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Acta Materialia 54 (2006) 5271–5279

Deformation and evolution of shear bands under compressiveloading in bulk metallic glasses

J.Y. Lee a, K.H. Han a, J.M. Park a, K. Chattopadhyay b, W.T. Kim c, D.H. Kim a,*

a Department of Metallurgical Engineering, Center for Noncrystalline Materials, Yonsei University,

134 Shinchondong Seodaemungu, Seoul 120-749, Republic of Koreab Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India

c Division of Applied Science, Chongju University, Chongju 360-764, Republic of Korea

Received 16 January 2006; received in revised form 6 July 2006; accepted 13 July 2006Available online 26 September 2006

Abstract

Shear band formation and failure mechanism in monolithic glasses and glass matrix composite exhibiting a wide range of plasticitywere investigated by interrupted compression experiments. The major shear bands in monolithic glasses appear rapidly after a smalldeformation, and their numbers remain almost same in the later stages of deformation. The path of the crack growth does not coincidestrictly with the shear band. The larger plastic strain in glasses exhibiting higher ductility is mainly accommodated in the primary shearband by forming larger shear offset prior to failure. The failure mechanism under compression is not pure shear, but mixed mode withevidence of a tensile component, which leads to the formation of microvoids (microcracks). Bridging of the microvoids leads to finalfracture. In the case of glass composite containing particles, the microcracks at the interface arrest the propagation of the existing shearbands and form additional shear bands, improving plasticity.� 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Bulk metallic glass; Deformation; High plasticity; Shear bands; Microvoid

1. Introduction

Although the functional application of metallic glass iswell established, the prospect of structural application ofmetallic glass has brightened with the discovery of a largenumber of bulk metallic glasses. The early studies onmechanical behaviour of metallic glasses established thepresence of inhomogeneous shear bands during the defor-mation process [1–3]. However, restriction on sampledimensions achievable during processing preventeddetailed studies of mechanical property under differentloading conditions. With the availability of bulk metallicglasses with very high strength and reasonable ductility,studies on mechanical behaviour of this class of materials

1359-6454/$30.00 � 2006 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2006.07.014

* Corresponding author. Tel.: +82 2 2123 2841/4255; fax: +82 2 3128281.

E-mail address: dohkim@yonsei.ac.kr (D.H. Kim).

have gained momentum. It is now well known that, whilehomogeneous deformation is possible at high temperatures[3], the deformation of metallic glass is inhomogeneous innature at lower temperatures. Owing to the absence oflong-range order, metallic glass exhibits a very high-yieldstress resulting in a very high accumulation of strain energy[4]. Most monolithic glasses show very little plasticityunder tensile loading [5,6]. However, under constraintloading such as compression, bending and indentation,these glasses exhibit plasticity [7–9]. Recently, a plasticstrain as high as 20% was reported under compression[10]. The deformation of metallic glass is shown to beelastic-perfectly plastic in nature [6,11,12]. However,reports indicate the existence of a strain rate effect on duc-tility. While most reports indicate a decrease in ductilitywith increasing strain rate [11,13,14], a recent study reportsan increase in plastic strain with increasing strain rateunder both tension and compression [15]. Plastic strains

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Table 1Ultimate compressive strength and total strain to failure of the metallicglasses and composites investigated in the present study

Compositions Compressivestrain (MPa)

Compressivestress (%)

Zr46.75Ti8.25Cu7.5Ni10Be27.5 1.95 4.0Ti55Zr10Be18Cu9Ni8 2.19 6.8Ni59Zr16Ti13Si3Sn2Nb7 2.90 8.2(Zr70Cu20Ni10)82Ta8Al10 1.70 16

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are localized within inhomogeneous shear bands, and thesebands play a crucial role in the deformation process. Thenature of the glass at shear bands is different from the rest,which shows up as a region of lighter contrast in the trans-mission electron micrographs [9,16]. It is suggested thatthese bands contain excess free volume resulting from theshearing process and exhibit strain softening [17,18].Understanding the evolution of shear bands is central tothe understanding of the mechanical behaviour of metallicglass. For example, branching of shear bands is shown tobe associated with enhanced ductility in both monolithicmetallic glasses [19] and in composites [20]. The presentpaper reports the results of a systematic and comparativestudy on the formation of shear bands at the specimen sur-faces under compressive loading as a function of the shearstrain for three chemically distinct monolithic glasses anda composite. These glasses exhibit varying degrees ofductility.

2. Experimental procedure

Ingots (30 g) with the compositions were prepared byarc-melting under Ar atmosphere. Raw materials of purityranging from 99.8% to 99.99% were used in the arc-meltingprocess. Each alloy was remelted at least three times toensure the compositional homogeneity. The injection cast-ing was performed to make bulk samples. Appropriateamounts of each alloy were remelted in quartz cruciblesand injected through a nozzle into Cu moulds.

Mechanical properties of BMG samples were measuredat room temperature under a compressive mode with astrain rate of 1.66 · 10�4. For the compression tests, sam-ples with a cylindrical shape (1 mm in diameter and2 mm high) and a rectangular shape (1.5 · 1.5 · 3.5 mm)were prepared. The samples were fixed in a jig designedto ensure parallelism of the ends. The surface of the frac-tured specimen was observed using scanning electronmicroscopy (SEM; Hitachi S2700) and optical microscope(OM; LEICA DMRN).

3. Results

3.1. Observation of shear band in bulk monolithic glasses

The three monolithic glasses in this investigation studiedshow different level of strength and ductility. The Zr-richglass (Zr46.75Ti8.25Cu7.5Ni10Be27.5) shows the least ductility,while the Nb-containing Ni-rich glass samples (Ni59Zr16-Ti13Si3Sn2Nb7) exhibits large plasticity. The glass com-posite ((Zr70Cu20Ni10)82Ta8Al10) with dispersion of Taparticles also exhibits significant enhancement of plasticity.A summary of the strength and ductility of these glasses isgiven in Table 1. All three monolithic glasses show a serra-tion in the plastic region in stress–strain plots. Such serra-tion is common feature for large number of glasses whenthey are tested at low strain rates. Generally, the serrationvanishes at high strain rates, with the transition strain rate

lying between 10�2 and 10�3 [13]. The present paperfocuses on the low strain rate regime. All the tests were car-ried out with a strain rate of 10�4 s�1. In order to under-stand the formation of shear band in these glasses,interrupted experiments were carried out at different strainsand the evolution of the shear band in the two perpendic-ular surfaces parallel to the stress axis was observed. Fig. 1shows the results for Zr-rich glass, which shows least duc-tility. The stress–strain curves for each interruption areshown in Fig. 1a. Fig. 1b–d shows the shear band forma-tion in one of the vertical pre-polished surfaces where thecrack that caused the failure evolved. Only a few shearbands could be observed in this surface, and most of themappeared after the first interruption, corresponding to astrain of �1.9%, representing a small deformation. Theangles of these bands with respect to stress axis are between40.5� and 41.0�, suggesting a large hydrostatic componentduring deformation. These are consistent with earlierobservations [13,21,22]. Although this can be taken to indi-cate that Von Mises’ criterion is not obeyed for metallicglass, experiments with superimposed hydrostatic pressurewere found to be inconsistent with this conclusion [23]. Thecracks responsible for the failure initiate at the major shearband where most of the plastic strain is localized. However,the fracture plane is close to but not exactly along thisshear band at an angle of �40� to the compression axis.The shear band itself is not strictly planar just before yield-ing and a deviation of �2.5� exists between the two ends ofthe band lying in the planar surface. Only five additionalsmaller primary shear bands parallel to this band appearedin this face of the sample with increasing strain. At largerstrain (Fig. 1c), additional shear bands appeared at roughly90� to the main shear band. These bands show a tendencytowards branching, suggesting that they have propagatedin other equivalent planes to accommodate the strain.

We now consider the shear band propagation in a glass(Ti55Zr10Cu9Ni8Be18) that shows relatively large plasticdeformation. Fig. 2a shows the interrupted stress–straincurves. Fig. 2b and c shows the shear band formation attwo perpendicular vertical surfaces of the specimen parallelto the compression axis at different strains obtained byinterrupting the test. The shear bands had appeared at anangle of �44� to the loading axis in the polished faces fairlyearly (Fig. 2b, at a strain of �1.6%). Fig. 2d shows thebands just before fracture. One can observe a major shearband which has accommodated large plastic strain and

Fig. 1. (a) Stress–strain curves for each interruption during compression test of Zr46.75Ti8.25Cu7.5Ni10Be27.5 monolithic glass; (b), (c) and (d) opticalmicrographs showing shear band formation at one of the vertical pre-polished surface of the specimen parallel to compression axis at different strains of1.9%, 2.4% (after first interruption) and 2.9% (after second interruption), respectively.

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Fig. 2. (a) Stress–strain curves for each interruption during compression test of Ti55Zr10Cu9Ni8Be18monolithic glass; (b), (c) and (d) optical micrographsshowing shear band formation at two perpendicular vertical pre-polished surfaces of the specimen parallel to compression axis at different strains of 1.6%,2.6% (after first interruption) and 4.2% (after second interruption), respectively. (e) SEM micrographs obtained form the vertical pre-polished surface(surface A in (d)) of the Ti55Zr10Cu9Ni8Be18 monolithic glass specimen showing the cavities at the shear band intersections.

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where the cracks responsible for fracture had nucleated.The number of additional parallel shear bands in this planeare again limited (six in this case). In particular, althoughthe main shear band in plane ‘A’ is relatively straight (itdeviate a small amount along the line before the fracture),the trace of it in the perpendicular plane ‘B’ reveals that its

00

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2000

2500

3000

(c)(b)

Stre

ss (M

Pa)

Strain 2 4

Fig. 3. (a) Stress–strain curves for each interruption during compression tmicrographs showing shear band formation at two perpendicular vertical pre-strains of 2.1%, 2.4% (after first interruption) and 3.7% (after second interrupresponsible for ultimate fracture has initiated.

path in the sample is curved. More importantly, one seesthe evidence of cavitations in this band just before fracture(see the inset in Fig. 2d). In this particular case, there is alsoa branching of the main shear band. The SEM micrographof the region near this branching is shown in Fig. 2e at adifferent magnification, revealing the multiple nucleation

Ni59Zr16Ti13Si3Sn2Nb7

Uniaxial compression Strain Rate = 1 x 10-4 s-1

(d)

(%)6 8

est of Ni59Zr16Ti13Si3Sn2Nb7 monolithic glass; (b), (c) and (d) opticalpolished surfaces of the specimen parallel to compression axis at differenttion), respectively; (e) SEM micrograph showing the region where crack

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of the shear band between the two bands formed by thebranching of the primary band, indicating a secondarystrain accommodation process. Such branching wasreported earlier in Zr-based glasses with enhanced plastic-ity [19]. The cavities at interactions are also marked byarrows.

A third example of shear band formation in a ductile Ni-based bulk metallic glass of composition Ni59Zr16Ti13-Si3Sn2Nb7 is now presented. Fig. 3b–d shows the shearbands in two perpendicular faces at different strainsmarked in the stress–strain diagram in Fig. 3a. Again, avery limited number of major shear bands can be observed.The angle of these bands with respect to the axis of com-pression is again close to 43�. With the increase in strain,the secondary shear band could be observed to originatefrom the main shear band for secondary accommodationof strains. Fig. 3e shows the region where the crack respon-sible for ultimate fracture was initiated. The path of the

0.00 0.02 0.04 0.06 0.08 0.10 0.12 00

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1000

1200

1400

1600

1800

2000(Zr70Ni10Cu20)82Ta8

Uniaxial compressioStrain Rate = 1 x 10

Stre

ss (M

Pa)

Strain

(b) (c)

Fig. 4. (a) Stress–strain curves for each interruption during compression test ofshear band formation at two perpendicular vertical pre-polished surfaces ointerruption), respectively; (c) optical micrograph showing the vertical pre-po(d) optical micrograph showing the interaction of the shear bands with the Ta

crack growth does not coincide strictly with the inhomoge-neous shear band consistent with earlier observation on theZr-based glass.

The above results indicate that the nature of the shearband formation is identical for three glasses of very differ-ent constituent elements. The morphology of these bandsalso does not change significantly with the variation in duc-tility. In order to get a more quantitative idea, the height ofthe shear steps in all the three cases was measured. In thecase of less ductile Zr-rich glass, the maximum shear stepheight in the main primary band (where fracture crackoriginated) is �9.7 lm. The other bands on average displaya shear offset height of �1 lm. Most of the observed strainsare accommodated by the major shear bands in this plane.In the case of a relatively more ductile Ti-rich glass, whichexhibits a strain of �4.2% (after second interruption;Fig. 2d), the shear step height displayed by the major pri-mary band is �36 lm, while the heights of the smaller

.14

Al10

n -4 s-1

(Zr70Cu20Ni10)82Ta8Al10 glass composite; (b) optical micrographs showingf the specimen parallel to compression axis at a strains of 3.6% (afterlished surface of the specimen parallel to compression axis after fracture;

particles.

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shear bands vary between 1 and 10 lm (average of �4 lm).The total displacement from these bands was carefullymeasured (a total of 15, which show displacement stepsat the edges). The estimated strain from step height iswithin 10% of the measured strain after yielding. Again,in Ti-rich glass, most of the plastic strain is confined to afew primary shear bands. In the case of Ni-based bulkmetallic glass which exhibits the maximum ductility amongthe three glasses studied in this investigation, the maximumshear height observed is �17 lm (Fig. 3d and e). There aretwo bands with similar height. Again, the shear steps onprimary bands account for most of the strain in the speci-men. However, more than one band is involved in themajor accommodation of the plastic strain.

It can be noted that the major shear bands appear rap-idly after a small deformation in all the samples of differentglasses and their numbers remain more or less the same inthe later stage of deformation. For Zr-rich glass, this num-ber is six in the face which later contained the fractureplane. The number is again similar for both the Ti- andNi-base glasses (six each). In contrast, the number of shearbands is much larger in the perpendicular surface, as can beseen from Fig. 2d.

3.2. Shear bands in composites

In order to obtain further insight, the development ofshear bands at different strains (obtained by interruptedtest) was followed for a metallic glass composite whichexhibits a large elongation. The glass composite of compo-sition (Zr70Ni10Cu20)82Ta8Al10 is similar to that studied byCang et al. [20] and sustains a compressive plastic strain ofbetter than �7%. This composite exhibits a strain harden-ing behaviour. Fig. 4a shows the interrupted stress–straincurves, while Fig. 4b and c show the shear bands at eachinterruption on the two perpendicular surfaces of the spec-imen. Unlike the monolithic glass, no major shear bandtraversing the full face of the specimen surfaces could beobserved. Instead, the surface contains a very large numberof shear bands well distributed across the specimen. Con-sistent with earlier observations [20], the specimen bucklesbefore the failure occurs. Most of the shear band makes anangle of less than 40� with the compression axis, suggestinga large hydrostatic component operating in this material.Fig. 4d shows the interaction of the shear bands with theTa particles. It is clear that the particles interact stronglywith the shear bands. There is a clear evidence of debond-ing of the matrix–particle interface due to this interaction,which inhibits the further growth of the shear band.

4. Discussion

It is well known that geometry plays an important rolein the plastic deformation of the metallic glass. This hasbeen quantitatively evaluated recently for the case of bend-ing [7,24]. Two important results from these reports areworth noting. First, the failure strain decreases with

increasing thickness under bend geometry. Second, thespacing of the shear band which forms to accommodatethe plastic strain varies linearly with thickness, while theshear band offset varies as the square of the thickness. Thusas the number of bands decreases, the increasingly largeplastic strain is accommodated in each band. Systematicstudies dealing with the effect of geometry on the morphol-ogy of the shear band under compression is not available,although it is well known that a larger aspect ratio affectsthe achievable plastic strain and formation of multipleshear bands [7]. The present results do not address thequestion of geometry. However, the results suggest that,in the case of monolithic glass, for a given geometry, thearrangements of the primary shear bands are similar andare independent of the chemistry of the glass and theamount of strain. Two important facts emerge from theseresults. The large plastic strain that some of these glassesexhibit are to a large extent accommodated in the primaryshear band by large shear offset prior to failure. For Ti-richglass, this value is as large as �36 lm. A second and morestriking observation is that all the primary slip bandsappear very early, approximately parallel to the ultimatefracture plane. Observation of the specimen surface alsoindicates that the surface containing these bands exhibitsrelatively less secondary shear banding. Surfaces normalto this, however, exhibit fairly large multiple shear bands,well distributed across the entire plane with a high ten-dency for branching. At large strains, the trace of the majorshear band (which ultimately trigger the fracturing process)in this plane is curved and has a zigzag appearance at alocal scale. The actual mechanism for the nucleation ofthe highly localized major shear bands at very early stageof deformation and the reason for the subsequent localiza-tion of large plastic strain in these bands are notclearly understood. This is particularly intriguing, as well-distributed multiple shear bands can be observed in otherequivalent planes with respect to the stress axis as evi-denced in plane ‘B’ in Fig. 2 for Ti-rich glass.

The initial nucleation of shear bands must be related toplastic instabilities in some microscopic regions. Althoughour understanding is incomplete, such regions can originateowing to the presence of residual stresses or the presence ofheterogeneities in the glass samples. Under compressiveloading, there are four equivalent shear planes along whichthese instabilities can grow to form the shear band. Theselection of a particular set of planes for the formation ofthe primary shear band must be probabilistic in nature.However, once the first band has formed, the results sug-gest that other instabilities, at least in the initial stages,are biased to grow on parallel planes, probably due tothe geometry of the stress field after the stress was releasedby the propagation of the first shear band. The experimentscannot resolve whether all the initial primary shear bandsin plane ‘A’ (see Fig. 2) formed simultaneously or sequen-tially. The roughly uniform spacing between these bandssuggests a possibility of sequential formation of thesebands similar to the sympathetic nucleation observed in

Fig. 5. (a) Optical micrograph (inset) showing an enlarged view of thearea marked in Fig. 2d (surface B) and SEM micrograph showing cavitiesat the shear band at the surface of Ni59Zr16Ti13Si3Sn2Nb7 glass. (b) SEMmicrographs observed from the fracture surface of Ni59Zr16Ti13Si3Sn2Nb7

glass after compression test, showing typical radiating vein patternsuggestive of operation of a local tensile component.

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the precipitation process in solid state. It is well recognizedthat the excess free volume associated with these bands willlead to a local dilatation of the shear bands [3,25]. Sincerest of the glass does not undergo plastic deformation, itconstrains the shear band. Thus, the dilatation results ina compressive stress, which acts normal to the shear plane.It is proposed that this stress is responsible for a flowbehaviour consistent with the Mohr Coulomb criterionand the observed deviation from the Von Mises criterion[22]. This also rationalizes why the external hydrostaticpressure does not affect the flow behaviour of the metallicglass [22].

It is noted that the experimental observations on mono-lithic glasses and the discussion above are based on the factthat offset of primary shear bands is a major contributor toplasticity. This is contrary to the results of the bendingexperiments where increased plasticity in thinner sampleswas correlated with increase in density of the secondaryshear bands [7,24]. Recently, Schroers and Johnson [10]reported large plasticity in Pd-based glasses and arguedthat a low G/B ratio, where G is the shear modulus andB is the bulk modulus, favours branching of the shearbands and therefore yields high plasticity. The glasses stud-ied in the present investigation have a relatively higher G/Bratio (>0.25), and thus such a mechanism may not be avail-able. Nevertheless, the presence of Ta particles in the com-posites which aid branching of the secondary shear bandsleads to enhanced ductility in much the same way as inlow G/B glasses.

Additional features associated with the shear bands canbe revealed by careful observation. With the increase inplastic strain, voids and microcrack appear in the shearbands. This can be seen in both Ti-rich and Ni-rich glasses.Some of the voids observed in Ti-rich glass at a strain of�4.2% after second interruption are highlighted inFig. 2d by arrows. One also observes a tendency for theformation of cavity or microcrack at the intersection ofthe shear bands, as marked by the box in the same figure.The enlargement of this region is shown in the inset inFig. 5a. However, such features are not confined only tointersecting slip bands. A SEM micrograph of slip bandsobserved in the surface of Ni glass strained to �3.7% afterthe second interruption is shown in Fig. 5a. The shear bandhas a zigzagged contour with voids and a microcrack dec-orating the band, the latter most likely formed by the join-ing of the voids. The emergence of voids at later stagesunder compressive loading needs rationalization. It isnow well established that shear localization and multiplepropagation in the same band occur because of the flowsoftening of the glass in the region of the band due toexcess free volume [26]. It is suggested that these free vol-umes spontaneously coalesce into nanovoids [27]. It isunclear whether these nanovoids can coalesce to formmicrovoids at large plastic strains. In an alternative sce-nario, materials flow in each shear band under the influenceof shear stress. At the convex region of the junctionbetween two shear bands, the materials will flow in both

the bands, leading to depletion at the corner. The situationis equivalent to the development of a tensile component atthe junction corner, which will aid the formation of cavitiesat these corners. Further, in normal compressive geometrythe plastic deformation along the major shear band canlead to a frictional force along the push rod–material inter-face [15]. This can lead to a deviation from pure normalloading and the emergence of a tensile component in theshear band. Recently, Zhang et al. [14] showed that radiat-ing vein patterns in the fracture surface is a signature of theoperation of a tensile component at a local level. Occa-sional observation of such a pattern in the fracture surface(Fig. 5b) further supports the above scenario. This is con-sistent with the conclusion reached recently on the fracturetoughness of metallic glass [28]. Unlike in the case of tensileloading, the cavities cannot grow and coalesce to form acrack. However, there is a possibility of stored elasticenergy due to compression getting released near the void,

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which can lead to the generation of microcracks from thesevoids. Failure can occur by bridging of these microcracks.

Introduction of ductile phases such as Ta in metallicglass composite alters the shear bands considerably. It isproposed that a plastic strain mismatch at the particle glassinterface is responsible for the generation of a large numberof local shear bands in these materials under compressiveloading [20]. Thus, the materials deform more homoge-neously. However, the particle will also strain harden veryrapidly and, in spite of the constraint of surrounding glassymatrix, will fracture. The incoherent interface between theglass and the particle is the most likely place for the initia-tion of the crack, and this will propagate along the bound-ary, resulting in a debonding of the interface. The resultsclearly support such a scenario, and the evidence of thepresence of microcrack at the interface between the particleand the glass can be clearly seen (Fig. 5). These regions willarrest the propagation of the existing shear bands, resultingin the formation of additional shear bands to sustain thedeformation process.

5. Conclusions

Although the three monolithic glasses (Zr46.75Ti8.25-Cu7.5Ni10Be27.5, Ti55Zr10Cu9Ni8Be18 and Ni59Zr16Ti13-Si3Sn2Nb7) exhibit different levels of ductility, themorphology and arrangement of the shear bands arealmost the same in the three glasses. The major shear bandsapproximately parallel to the ultimate fracture planeappear rapidly after a small amount of deformation(<2% strain), and their numbers remain more or less samein the later stage of deformation. Therefore, the larger plas-tic strain in glasses exhibiting higher ductility is to a largeextent accommodated in the primary shear band by the for-mation of larger shear offset prior to failure. For Ti55Zr10-Cu9Ni8Be18 glass, this value is as high as �36 lm.

From observation of the specimen surface during com-pression, the failure mechanism of the metallic glass is pro-posed as follows: (1) the tensile component developed atthe junction of two shear bands leads to the formation ofmicrovoids; (2) the stored elastic energy in the glass matrixis released by the formation of microcracks from microv-oids; and (3) bridging of the microcracks existing at theshear bands leads to the final fracture. Observation of thefracture surface also supports that the failure mechanismis not pure shear but a mixed mode.

In the case of glass composite containing particles((Zr70Cu20Ni10)82Ta8Al10), the shear band formation andfailure mechanism are totally different from those of the

monolithic glass. A very large number of shear bands arewell distributed across the specimen surface. The micro-crack initiates at the incoherent interface between the glassand the particle, and propagates, resulting in debonding ofthe interface. The failure of the glass composite occurs afterbuckling of the sample.

Acknowledgements

The authors are grateful for the financial support fromthe Creative Research initiatives of the Korean Ministryof Science and Technology. One of the author (K.C.) thankDRDO, Government of India, for support.

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