough” BMGs, e.g. Cu49Hf42Al9 [16] or

50 μm Fig. 2. Vein patterns on the compressive fracture surface of a Cu60Zr20Ti10Hf10 BMG. The average size of the patterns is 16 lm and the mode II toughness is 54 MPa m1/2.

Zr55Cu30Al10Ni5 [17]. For instance, Cu49Hf42Al9 is a tough BMG that usually fails through shear (Fig. 4a). However, when brittle Cu44.5Hf42.9Al7.8O4.8 dendrites are dispersed in a glassy matrix (Fig. 4b), it exhibits dual fracture surface features – a small area fraction shows vein patterns but most of the fracture surface exhibits nanoscale, quasicleavage features (100 nm-sized), as reproduced in Fig. 4c. These nanoscale features are nearly identical to those found in La- or Mg-based glasses. Similarly, a change in fracture mode from shear to quasi-cleavage has been reported for the Zr55Cu30Al10Ni5 glass when it is dispersed with a brittle crystalline phase, induced by oxygen contamination [17]. Oxide inclusions are also known to initiate fracture and reduce both the magnitude of toughness as well as Weibull modulus in a range of Fe-based glasses [18]. The issue, then, is whether the perceived brittleness of La-based glasses could also be due to the oxide particles in the glassy matrix. To confirm the role of oxides in inducing brittle fracture, an oxygen-rich composition, La54Al24Co5Cu10Ni5O2, has been investigated. Oxygen was introduced by melting the alloy with CuO powder. As shown in the SEM image (Fig. 5a) the glass contains copious oxide particles. The failure mode in compression tests is no longer shear, as shown in Fig. 5b. The alloy breaks into many pieces and as expected, the fracture surface is dominated by nanoscale fractographic features (Fig. 5c), instead of micrometre-scale shear band vein patterns. Mg-based systems are believed to be another family of brittle glasses. As shown in Fig. 6a, an as-cast specimen of Mg65Cu25Tb10 also shows mixed oxide particles (of Mg and Tb) in a glassy matrix. The alloy shatters into many pieces upon compression and a typical fractured piece shows two distinct regions, I and II, which correspond to shear failure and brittle fracture (Fig. 6b). As with the La- and Cu-based glasses, region I shows microscale vein patterns (10 lm) and region II shows nanoscale features. Clear crack initiation sites are seen in region II (Fig. 6c), which are, in fact, clusters of oxides (Fig. 6d and e). The areas representing brittle fracture show 100 nm-scale features (Fig. 6f). Similar findings were also made for the Mg65Cu25Gd10 and Mg64Ni21Nd15 glasses. Fig. 7a and b shows shear failure in the Mg64Ni21Nd15 glass and Fig. 7c shows brittle fracture that clearly initiates from oxide particles. The fracture surface again consists of features (not shown) similar to Fig. 6f. Fig. 8 documents the length scale of shear band vein patterns observed in the Ce- and Au-based glasses. The above data reveal that La- and Mg-based BMGs are capable of legitimate shear flow, in which case the fracture surface shows coarse shear band vein patterns on a length scale of 10–20 lm. When failure occurs not through shear, but by quasi-cleavage, the corresponding fracture surface shows nanoscale features with a length-scale finer than 1 lm. Importantly, such nanoscale features are universal to all BMGs undergoing brittle fracture. Apart from the Cu49Hf42Al9 mentioned above (Fig. 4b), even one of the toughest BMGs, Zr41.2Ti13.8Cu10Ni12.5Be22.5 exhibits

S.V. Madge et al. / Acta Materialia 60 (2012) 4800–4809

4803

b

a

50 µm

c

I

d

II

2 µm

e

10 µm Fig. 3. SEM secondary electron images of fracture surfaces in a La55Co5Cu10Ni5Al25 bulk glass. (a) Plan view of 45° shear failure in a specimen; (b) the fracture surface shows micrometre-scale (15 lm) vein patterns. (c) Other specimens show shear as well as brittle fracture, marked as regions I and II respectively. (d) Region II shows nanoscale features (<1 lm) and La-oxide particles. (e) A polished section showing La-oxide particles in a glassy matrix, with interfacial cracks (circled particle).

conchoidal fractographic features on the 100 nm lengthscale in the case of quasi-cleavage fracture [19]. On a similar note, the otherwise tough Zr55Cu30Ni5Al10 glass changes its fracture mode to quasi-cleavage (with nanometre-scale dimples), when it is dispersed with 7 vol.% of brittle La-rich phases [20]. Evidently, these nanoscale features are not shear band vein patterns and thus inappropriate in estimating toughness using Eq. (1). For example, using 100 nm as the process zone size for Vit1 yields a toughness value of only 3.8 MPa m1/2, which is clearly unrealistic, since KIc and KIIc are known to be about 16– 18 MPa m1/2 [11,12]. Table 1 summarizes the current experimental observations, i.e. compressive yield strength, Poisson’s ratio (m) and Young’s modulus (E), the scale of fractographic features, i.e. microscale vein patterns as well as nanoscale fea-

tures. For better comparison, Table 1 also includes data for additional glasses, i.e. those based on Fe, Cu–Hf–Al, Pd-, Pt-, Zr-based and some oxide glasses. The values are taken from references stated in Table 1. Eq. (1) has been used to estimate the fracture toughness (KIIc) and the fracture energy, G (kJ m2), has been calculated using Eq. (2): G¼

K 2IIc ð1  m2 Þ E

ð2Þ

It should be emphasized that for alloy Fe1, shear failure was not seen in our compression testing experiments; instead, the alloy always failed in a brittle manner (and this was not obviously related to oxides, as will be discussed later). Hence it was not possible to calculate toughness from the fractographic features. So, we have used the notch

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a

100 μm

b

c

20 μm

200 nm

Fig. 4. Fractography of a tough Cu49Hf42Al9 glass. (a) At low (250 ppm) oxygen, the glass is single-phase and upon fracture, coarse shear band vein patterns are seen. (b) At higher oxygen contents (1700 ppm), a dispersion of Cu44.5Hf42.9Al7.8O4.8 dendrites in a glassy matrix is seen and (c) fracture proceeds largely through the quasi-cleavage mode, typified by nanoscale fractographic features, identical to those exhibited by Mg- or La-based glasses.

b

a

20 µm

0.5 mm

c

2 µm Fig. 5. (a) SEM image showing copious oxides in a glassy matrix of La54Al24Co5Cu10Ni5O2. (b) The fracture mode is not shear, but brittle fracture. (c) The fracture surface mostly shows nanoscale features, typically associated with brittle glasses, instead of micrometre-scale vein patterns.

toughness data reported in Ref. [22] where failure occurred via mode I and not shear, due to the brittleness of the alloy. Nonetheless, it has been included in Table 1 for comparison with other glasses and to emphasize that the Fe-based glass is still much tougher than oxide glasses.

Apart from the Fe-BMG, the “brittle” BMGs seem capable of shear flow and it is the scale of micrometre-scale vein patterns that should be used in estimating fracture toughness. Still, Table 1 lists both the size of micrometrescale vein patterns as well as the nanoscale features. Eq.

S.V. Madge et al. / Acta Materialia 60 (2012) 4800–4809

a

4805

b

II I

20 µm

c

0.5 mm

d

50 µm

100 µm

e

f

20 µm

200 nm

Fig. 6. (a) Mixed oxides of Mg and Tb in a Mg65Cu25Tb10 glassy matrix. (b) A fractured piece of the alloy after compression testing. Like the La-based glass, two regions, I and II are seen, that correspond to shear failure and brittle fracture respectively. (c) Region I shows vein patterns with a size of 10 lm. (d) Region II consists of a flat, mirror-like fracture surface. Clear crack initiation sites are visible, as pointed by the arrow. (e) A closer view of a crack initiation site, which is a cluster of oxide particles. The dotted circle highlights an individual oxide particle. (f) Typical nanoscale fractographic features are seen in region II.

(1) has been used to calculate toughness for both feature sizes, only to emphasize the resulting error when using the nanoscale features in the calculations. Table 1 clearly shows that the mode II toughness and fracture energy of both La- and Mg-based glasses are much higher (up to two orders of magnitude) than the values obtained using nanoscale fractographic features. It is instructive to plot the fracture energies as a function of Poisson’s ratio, as shown in Fig. 9a and b. Fig. 9a deliberately assumes that for the glasses based on Ca, Mg, La and Ce, the nanoscale features represent the true length scale of shear band vein patterns (i.e. ignores the microscale vein patterns), just to emphasize the error in the toughness data. The fracture energy across the entire range of BMGs covers four orders of magnitude, with a critical Poisson’s ratio for brittle–ductile transition of 0.32, as pointed out earlier [5]. However, rare-earth and Mg-based glasses show microscale vein patterns for mode II fracture

and, when comparing all BMGs, it is these features that should be used for estimating mode II toughness. Fig. 9b plots the mode II fracture energy vs. the Poisson’s ratio for all glasses, except Fe1 and the oxide glasses (since they do not show shear failure). For the latter, the mode II/ mode I fracture energy ratio is typically only 4–5 [26], thus leaving our conclusions unchanged. All metallic glasses now lie in a class quite distinct from the oxide glasses, and the variation in fracture energy is now only about two orders of magnitude for the entire series of BMGs. For metallic glasses, toughness increases with Poisson’s ratio, with the Au-based glass being a notable exception. However, the present data do not suggest a sharp brittle– ductile transition across various BMGs, that occurs at a critical value for m, (i.e. 0.31–0.32). The above discussion reveals that La- and Mg-based BMGs are intrinsically tougher than usually thought. This would explain their good wear resistance (Fig. 1), which is

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a

Brittle Fracture

Shear Failure

b

0.5 mm

50 µm

c

Oxides

50 µm Fig. 7. Duality of fracture in a Mg64Ni21Nd15 BMG. (a) Shear failure in the glass and (b) the corresponding shear band vein patterns. (c) Quasi-cleavage fracture in the same glass, initiating from oxide inclusions.

b

a

50 µm

50 µm

Fig. 8. SEM images showing the length-scale of vein patterns on (a) Au49Ag5.5Pd2.3Cu26.9Si16.3 and (b) Ce60Al20Cu10Ni10 bulk glasses.

commensurate with their hardness, as with other metallic alloys. Had their toughness been as low as ceramics, the wear resistance would have been much lower. The apparent brittleness of these materials is an extrinsic effect caused by the presence of oxides that act as flaws in a high-strength material, changing the fracture mode from shear to quasi-cleavage. It is expected that in the absence (or a reduction in the volume fraction) of oxides, the glasses would undergo shear failure, as already seen for La55Al25Co5Cu10Ni5 in this work. However, the high reactivity of

Mg- and La-based alloys means that it is difficult to avoid the oxides completely. Moreover, the binary phase diagrams La–O [27] and Mg–O [28] show that there is little solid solubility for oxygen in these alloys. In the case of Mg, there is no solubility for oxygen even in the liquid state. This is in stark contrast to Zr–O or Ti–O systems [28], which possess significant solubility for oxygen in both solid and liquid states. Past work has shown that dissolved oxygen in a Cu–Hf–Al glass [16] does not deteriorate toughness significantly – it is the precipitation of

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Table 1 Summary of BMG toughness data. Alloy

Yield strength (MPa)

Scale of vein patterns (lm)

KIIc (MPa m1/2)

m

E (GPa)

G (kJ m2)

References

La55Al25Co5Cu10Ni5 (La)

875

47

0.308

50.6

Mg65Cu25Tb10 (Mg2)

900

0.309

51.3

Mg64Ni21Nd15 (Mg3)

838

0.324

50

13.9 0.58 5.35 0.059 8 0.07 6

This work and [2]

910

27.2 5.5 17.3 1.8 21.3 2 18.4

0.34

Mg65Cu25Gd10 (Mg1)

24.1 1 9 0.1 14 0.1 12

Ca65Mg15Zn20 (Ca)

364

26.42

800

0.313

30.3

Au49Ag5.5Pd2.3Cu26.9Si16.3 (Au) Cu49Hf42Al9 (Cu1) Cu60Zr20Ti10Hf10 (Cu2)

1076

1.67 8.79 0.75 19.6 10 25.4

0.3

Ce60Al20Cu10Ni10 (Ce)

0.1 13.2 0.076 15 5 13.9

0.406

74.4

0.049 2.65 0.019 11.4 3 7.2

2150 2100

34 16.3

79.2 53.6

0.351 0.369

115.3 101.1

47.8 24.9

– 1420

– –

1800

60

51 203 84 86

0.41 0.42 0.42 0.353

88.8 109.2 94.8 101.3

24.4 310 61.3 63.9

This work and [24] [14,16] This work and [2,4] [5] [25] [5] [2]

–

–

–

0.316

213

0.72

[22]

– – – –

– – – –

– 0.5 0.2 0.5

0.33 0.166 0.211 0.266

177 72.9 67.2 87.0

11.1 0.003 0.004 0.003

[22] [5] [5] [5]

Pd77.5Cu6Si16.5 (Pd1) Pd79Ag3.5P6Si9.5Ge2 (Pd2) Pt57.5Cu14.7Ni5.3P 22.5 (Pt) Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Zr) Fe48Cr15Mo14C15B6Er2 (Fe1) Fe66Cr3Mo14C15B6 (Fe2) Fused silica Window glass Toughened glass

This work This work and [2] This work and [21] [23] This work and [2]

The rows in italic illustrate the data extracted from nanoscale fractographic features.

oxygen-containing dendrites in a glassy matrix that causes severe embrittlement. At this juncture, it is worth comparing the oxygen levels in these alloys. Notwithstanding the careful processing, the Mg- and La-based glasses were found to have typical oxygen contents of 1000– 1800 ppm. As mentioned earlier, at 1700 ppm of oxygen, the tough Cu49Hf42Al9 glass shows Cu44.5Hf42.9Al7.8O4.8 dendrites in a glassy matrix, and hence fails in a brittle manner, similar to Mg-based glasses [16]. The low oxygen solubility in Mg- or La-based alloys means that any oxygen in the system will appear as oxide inclusions; and their high reactivity ensures that such oxides will always be present. The alloy fabrication technique is another factor that influences oxygen contamination. Arc-melting, often used for Zr- or Cu-based glasses, has the advantage of having a getter, which reduces oxygen pick-up. Induction melting, used especially for Mg-based glasses, usually lacks this facility, potentially leading to higher oxygen levels in the alloy. Besides, oxygen pick-up in Mg-based alloys is likely to go undetected, since their glass-forming ability (GFA) remains unaffected by oxygen contamination – in fact, Xi et al. [29] report that these alloys can be synthesized in open air. Yet, the effect of oxide inclusions on toughness is devastating. Coincidentally, these severely oxidation-prone alloys based on Mg, La or Ce also tend to have Poisson’s ratios between

0.3 and 0.32, giving the appearance of a sharp ductile–brittle transition for BMGs as a function of m, as demonstrated in Fig. 9a. It would be useful to conduct fatigue precracked tests (for minimizing mode II loading) to demonstrate the nature of the ductile–brittle transition in other stress states, as this clearly affects such transitions in crystalline body-centred cubic (bcc) alloys [30,31]. It could be argued that the failure mode, i.e. shear vs. brittle fracture, is itself controlled by the Poisson’s ratio – the lower the m, the greater the probability of brittle fracture and the oxides merely exacerbate the existing brittleness of alloys with a low m (i.e. Mg- or La-based glasses). However, it is crucial to note that quasi-cleavage fracture is not limited to the alloys with a low m, i.e. based on Mg or La. Even the tough BMGs like Cu- or Zr-based ones can be made to behave like the brittle glasses, by introducing oxygen-containing dendrites (e.g. see Figs. 4b,c) or other brittle phases [16,17,20]. On the other hand, the “brittle” glasses also exhibit shear fracture upon a reduction in their oxide content, as demonstrated for the La-based glass in Figs. 3 and 5. So, it appears that in the absence of oxides, most of these BMGs show shear failure when tested in this manner and the reduction in toughness with m is only gradual. It must be emphasized that there are genuine instances where the failure mode (shear vs. brittle fracture) does seem

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S.V. Madge et al. / Acta Materialia 60 (2012) 4800–4809 1000

νc

Pd2

Pd2

Pt Pd1 Au

Cu2

10 Ce

1

La

Fe1

0.1

Mg2 Mg1

0.01

Mg3

Ca

1E-3

2

2

Cu1 Fe2

1000 100

Zr

100

Fracture Energy (kJ/m )

b Fracture Energy (kJ/m )

a

Zr Cu1 Ce Fe2 La

10

Mg2 Mg1 Ca

1E-4

Cu2

Au

Mg3

Fe1

1

Metallic Glasses

0.1 0.01 Oxide Glasses

1E-3

Oxide Glasses

Pt Pd1

1E-4 0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

Poisson's ratio (ν)

0.16

0.20

0.24

0.28

0.32

0.36

0.40

0.44

Poisson's ratio (ν)

Fig. 9. (a) The correlation of fracture energy with Poisson’s ratio for the glasses listed in Table 1. For the alloys based on La, Mg, Ce, the toughness has been calculated based on the nanoscale fractographic features, hence they seem brittle. The data for “tough” glasses like Zr- or Cu-based ones are derived from their micrometre-scale vein patterns. The toughness appears to sharply reduce below a critical Poisson’s ratio of 0.32. (b) The correlation between mode II fracture energy (based on shear band vein patterns) and Poisson’s ratio. The relevant data can be found in Table 1. All BMGs are much tougher than oxide glasses and their toughness gradually increases with Poisson’s ratio (apart from exceptions like Fe1 and Au), instead of an abrupt increase that occurs at a critical value of the Poisson’s ratio.

to be dramatically influenced by m, e.g. relaxation-induced embrittlement in a Zr-based glass [5], which exhibits brittle fracture below a critical m of 0.32. Also, the Fe1 glass (m = 0.316) in the present work is profoundly brittle in compression (i.e. did not show shear failure) and this could not be ascribed to any extrinsic factors like oxides/pores. Now, the key issue is whether this brittleness can be attributed to m alone. The Mg- and Ca-based systems have an even lower m than Fe1 and yet they are capable of shear failure and are relatively tough. At the other extreme is the Au-based glass, which has a high m, fails through shear, and yet has an unexpectedly low toughness. So the present data do not support the notion of a universal, critical value of m that sharply divides the tough and brittle BMGs. In a broad sense, the toughness increases with Poisson’s ratio, but the alloy chemistry also seems to play an important role. Previous work on Fe–Cr–Mo–P–C–B glasses has shown that the use of a metalloid confers a certain degree of covalency to atomic bonding and the metallic character of the bond increases in the order C through B to P [32]. On the other hand, as seen in Fig. 9b, all the noble metal-based glasses contain Si or P, and yet, despite similar Poisson’s ratios, their toughness varies very significantly. Clearly, the toughness of BMGs is influenced not only by m but also by the chemical composition, in a way not well understood. Possibly short-range ordering (SRO) may be affecting toughness. The notch toughness tests reported earlier [2,5] are really mixed mode I/II tests and the compression tests are effectively mode II. It is clear that for mode II failure in BMGs tested under uniaxial compression, there is no abrupt ductile–brittle transition (DBT) occurring at a critical Poisson’s ratio. Of interest is whether the toughness–m correlation also depends on the stress state. In crystalline alloys, the fracture mode (shear vs. cleavage) can be influ-

enced by the stress state. For example, the fracture mode of pearlitic eutectoid steels can vary with the testing technique, e.g. tensile testing of cylindrical specimens, plain strain tensile testing or torsion testing [33]. Also, with brittle crystalline alloys, a superimposed hydrostatic pressure can increase ductility [31,34,35]. It is not yet known whether BMG toughness can also be similarly influenced by the testing technique and if it is, how the toughness is controlled by m. Could there be a sharp DBT with varying m in the case of pure mode I loading? These are some of the open questions, which may be answered through more work on BMG specimens free from oxides/pores and careful toughness testing, e.g. by ensuring that KIc data are not heavily influenced by mode II contribution as a result of extensive shear banding and consequent blunting of a fatigue pre-crack. From a processing viewpoint, a strategy to avoid oxide inclusions in BMGs can involve processing under a high-purity inert atmosphere, electrolytic deoxidation of molten alloys [36] and/or some kind of a melt-filtration technique to remove the ubiquitous oxide particles in certain BMG melts. Finally, although BMGs are often considered isotropic, they can show anisotropic elastic properties, induced, for example, by creep [37], thus raising the possibility of an orientation dependence to the toughness of metallic glasses, which may be investigated further. The current work is expected to have wider implications in understanding the mechanical behaviour of BMGs. Situations where extrinsic effects may be important are as follows. It is known that adding minor amounts of rare earths metals (Y or Gd) to Zr- or Cu-based alloys improves GFA by reducing dissolved oxygen in the melt, which precipitates as oxide particles [38]. However, the higher GFA of Cu-based BMGs can be accompanied by reduced toughness, without a significant change in the Poisson’s ratio [14]. A possibility to be explored is whether the

S.V. Madge et al. / Acta Materialia 60 (2012) 4800–4809

embrittlement is extrinsic, owing to the oxide inclusions. Another interesting report has been on the role of fluxing in improving the compressive plasticity of Pd-based BMGs [39], which is apparently due to a change in the intrinsic glassy structure. It may be worth investigating whether the enhanced plasticity is also a consequence of the removal of impurities (oxides etc.) by fluxing. 4. Conclusions The following inferences can be drawn from this study. 1. A variety of BMGs has been investigated using uniaxial compression testing. BMGs can exhibit both micrometre-sized shear band vein patterns and nanoscale conchoidal features on their fracture surfaces. Only the length scale of shear band vein patterns can be used to obtain a reliable estimate of the mode II fracture toughness. 2. The present study has shown that Mg-, La-, or Ce-based glasses, often considered to be brittle like oxide glasses, are in fact much tougher and are similar to other metallic glasses. The presence of brittle phases like oxides in a glassy matrix can change the fracture mode from shear to quasi-cleavage, thereby embrittling otherwise tough materials, including Zr- and Cu-based BMGs. Glassy alloys like those based on Mg- or rare-earth metals are very prone to oxidation and their limited oxygen solubility always leads to oxide inclusions in a glassy matrix, despite careful processing, and their apparent brittleness is a consequence of such extrinsic factors. 3. The variation in mode II fracture energy (G) with Poisson’s ratio (m) for a variety of BMGs has been plotted. On an average, a higher m favours a higher G, but the variation is gradual, without involving an abrupt change in G around a critical value of m. 4. Certain alloys are outliers (e.g. Au- or Fe-based glasses) since their fracture energies are low in comparison to their m. And this does not appear to be related to extrinsic factors. Also, among the alloys with a very high m (Au-, Pd-, Pt-based glasses), significant variability in G has been noted, suggesting that the alloy chemistry also affects BMG toughness, independent of m. Thus, the interplay between alloy composition, Poisson’s ratio and toughness of BMGs is not fully understood and would be an exciting area for further work.

References [1] Schuh CA, Hufnagel TC, Ramamurty U. Acta Mater 2007;12:4067. [2] Xi XK, Zhao DQ, Pan MX, Wang WH, Wu Y, Lewandowski JJ. Phys Rev Lett 2005;94:125510.

4809

[3] Gu XJ, Poon SJ, Shiflet GJ, Lewandowski JJ. Acta Mater 2010;58:1708. [4] Deibler LA, Lewandowski JJ. Mater Sci Eng A 2012;538:259. [5] Lewandowski JJ, Wang WH, Greer AL. Philos Mag Lett 2005;85:77. [6] Zhang Y, Greer AL. J Alloys Compd 2007;434–435:2. [7] Greaves GN, Greer AL, Lakes RS, Rouxel T. Nat Mater 2011;10:823. [8] Madge SV. PhD thesis, University of Cambridge;2003. [9] Greer AL, Rutherford KL, Hutchings IM. Int Mater Rev 2002;47:87. [10] Maddala D, Hebert RJ. Scripta Mater 2011;65:630. [11] Flores KM, Dauskardt RH. Intermetallics 2004;12:1025. [12] Lowhaphandu P, Lewandowski JJ. Scripta Mater 1998;38:1811. [13] Varadarajan R, Thurston AK, Lewandowski JJ. Metall Mater Trans A 2010;41A:149. [14] Jia P, Zhu Z, Ma E, Xu J. Scripta Mater 2009;61:137. [15] Wesseling P, Nieh TG, Wang WH, Lewandowski JJ. Scripta Mater 2004;51:151. [16] Madge SV, Wada T, Louzguine-Luzgin DV, Greer AL, Inoue A. Scripta Mater 2009;61:540. [17] Leonhard A, Xing LQ, Heilmaier Gebert A, Eckert J, Schultz L. Nanostruct Mater 1998;10:805. [18] Shamimi Nouri A, Gu XJ, Poon SJ, Shiflet GJ, Lewandowski JJ. Philos Mag Lett 2008;88:853. [19] Jiang MQ, Ling Z, Meng JX, Dai LH. Philos Mag 2008;88:407. [20] Madge SV, Sharma P, Louzguine-Luzgin DV, Greer AL, Inoue A. Intermetallics 2011;19:1474. [21] Wang WH. Prog Mater Sci 2011;57:487. [22] Lewandowski JJ, Gu XJ, Shamimi Nouri A, Poon SJ, Shiflet GJ. Appl Phys Lett 2008;92:091918. [23] Wang G, Liaw PK, Senkov ON, Miracle DB. Met Mater Trans A 2011;42:1499. [24] Schroers J, Lohwongwatana B, Johnson WL, Peker A. Appl Phys Lett 2005;87:061912. [25] Demetriou MD, Launey ME, Garrett G, Schramm JP, Hofmann DC, Johnson WL, et al. Nat Mater 2011;10:123. [26] Hutchinson JW, Evans AG. Surf Coat Technol 2002;149:179. [27] Okamoto H. J Phase Equilib Diff 2005;26:292. [28] Massalski TB. Binary alloy phase diagrams. Materials Park, OH: ASM International; 1990. [29] Xi XK, Wang RJ, Zhao DQ, Pan MX, Wang WH. J Non-Cryst Solids 2004;344:105. [30] Knott JF. Fundamentals of fracture mechanics. London: Butterworths; 1973. [31] Lewandowski JJ, Lowhaphandu P. Int Mater Rev 1998;43:145. [32] Gu XJ, Poon SJ, Shiflet GJ, Widom M. Acta Mater 2008;56:88. [33] Lewandowski JJ, Thompson AW. Met Trans A 1986;17:461. [34] Liu DS, Lewandowski JJ. Met Trans A 1993;24:609. [35] Bridgman PW. J Appl Phys 1947;18:246. [36] Bossuyt S, Madge SV, Chen GZ, Castellero A, Deledda S, Eckert J, et al. Mater Sci Eng A 2004;375:240. [37] Concustell A, Godard-Desmarest S, Carpenter MA, Nishiyama N, Greer AL. Scripta Mater 2011;64:1091. [38] Fu HM, Wang H, Zhang HF, Hu ZQ. Scripta Mater 2006;55:147. [39] Chen N, Pan D, Louzguine-Luzgin DV, Xie GQ, Chen MW, Inoue A. Scripta Mater 2010;62:17.