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Intermetallics 46 (2014) 164e172

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Intermetallics

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Elevating the fracture toughness of Cu49Hf42Al9 bulk metallic glass:Effects of cooling rate and frozen-in excess volume

Zhen-Dong Zhu a, Evan Ma b, Jian Xu a,*

a Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016, ChinabDepartment of Materials Science and Engineering, Johns Hopkins University, 3400 N. Charles Street, MD 21218, USA

a r t i c l e i n f o

Article history:Received 12 July 2013Received in revised form5 November 2013Accepted 11 November 2013Available online

Keywords:B. Glasses, metallicB. Fracture toughnessB. Brittleness and ductilityB. Elastic properties

* Corresponding author. Tel.: þ86 24 23971950; faxE-mail address: jianxu@imr.ac.cn (J. Xu).

0966-9795/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.intermet.2013.11.006

a b s t r a c t

A major challenge for the structural applications of bulk metallic glasses (BMGs) is to improve theirfracture toughness. Here we demonstrate that by increasing the cooling rate during the casting of liquidCu49Hf42Al9 into BMG, using a mixed argon and helium atmosphere, the notch toughness of the resultantBMG can be tripled relative to that obtained at slower cooling rates. The much elevated toughness isattributed to a ten-fold increase in the size of the plastic zone at crack tip, due to the proliferation ofshear banding facilitated by enhanced propensity for shear transformations. The latter propensity isexplained by the reduced shear modulus and microhardness, as well as increased enthalpy recovery, allof which are rooted in structural disorder as reflected by the lowered density and increased frozen-inexcess volume. Such a structure-property correlation is systematically demonstrated by monitoring allthese properties over a range of diameters of the as-cast BMG rods that correspond to cooling rate levelsfrom 40 K/s to 103 K/s.

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1. Introduction

Over the past two decades, bulk metallic glasses (BMGs) haveattracted considerable interest [1]. In particular, their high strengthand processing advantages make them promising for applicationsas structural components. The bottleneck problem in this regardappears to be their low ductility [2]. In general, for structural ma-terials with high strength and limited ductility, their fracturetoughness, i.e., the resistance to crack propagation, is of paramountimportance for their use in engineering [3,4] and reliability (forBMGs, examples include electronic casings and biomedical de-vices). For BMGs, while a couple of them have been shown veryrecently to possess fracture toughness on par with the best crys-talline engineering alloys [4e6], the majority of them are inferior toconventional alloys in terms of fracture toughness. There is,therefore, a pressing need to come up with strategies that canmarkedly increase the fracture toughness of BMGs.

It is well known that for any given alloy, its processing historycan influence the fracture toughness. This also seems to be the casefor BMGs [7e9]. For example, Kawashima et al. [10] found that thefracture toughness of Zr55Cu25Ni10Al10 BMG samples is noticeablydifferent from batch to batch. In particular, the cooling rate used

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during the casting of the melt to form the glassy ingot is a pro-cessing parameter that may be tuned to change the fracturetoughness of the BMG obtained. Gu et al. [11,12] claimed that theBMG fabricated with higher cooling rate possesses higher tough-ness. However, quantitatively how much change in fracturetoughness can be brought about by varying the cooling rate duringBMG formation remains unclear.

Regarding the effects of cooling rate, the different residualstresses due to the different cooling rates could be an additionalissue. As indicated by Gilbert et al. [13], significant variability wasobserved in the fracture toughness data of the Zr41.2Ti13.8Cu12.5-Ni10Be22.5 BMG (Vit1). The highest measured KIC value wasw68 MPa Om (taken from a 7-mm thick as-cast plate); the lowestwas w30 MPa Om (measured with a 4-mm thick sample byremoving w1.5 mm from the surface of a 7-mm thick plate). Thisviability was believed to be associated with residual stresses at thesurface of castings. However, it has been a long-standing challengeto determine the residual stress in a BMG [14e16]. Aydiner et al.[15] showed that high stresses can be attained in a BMG cylinderdue to thermal tempering; about �300 MPa compression on thesurface balanced by þ150 MPa tension in the middle. Through thethickness of a BMG plate, the stress variation is roughly parabolic,with surface compression balanced by internal tension, just asthermal tempering of conventional oxide glasses [14]. Launey et al.[17] claimed that the residual compressive stress at the surface forthe as-cast Zr44Ti11Ni10Cu10Be25 BMG (Vitreloy 1b) can be relieved

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172 165

by annealing at 573 K (w0.9Tg, where Tg is glass transition tem-perature) for 2 min, without much annihilation of free volume.Removal of residual stress decreased the KIC by 30% from51 MPa Om to 34 MPa Om. However, such a release of the residualstress would be accompanied simultaneously by structural relax-ation. In other words, the lower fracture toughness for specimenstaken from the central portion of a thick BMG plate can be attrib-uted to much relaxed structure associated with the slower coolingrate experienced. Therefore, whether the residual stress is a pre-dominant factor influencing the fracture toughness remainsunsettled.

The range of glass-forming cooling rate during BMG fabrication[18] is well known to the community. The actual cooling rate hasthe following functional dependence on the dimension (R) of thesample, such as cylinder diameter or strip thickness,

_TðK=sÞ ¼ 10R2ðcmÞ : (1)

Usually under copper mold casting, the critical glass-formingcooling rate of BMG ranges from w1 K/s to nearly 103 K/s.

Relatively speaking, the effects of cooling rate on other BMGproperties are better characterized. It is well known that a fastercooling rate leads to a higher Tg. There have been many studiesreporting that more excess volume would be trapped inside theeventual glass processed at higher cooling rates [19]. For example,Chen [20] showed that the density of very thin Pd77.5Cu6Si16.5 rib-bons is about 0.2% lower than that of specimens produced as cyl-inders of 2 mm in diameter. Hu et al. [21] found that an increase ofthe cooling rate of Pd40Cu30Ni10P20 from 1.6 to 500 K/s leads to adensity decrease by w0.2% in the BMG obtained. Bobrov et al. [22]reported that as-quenched Pd40Cu30Ni10P20 glassy ribbons are0.45% less dense than the BMG sample at the same composition.Nagel et al. [23] estimated that the quenched-in excess volume inthe Zr46.7Ti8.3Cu7.5Ni10Be27.5 BMG at cooling rates as low as 1e2 K/sis of the order of 1%. Moreover, the presence of quenched-in excessvolume in the ZreCueNieAl and PdeCueNieP glassy alloys hasbeen measured using in situ X-ray diffraction in transmission[24,25]. One could in fact picture that freezing the metallic glassesat a slower cooling rate is equivalent to structural relaxation of theglass by aging at temperatures below Tg.

The frozen-in excess volume is often loosely interpreted as anincrease of “free volume” content in the metallic glass [26]. In otherwords, the higher the cooling rate, themore the excess free volume.The frozen-in excess volume was also treated as an increasedconcentration of interstitialcy-like defects by Granato [27]. Here theinterstitialcies are interstitials in the dumb-bell form with twoatoms occupying a potential well normally occupied by one atom[22,27,28]. Another alternative way to look at the cooling-rate ef-fects is from the energy landscape perspective [19,29,30]: atdifferent cooling rates the BMG falls into megabasins with differentdepth and is therefore characterized by different configurationalenthalpy.

Apart from the fracture toughness, there are also numerousinvestigations of the effects of cooling rate during glass formationon various mechanical properties of BMG. Jiang et al. [31] reportedthat the hardness of a Cu60Zr30Ti10 BMG is about 10% higher than itsribbon counterpart. Gu et al. [11] showed that the shear modulusand Young’s modulus of Ti40Zr25Cu12Ni3Be20 BMGs increase withdecreasing cooling rate, while the bulk modulus remains un-changed. It has also been noticed [12,32,33] that the BMGs pre-pared using faster cooling rate exhibited an improvement incompressive plastic strain. In addition, regarding the residual-stresseffect, it is interesting to note that Wang et al. [34] showed thattensile residual stress reduced hardness significantly, while

compressive residual stress produced only small effect on thehardness.

Moving forward from these previous studies, in this paper wefocus our attention on a quantitative assessment of the possiblechange of fracture toughness induced by the variation of coolingrate. The Cu49Hf42Al9 BMG is selected as our model system, owingto its high glass-forming ability (GFA) and moderate toughness[35e37]. Its robust GFA provides the room to tune the cooling rateduring BMG formation: the cooling rate can be varied by fabri-cating a range of diameter/thickness of the as-cast BMG cylinders/plates, see Eq. (1). The different cooling rates change the internalstructure of the BMG, and allow the correlation with the concen-tration of frozen-in excess volume. Meanwhile, the robust GFA alsomakes it feasible to quantitatively assess the BMG toughness, usingsamples with sufficiently large dimensions that standard ASTMtesting protocol becomes applicable. The notch toughness [5,8,38]characterized in this study showed a large increase for the coolingrate range employed. In addition to fracture toughness, we willalso examine the effect of cooling rate on several propertiesincluding the density, microhardness, enthalpy recovery, andelastic constants, which are all expected to depend on, and thus tobe indicators of, the BMG internal structure. Such a systematiccharacterization provides us with a comprehensive picture of thechanges in the BMG structure and mechanical responses, andsheds light on the origin responsible for the BMG tougheningobserved.

2. Experimental

The fabrication of the Cu49Hf42Al9 (in atomic percentage) BMGrods of 2e10 mm in diameter, using copper mold casting in Ar at-mosphere, has been described elsewhere [35,36]. The density ofBMG was measured at room temperature using Archimedeanmethod with Sartorius electrical balance (Gottingen, Germany)with a weight resolution of 10 mg. Distilled water was used asworking fluid. For a given rod diameter, at least three specimenstaken from independent as-cast BMG rods were tested to obtain anaverage value. The weight of a specimen for density measurementwas typically in the range of 1e2 g. Vickers microhardness wasmeasured in a MVR-HS hardness tester (Kawasaki, Japan) using aload of 300 N and 20 s hold time. The microhardness value given isthe average of 20 individual measurements. To exclude the uncer-tain effects of residual stresses on sample surfaces, hardness mea-surements were made at different locations spreading over theentire cross-section of the cylindrical or plate specimens.

Enthalpy recovery of the BMG were assessed in a PerkineElmerdifferential scanning calorimeter (DSC-Diamond; PerkinElmer,Shelton, CT) with alumina container under flowing purified argonat a heating rate of 0.33 K/s. Elastic properties of the BMGs weremeasured by resonant ultrasound spectroscopy (RUS) (Quasar,Albuquerque, NM). For each BMG rod diameter, at least threesamples with aspect ratio of about 0.8e1 taken from independentas-cast rods were used for measurement to ensure that the result isstatistically meaningful. The surface layer of the sample wasremoved by grinding, to ensure cylindricality and to reduceresidual-stress effects in the cast rods.

BMG plateswith three different cooling rateswere fabricated forthe assessment of notch toughness (KQ). The plates with di-mensions of 4 mm � 20 mm � 30 mm were prepared by tiltingcopper hearth casting, whereas the plates with cross-section of2.1 mm � 5 mm and about 20 mm in length were fabricated viasuction casting. In addition, 2.1-mm-thick plates were prepared bysuction casting in an atmosphere mixed with He and Ar at a ratio of1:1, to generate a faster cooling rate (due to the higher thermalconductivity of helium). To minimize the residual-stress effect, a

Fig. 1. (a) Changes of density and Vickers microhardness and (b) relative change offrozen-in excess volume, as a function of the diameter of as-cast Cu49Hf42Al9 BMG rods.

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172166

surface layer of at least 100 mm in thickness in the as-cast plateswasremoved by grinding.

Single-edge notch bending (SENB) tests were used fortoughness measurement. Sample with a dimension of B(thickness)¼ 2 mm,W (width)¼ 4 mm, S (span)¼ 16mmwere cutby electrical-discharge-machining from as-cast plates and thengrounded. Notches on the specimen were made by using a low-speed diamond wire saw. The notch root radius and depth is150 mm and 0.45e0.55 W, respectively. The three point bending(3PB) tests were performed on Instron 5848 micromechanicaltester (Norwood, MA) under displacement control (0.1 mm/min).For each condition of the BMG, at least five specimens were testedto ensure the reproducibility. Following ASTM standard E399, theKQ, the Mode I stress intensity factor, was calculated as presented inprevious work [5].

Fracture surfaces of the failed samples were examined in aQuanta 600 scanning electron microscope (SEM) (FEI, Eindhoven,Netherlands).

3. Results

Before discussing the fracture toughness behavior, we first sur-vey the cooling rate effects on the density, microhardness, enthalpyrecovery in DSC experiments, and elastic moduli. These are valu-able indicators of structural changes induced by the differentcooling rates, and establish the general trends and scopes. Ananalysis of these correlations sets the stage for probing into andunderstanding the fracture toughness changes.

3.1. Cooling-rate dependence of the frozen-in excess volume andhardness

As well documented, a change in the density of as-cast BMGprovides direct evidence of the presence of frozen-in excess vol-ume. Fig. 1a displays the measured density and Vickers micro-hardness as a function of the diameter of the as-cast Cu49Hf42Al9BMG rods. Upon increasing the rod diameter from 2 mm to 10 mm,the BMG density increases from 10.827 � 0.010 g/cm3 to10.899 � 0.004 g/cm3. The relative change in the density is w0.7%.The excess volume frozen in the BMG is taken to scale with thevolume difference between the BMG and its crystalline counter-part, the arc-melted crystalline Cu49Hf42Al9 master alloy, which isused as a reference state (r ¼ 10.937 � 0.001 g/cm3). As seen inFig. 1b, this frozen-in excess volume, defined and expressed interms of excess volume relative to the reference state (DVf%), de-creases with increasing rod diameter, from w1% at 2 mm to w0.4%at 10 mm.

According to Eq. (1), the cooling rate experienced by the 2-mm-and 10-mm-diameter rod is approximately 103 K/s and 40 K/s,respectively. In other words, our variation in the diameter of as-castBMG rods corresponds to about two orders of magnitude of changein the cooling rate. As shown in Fig. 1a, the slower-cooling results ina noticeable densification, with respect to the faster-cooled case.Similar findings have been observed in previous studies of otherBMGs [11,21].

Along with the density increase, the hardness (Hv) of BMG alsoincreases simultaneously, as shown in Fig. 1a. The Hv value in-creases from 6.12 GPa (2-mm rod) to 6.48 GPa (10-mm rod), i.e., a6% change. Combining Fig.1awith the information in Fig.1b, we seethat reducing the frozen-in excess volume by w0.1% appears tobring about a w1% increase in hardness. For comparison, thecomplete set of measured density and microhardness data forvarious diameters are summarized in Table 1.

It was observed in SEM images (not shown) of Vickers indentsthat, different from the 10-mm specimen, pile-up in the form of

semi-circular shear bands is obvious around the indent of 2-mmspecimen. This indicates that plastic deformation operated bymultiple shear banding events took place in the latter faster-cooledBMG, which, as discussed above, is softer and has higher concen-tration of excess volume. Such plastic-deformation zone sizearound the indents has been suggested to be associated with thedeformability of BMGs [39,40].

3.2. Correlation of frozen-in excess volume with enthalpy recovery

It has been well established that the enthalpy release below Tgdirectly correlates with the extent of structural relaxation ofmetallic glasses [41,42]. Fig. 2 shows the DSC curves associatedwiththe structural relaxation during constant-heating-rate scans of theas-cast BMG rods with various diameters. As the rod diameter ofBMG decreases, recovery enthalpy prior to glass transition in-creases, in the temperature range of 500e800 K. Meanwhile, theonset temperature of crystallization of the BMG remains at 863 K,irrespective of the sample diameter (or cooling rate). Note that theheat release associated with structural relaxation starts even at500 K (w0.6Tg, Tg ¼ 777 K). A release of residual stress in thecastings via thermal annealing would therefore always be accom-panied by changes in the glass structure.

In order to quantitatively characterize the released enthalpy, wetreated the 10-mm-diameter BMG rod as a nominally “fully-relaxed” quasi-equilibrium state. Its DSC curve was used as a“baseline”. The recovery enthalpy, DH, of the BMG with various

Table 1Density (r), Vickers microhardness (HV), enthalpy recovery (DH), Young’s modulus (E), shear modulus (G), bulk modulus (B) and Poisson ratio (n) of as-cast Cu49Hf42Al9 BMGrods with various diameters (d).

d (mm) r (g/cm3) HV (GPa) DH (kJ/mol) E (GPa) G (GPa) B (GPa) n

2 10.827 � 0.010 6.12 � 0.04 2.00 114.0 � 0.1 42.2 � 0.1 127.0 � 1.0 0.351 � 0.0013 10.848 � 0.007 6.21 � 0.07 1.78 114.5 � 0.3 42.3 � 0.1 129.8 � 0.8 0.353 � 0.0014 10.863 � 0.007 6.22 � 0.07 1.38 114.3 � 0.3 42.3 � 0.1 128.2 � 1.5 0.352 � 0.0016 10.881 � 0.009 6.29 � 0.06 0.55 115.3 � 0.3 42.7 � 0.1 129.3 � 0.1 0.352 � 0.0018 10.887 � 0.003 6.40 � 0.05 0.62 116.7 � 0.1 43.2 � 0.04 129.1 � 0.02 0.350 � 0.00110 10.899 � 0.004 6.48 � 0.04 0 117.2 � 0.1 43.6 � 0.05 126.1 � 2.0 0.345 � 0.002

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172 167

diameters was calibrated by subtracting this baseline from eachcurve, for the temperature range from the onset temperature ofrelaxation to Tg. As tabulated in Table 1, the fastest cooled Cu49H-f42Al9 BMG, at 2-mm-diamter, exhibits the largest recoveryenthalpy, DH¼ 2.0 kJ/mol. At 8 mm, DH is reduced byw70% to onlyw0.62 kJ/mol.

To directly correlate the frozen-in excess volume and enthalpyrecovery, Fig. 3 plots the DVf% against DH. They exhibit a good linearrelationship with slope (b’) of about 260 kJ/mol (or 2.8 eV).Evidently, the frozen-in excess volume in as-cast BMG directlyscales with the enthalpy recovery during the relaxation. Thephysical meaning regarding the b’ value will be discussed later inSection 4.

3.3. Correlation of frozen-in excess volume with elastic constants

The measured elastic constants of as-cast Cu49Hf42Al9 BMG rodswith various diameters are summarized in Table 1 as well,including the Young’s modulus E, shear modulus G, bulk modulus Band Poisson’s ratio n. Fig. 4a illustrates changes in the G and B withdiameter (d) of as-cast BMG rods. An increase in d from 2 mm to10 mm, or correspondingly a decrease in cooling rate by two ordersof magnitude, leads to a G increase of about 3%, from 42.2 GPa to43.6 GPa. In comparison, the change of B is insignificant, within themargin of error of the data points.

Fig. 4b shows changes in the Young’s modulus and Poisson’sratio with d. Similar to G, the increase of E is about 3%. The relativechange of E and G is nearly the same, which is expected because theE and G is proportional to the yield strength in uniaxial loading (sy)and in shear (sy), respectively, and sy ¼ sy/2. The Poisson’s ratio, asshown in Fig. 4b, shows a noticeable decline (w1.5%) in the d ¼ 6e

Fig. 2. DSC scans at a heating rate of 0.33 K/s for as-cast Cu49Hf42Al9 BMG rods withvarious diameters.

10 mm, as a result of the combined effects of both the shearmodulus and bulk modulus. It is interesting to note that thesensitivity of properties to the cooling rate (or excess volume in theBMG) can be ranked in the following order: Hv > (G or E)> n > r.

Fig. 5 shows a plot of Vickers microhardness and shear modulusagainst density of as-cast Cu49Hf42Al9 BMGs with various di-ameters. The density and microhardness or shear modulus of theBMG manifest good linear relationship, with linear regression co-efficient R of 0.92 and 0.82, respectively. This plot makes it clearthat denser BMG possesses higher hardness and shear modulus.Such a linear relationship between the shear modulus and densitywas also found in the case of Pd40Ni10Cu30P20 BMG [43].

3.4. Effect of glass-forming cooling rate on notch toughness

With the general behavior already established, we now shift outattention to the cooling-rate effect on fracture toughness, the mainfocus of this study. Based on the information already collectedabove, we prepared three groups of Cu49Hf42Al9 BMG strips pro-cessed under different conditions. (i) 4-mm-thick plates cast underAr atmosphere (denoted as 4 TA); (ii) 2-mm-thick plates cast underAr atmosphere (denoted as 2TA); (iii) 2-mm-thick plates cast inmixture atmosphere of 50 vol. % Ar and 50 vol. % He (denoted as2TH).

To estimate the cooling rate experienced by these BMG plates,we make use of the plots already established for the density andhardness of as-cast rods (see data in Table 1) and Eq. (1). In other

Fig. 3. Correlation between relative change of excess volume and enthalpy recovery(DH) associated with structure relaxation of Cu49Hf42Al9 BMG fabricated with differentglass-forming cooling rates. The dash line is from linear fitting.

Fig. 4. Change of (a) shear modulus (G) and bulk modulus (B) and (b) Young’s modulus(E) and Poisson’s ratio (n) with rod diameter of as-cast Cu49Hf42Al9 BMG.

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172168

words, the cooling rate of BMG plates can be estimated from theirmeasured density and hardness, as shown in Fig. 6a and b usingdash lines and shadow areas. The cooling rate of the 4TA, 2TA and2TH BMG plates is at the level of 40e100, 100e250 and 200e450 K/s, respectively. In addition, the cooling rate of the 4TA plate isapproximately equivalent to that of the as-cast BMG rods of 6e

Fig. 5. Correlation of Vickers microhardness and shear modulus with density of as-castCu49Hf42Al9 BMG fabricated at different cooling rates. The line is given by linear fitting.

10 mm in diameter. In comparison with the 4TA, the cooling rate ofthe 2TH is about 5 times faster. Along the same line as illustrated inprevious sections, the 2TH BMG frozen in the He-containing at-mosphere is expected to contain more excess volume. With respectto the arc-melted master alloy, excess volume (DVf%) for the 4TA,2TA and 2TH BMG plates is determined to be w0.4%, w0.6% andw0.7%, respectively.

Using the 3PB testing, the notch toughness (KQ) of the 4TA, 2TAand 2TH BMG plates was determined to be 26 � 2, 56 � 9 and79 � 10 MPa Om, respectively. According to ASTM E399, the planestrain condition of a specimen requires a plate thickness B via thefollowing relation,

B � 2:5�KQ

sy

�2

: (2)

The sy of Cu49Hf42Al9 BMG is 2.3 GPa [35]. Eq. (2) suggeststhat the 4TA and 2TA configurations are under the plane straincondition while the 2TH is under plane stress condition, whichmay contribute to the elevated toughness of 2TH. If so, theincreased toughness would be due to the transition of the stressand strain condition. For a better and fair comparison, we convertthe KQ of the BMG with different thermal history to energy releaserate (GC), based on the relation between GC and stress intensityfactor (KQ) [44]:

GC ¼K2Q

E0: (3)

Under the plane stress condition, E0 ¼ E, while under the planestrain condition, E’ ¼ E/(1 � n2).

Based on the estimated cooling rate (see Fig. 6) and the data inFig. 4b, the Young’s modulus of 4TA, 2TA and 2TH BMG plates isattained to be 116 GPa, 115 GPa, and 114 GPa, respectively. TheirPoisson’s ratio is taken as 0.352. As a result, the converted GC fromthe KQ values is 5 kJ/m2, 24 kJ/m2 and 56 kJ/m2, respectively, whichhave been listed in Table 2 as well. Apparently, the energy releaserate or fracture toughness of the BMG can be considerablyenhanced by faster cooling or incorporating more excess volume.As shown in Fig. 7a, the relatively low GC of the Cu49Hf42Al9 BMG iselevated by a factor of ten, by intentionally increasing cooling rateunder He-containing atmosphere. The magnitude of the KQ ach-ieved is in fact now comparable to that of a much tougher Zr-basedBMG, Zr56Co28Al16 (KQ ¼ 77 � 8 MPa Om) [5].

Based on the relation between plastic zone radius (rp) at crack(notch) tip under plane-stress condition and the toughness andyield strength of material,

rp ¼ 12p

�KQ

sy

�2

; (4)

the rp of the 4TA, 2TA and 2TH BMG plates would be expected to be20, 125 and 250 mm, respectively. Here, the sy is approximated by0.95Hv/3 since the tensile yield strength of BMG is only w0.95 ofcompressive yield strength [45]. The compressive strength ofCu49Hf42Al9 BMG (measured with the cylinder of 1.5 mm indiameter) is 2.3 GPa, about 11% higher than the value estimatedfrom themicro-hardness (6.9 GPa). The plastic zone radius ahead ofcrack/notch, as presented in Fig. 7b, is enlarged by as much as oneorder of magnitude.

Fig. 8a, c and e displays SEM images of the side views of frac-tured plates after 3PB testing. In the case of 4TA with the lowestcooling rate and KQ ¼ 25 MPa Om, only a few visible shear-bandoffsets are present on the sample surface ahead of the notch tip,as seen in Fig. 8a. In contrast, a number of shear-banding offsetsappear ahead of the notch tip for the 2TA plate withKQ ¼ 56 MPa Om, as shown in Fig. 8c. The area containing shear-

Fig. 6. (a) Density and (b) Vickers microhardness versus estimated glass-formingcooling rate converted from rod diameter of as-cast Cu49Hf42Al9 BMG. The line isgiven by linear fitting.

Fig. 7. (a) Energy releases rate and (b) calculated plastic zone radius versus estimatedglass-forming cooling rate (converted from rod diameter of as-cast Cu49Hf42Al9 BMG)of as-cast Cu49Hf42Al9 BMG.

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172 169

banding deformation is extended to about 200 mm in size. Evenmore numerous shear-banding offsets and a larger area of shear-banding extension (w300 mm in size) are observed in the 2THBMG plate with the fastest cooling rate. This is also consistentwith the highest toughness of this specimen, KQ ¼ 87 MPa Om.Moreover, the plastic zone size in the sample side-surface observedunder SEM is indeed comparable to the estimated rp calculatedusing Eq. (2).

Fig. 8b, d and f displays SEM images taken from fracture surfaceof BMG plates corresponding to Fig. 8a, c and e. In all cases, thefracture surface ahead of the notch exhibits two types of patterns,smooth zone and vein pattern zone. Along the crack advancingdirection, the extended length of the smooth zone for the 4TA, 2TA

Table 2Density (r), Vickers microhardness (HV), notch toughness (KQ), energy release rate (GC) anseveral conditions.

Denotation Plate thickness (mm) Cooling atmosphere r (g/cm3)

4TA 4 Pure Ar 10.891 �2TA 2 Pure Ar 10.871 �2TH 2 He:Ar ¼ 1:1 10.858 �

and 2TH BMG plates is about 4, 8 and 20 mm, respectively, whereasthe vein pattern zone extends to 40, 80 and 130 mm, respectively. Aspreviously documented [5,46], the smooth zone (or shear-offsetzone) was generated at an initial stage of shear-banding eventscaused by large stress concentration at notch root under appliedloading.

4. Discussion

We now analyze further the origin of the improved toughness.As shown in Fig. 7b, the plastic zone size of the BMG is drasticallyenlarged as the BMG-forming cooling rate increases. Quantitatively,the rpwas raised from the level of 125 mmof the slow-cooled 2TA to

d calculated plastic zone size (rp) of as-cast Cu49Hf42Al9 BMG plates fabricated under

HV (GPa) KQ (MPa Om) GC (kJ/m2) rp (mm)

0.002 6.40 � 0.05 26 � 2 5 20 � 10.010 6.28 � 0.04 56 � 9 24 � 8 125 � 350.003 6.24 � 0.05 79 � 10 56 � 13 250 � 50

Fig. 8. SEM images of fractured Cu49Hf42Al9 BMG specimens after 3PB testing. (a), (c) and (e) are side views of 4TA, 2TA and 2TH plates with KQ ¼ 25, 56 and 87 MPa Om,respectively. (b), (d) and (f) show the fracture surface near notch root corresponding to (a), (c) and (e), respectively.

Fig. 9. Correlation between shear modulus multiplied by molar volume (GVm) andenthalpy recovery associated with structural relaxation of Cu49Hf42Al9 BMG, forincreasing rod diameter from 2 mm to 10 mm. The line is given by linear fitting.

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172170

250 mm for the fast-cooled 2TH, as seen in Table 2. Such remarkableincrease of the rp is consistent with the increase of energy releaserate GC, namely, of the toughness. The reason for the enlarged rp isthe proliferation of shear bands ahead of the notch/crack tip. Theshear band formation involves cooperative actions of numerousshear transformations in shear transformation zones (STZs) [2].Apparently, the shear transformations are promoted in fast-cooledBMGs, due to the frozen-in excess volume and associated localdisorder that lead to more local configurations prone to changesunder imposed stresses [47,48].

This effect can be appreciated by inspecting the cooperativeshear model (CSM) [49], in which the total potential energy barrierfor a plastic event in a metallic glass, W, can be expressed as

W ¼�8=p2

�g2c GzU; (5)

where the gc ¼ 0.0267 is universal shear train, G is shear modulus, zis a correction factor and U is an activation volume. As the faster-cooled BMG with more frozen excess volume (equivalent to lowerdensity) exhibits lower G, as shown in Fig. 4a, a lower energy bar-rier is expected. As a result, more shear transformations can beactivated to favor subsequent shear band formation under

Z.-D. Zhu et al. / Intermetallics 46 (2014) 164e172 171

stressing, leading to plastic events across a larger region, andconsequently higher fracture toughness.

The shear energy barrier can be written as WfGVm [50,51],where Vm is the molar volume of the alloy. In Fig. 9, we plot theenthalpy recovery, DH, against GVm. There appears to be a corre-lation, which seems to suggest an inverse scaling between theexcess enthalpy of configurational disorder DH and the averageactivation barrier for configurational hoping [52]. A looser andmore disordered configuration (higher DH) signals a reduced bar-rier (W) and hence increased propensity for inelastic relaxation andshear transformations.

The reduced G at increased cooling rates, with B staying largelyunchanged, leads to increased Poisson’s ratio (see the trend in Fig. 4for example). The tendency of a higher n favoring higher toughnesshas been repeatedly discussed in the literature [1,4,5,11,12]. Asnoted before [43,53], a relatively small increase in density cansignificantly affect the mobility of the atoms, local atomic order andpropensity for rearrangements. For example, a less relaxed glasshas a wider range of atomic environments and slightly less densepacking, allowing local displacements that differ from those pre-scribed by the macroscopic strain. A denser glass has decreasedinteratomic spacing and topological changes that make theanelastic internal rearrangements more difficult [2]. Shear modulusis more sensitive to atomic arrangements than the bulk modulus[53]. The current finding that the shear modulus rather than thebulk modulus correlates with the density, as shown in Fig. 5, thusseems reasonable.

Regarding the connection between enthalpy recovery andexcess volume in the BMG, the factor b’ in DH ¼ b’DVf was found tobe w2.8 eV in our cases, as shown in Fig. 3. It was suggested pre-viously that the relative change of excess volume can be treated asfree volume per atomic volume [41,42]. In such a case, b0 can beunderstood as the energy to create a vacancywith themagnitude ofone atomic volume. It implies that b0/2 should be close to vacancyformation energy (Evac) [42]. For crystal metals, the Evac is usually inthe range of 1e2 eV. In our case, b’/2 is 1.4 eV, within the range ofthe Evac. However, there have also been many cases where the b’

value is 2e3 times larger than Evac [42,54,55].In terms of the “interstitialcy model” [27,28], the relative change

in the concentration of interstitialcy-like defects in metallic glass,DC, would correlate with the relative change of the shear modulus,DG, which are temperature- (T) and time- (t) dependent variables.The scaling relationship is

DGðT; tÞ=G ¼ �bDCðT; tÞ; (6)

where the b is a shear softening parameter, in the range of 20e30.This expectation was confirmed [43] for the Pd40Ni10Cu30P20 BMG,but Chen [20] reported that the�dlnE/dlnV values of several Fe-, Ni-,Pd- glasseswere onlyabout 17. For our data ford¼ 2e10mm, in a plotof relative change in shearmodulus against the relative change in theexcess volume, the �dlnE/dlnV value (or the b) is only 4.8, muchsmaller than that required by the interstitialcy scenario. In otherwords, our finding does not seem to support the interstitialcy model.

Moreover, it is instructive to recall the findings and insight frommolecular dynamics (MD) simulation. For the Zr54Cu46Al7 metallicglass, Cheng et al. [48] revealed that with increasing cooling rate forglass formation, the resistance to flow initiation and propensity forstrain localization into softened regions were reduced. From theperspective of short-range order on the atomic scale, the fraction ofCu-centered full icosahedra with atomic coordination number of12, and the fraction of atoms involved in Cu-centered polyhedral,decrease with increasing cooling rate. This renders the metallicglass more prone to spread-out plastic flow and less susceptible tostrain localization, which was in fact also shown graphically for

Cu64Zr36 metallic glass samples quenched at different cooling rates[53]. Therefore, the enhanced toughness by faster cooling in thecurrent work can also be understood from a change in the atomic-scale structure in the glasses. As perhaps expected, reducing theresistance to flow initiation and the propensity for severe strainlocalization is beneficial for the toughening of BMGs.

Finally, on the effect of residual stresses in the surface of as-castBMG plates, the model by Aydiner et al. [14] suggests that surfacecompressive stress and mid-plane tensile stress are significantlydependent on the plate thickness. For their 8.25-mm thick plate ofVit 1 BMG, the stresses of surface compression and mid-plane ten-sion were predicted to be on the level of �200 MPa and þ90 MPa,respectively. The magnitude was reduced to the level of �80 MPaand þ40 MPa, respectively, when the plate thickness was reduceddown to 2.5mm that is comparable to the size of specimenswe usedfor notch toughness assessments. In this case the residual stress onlyamounts to w4% of the yield strength for such thin plates. From adistortion and mechanical failure point of view, therefore, such lowstresses can be neglected. In other words, we suggest that thefrozen-in excess volume play a dominant role in influencing thetoughness of BMG thin plates. Some discussions on the effects ofcompressive surface stress in enhancing the nucleation of shearbands near the surface can be found elsewhere [56e58].

5. Conclusions

By varying the diameter of as-cast Cu49Hf42Al9 BMG rods, thecooling rate experienced by the BMG during its formation waschanged from approximately 40 K/s to 103 K/s. This results in asignificant rise in the frozen-in excess volume in the BMG withrespect to the crystalline reference, from w0.2% to w1%. Thischange in the glass density/structure leads to significant increasesin Vickers microhardness, Young’s modulus, shear modulus, andenthalpy recovery. Among these indicators, Vickers microhardnessappears to be the most sensitive in responding to the variation ofexcess volume in the BMG.

Increasing the cooling rate during BMG fabrication, such ascasting under argon atmosphere mixed with helium, has aremarkable effect to significantly improve the toughness of BMG.Meanwhile, the toughness improvement also correlates with theother changes in BMG properties, such as the decreased hardness/strength, Young’s modulus and shear modulus. The enhanced BMGtoughness is associated with an obviously extended plastic zone atthe crack tip (the radius was increased by one order of magnitude),due to the proliferation of shear bands. The shear transformationsare facilitated by the increased excess volume and structural dis-order. These structural origins consistently manifest themselvesthrough the various properties.

Acknowledgments

This work was supported by National Natural Science Founda-tion of China under Grant No. 51171180. E.M. was supported at JHUby US-NSF-DMR-0904188. The authors also thank Prof. J.K. Shangfor insightful discussion.

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