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International Journal of Impact Engineering 60 (2013) 37e43

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International Journal of Impact Engineering

journal homepage: www.elsevier .com/locate/ i j impeng

La-based bulk metallic glass failure analysis under static and dynamicloading

Jun Liu*, V.P.W. ShimImpact Mechanics Laboratory, Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260,Singapore

a r t i c l e i n f o

Article history:Received 9 January 2013Received in revised form8 April 2013Accepted 13 April 2013Available online 23 April 2013

Keywords:Bulk metallic glassShear bandSplit-Hopkinson Pressure Bar (SHPB)Modelling of temperature evolutionStrain rate effects

* Corresponding author. Tel.: þ65 92268572.E-mail addresses: liujun@nus.edu.sg, nickliujun@g

0734-743X/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.ijimpeng.2013.04.004

a b s t r a c t

Samples of La-based bulk metallic glass were tested under both static and dynamic compression, andtheir failure analysed. The strain rates imposed ranged from 10�4/s to 103/s. Quasi-static compressionwas performed using an Instron universal testing machine and dynamic compression was applied bymeans of a Split-Hopkinson Pressure Bar (SHPB). This study focuses on: (1) Shear band characteristicsunder static and dynamic compression. A high-speed optical camera was used to capture visual images ofshear band initiation; fracture surfaces were also examined by SEM; (2) Modelling of shear band tem-perature evolution within the specimen, with the aid of high-speed infrared camera images, to capturethe temperature profile of the shear bands; (3) Effect of strain rate on response of La-based BMG. It ispostulated that the negative strain rate dependence observed arises from the non-uniform direction ofstress within the material, and stress concentration inside specimens.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Bulk metallic glasses (BMGs) have attracted increasing attentionin recent years because of their high strengths and hardness.However, because of the lack of post-yield hardening, plasticdeformation in BMG generally concentrates within an extremelythin shear band (w20 nm) [1], which leads to rapid catastrophicfailure, limiting the application of BMG in actual structures. Thischaracteristic has motivated extensive study into the nature of suchshear bands and the failure mechanisms of BMG. However, becauseof limitations in experimental techniques, the precise nature ofBMG failure remains unclear. Furthermore, recent experimentalresults [2e14] indicate that different classes of BMGs possessdifferent failure mechanisms and fracture behaviour. This moti-vates further experimentation to obtain a better understanding ofthe deformation mechanisms in BMG material.

In this study, various experimental techniques are combined,and hierarchical multi-scale modelling of heat conduction is un-dertaken to examine the failure of La-based amorphous alloys. Thisincludes the effect of strain rate, temperature distribution profileand shear band characteristics. To date, there appears to be nopublished information on shear band temperature characterisation

mail.com (J. Liu).

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and dynamic constitutive behaviour of this class of BMGs. Thepresent investigation contributes to a better understanding ofdeformation in this type of material, and could serve as a guide forfuture development of La-based BMG composites.

2. Material fabrication and testing

Monolithic La62Al14Cu12Ni12 amorphous alloy was prepared byarc-melting a mixture of La (99.9%), Al (99.9%), Ni (99.98%) and Cu(99.9999%) in an argon atmosphere. The molten alloy was theninjected into a copper mould to produce ingots. The as-cast ingotswere machined into small cylindrical specimens of 4 mm diameter.Samples with two aspect ratios were fabricated, 1:1 and 2:1, forboth static and dynamic compression tests, to ascertain whetherthere is a size effect. The amorphous nature of the microstructurewas examined by X-ray Diffraction (XRD).

Compression tests at quasi-static strain rates were performedusing an Instron 8874 universal testing machine. The specimencontact surfaces were lubricated using molybdenum disulphide(MoS2) to reduce friction, and the strain rates ranged from 5�10�4/s to 5 � 10�2/s, which were obtained from strain gauges mountedon the specimens. Dynamic compression tests were conductedusing a Split-Hopkinson Pressure Bar (SHPB) device. Since thematerial is brittle and fails at small strains, pulse shaping was usedto enhance the reliability of results. Annealed copper disks wereemployed as pulse shapers, and inserted between the striker and

(a) (b)

(c) (d)

0 7t t s

0 14t t s 0 21t t s

0t t

Fig. 2. Optical images of shear band evolution for static compression.

J. Liu, V.P.W. Shim / International Journal of Impact Engineering 60 (2013) 37e4338

the input bar to promote stress equilibrium and a constant strainrate before fracture occurs. The brittle nature of the material resultsin early catastrophic failure (around 15 ms w 25 ms after loading),which limits the strain rate that can be imposed. In the tests, thestrain rates ranged from 600/s to 1500/s. High-speed optical andinfrared (IR) cameras were used to capture features of the shearbands at fracture. The fracture surfaces were observed using fieldemission scanning electron microscopy (FE-SEM).

3. Analysis of results

3.1. Shear band characteristics

Fig. 1 shows a typical quasi-static compressive stressestraincurve for La62Al14Cu12Ni12 BMG alloy. It indicates that there isessentially no plastic response, and the sample fails by catastrophicfracture. To investigate the failure process in more detail, an opticalhigh-speed camera was used to capture images of the shear bandfor static and dynamic compression, as shown in Figs. 2 and 3 (thetime intervals between the images are approximately 7 ms and 4 ms,respectively). The instants the images correspond to are indicated,and t0 is a reference time. These show clearly how the shear bandsinitiate and propagate to the point of fracture; the process isaccompanied by the emission of sparks, indicating a large tem-perature increase within the shear band, and the entire durationspans just tens of microseconds. It is noted that the fracture pat-terns for static and dynamic loading differ. Under quasi-staticloading, only one major shear band is evident. However, for dy-namic loading, catastrophic failure occurs by fracture of the sampleinto several fragments. Fig. 4 illustrates the fracture of differentsamples under dynamic compression, and shows that this frag-mentation response is consistent e i.e. multiple shear bands aregenerated instead of only one in static loading.

Fig. 5 shows SEM images of different regions on a fracturesurface of a sample after static compression. The vein patternmorphologies indicate micro-plasticity at fracture, while the U-shaped dimples (indicated by the white arrows) reveal the direc-tion of plastic flow, which corresponds to the black arrows in thefigure. How the shear band propagates and how the heat gener-ated influences plastic flow can be clearly seen. The total fracturesurface can be divided into three regions, and the location of theseareas on the fracture surface, as well as the flow direction, areshown in Fig. 5(a). Fig. 5(b) displays a regular strip-like veinpattern, which defines the commencement of shear band initia-tion, when heating at this location is not obvious. Fig. 5(c) corre-sponds to an area where the heat generated by plastic deformationhas accumulated within the shear band and become significant;there is a clear transition from a regular strip-pattern to largeirregular dimples. In Fig. 5(d), heating within the shear band is

Fig. 1. The true stressestrain curve for static compression.

significant and affects the deformation; hence, the plastic flow isquite different from that in region (b). The large dimples andmolten droplets indicate that heating in this region is substantialand has altered the material behaviour during shear band propa-gation. However, although the dimple pattern is irregular, thedimple direction is still consistent, and the flow direction can beidentified via the U-shaped profiles.

Fig. 6 shows SEM images of a fracture surface after dynamiccompression. Although it also has a dimple-like morphology likethe fracture surface for static compression, the details are quitedifferent. Fig. 6(a) shows a localised area of the fracture surface, andthe arrows identity the strip pattern directions. Fig. 6(b) is amagnification of area (b) in Fig. 6(a); the arrows indicate the di-rection of the U-shape dimples. They shows that these U-shapedimples no longer align with the direction of the strip pattern.Furthermore, Fig. 6(c) and the magnification of area (d) in Fig. 6(d)show that it is almost impossible to identify the flow directionthrough the dimple structure. From Figs. 5 and 6, it can be seen thatthe vein-pattern for a statically-compressed sample has a moreuniform direction compared with the dynamically-compressedsample, which indicates that the stress distribution inside thedynamically-loaded sample is more complex and heterogeneous.

3.2. Heat evolution in shear band

Earlier researchers assumed that the highly localised cata-strophic fracture in BMG comes from local adiabatic heating [15],similar to what happens in crystalline materials [16]. However,with the development of BMG micro-mechanism deformationtheory, there is a growing conclusion that nano-level structuralinstability, caused by the initiation of free volume [17] and

(a) (b)

(c) (d)

0 4t t m0t t

0 8t t m 0 12t t m

Fig. 3. Optical images of shear band evolution for dynamic compression.

(a) (b)

(c) (d)

(b)

(d)

Fig. 6. Fracture surface after dynamic compression.

(a) (b)

(c) (d)

Fig. 4. Multiple fragmentation in different samples subjected to dynamic compression.

J. Liu, V.P.W. Shim / International Journal of Impact Engineering 60 (2013) 37e43 39

activation of a shear transformation zone (STZ) [18], is the domi-nant mechanism for the creation of shear bands inside BMG.Recently, Dai and Bai developed a coupled free volume-temperature instability analysis [19] for BMG alloy. Their theoryhighlighted that the formation and propagation of shear bands inBMG are not determined solely by temperature or internal struc-ture, but actually a combination of thermal softening and freevolume creation. In order to examine this proposition in moredetail, detecting the temperature rise within a shear band andexamining the role of thermal conduction are important for un-derstanding the mechanisms behind shear band behaviour.

Some work on evaluation of the maximum temperature in ashear band, using experimental data and constitutive modellinghas been done [20,21], and it is believed that the temperature willexceed the melting point, which is around 900 �C, since largemolten droplets have been observed on fracture surfaces. With thedevelopment of high-speed infrared (IR) photography techniques,people have done considerable work to study adiabatic shear bandbehaviour through experiments. Guduru et al. [22e24] investigateddynamic shear banding in metallic materials using an IR camera,and demonstrated the evolution of the temperature field at a cracktip and the development of a plastic zone. Researchers at the Uni-versity of Tennessee have undertaken experiments to study tem-perature evolution during the initiation and propagation of shearbands in BMG, including direct measurement of temperature fordynamic shear bands [25e27], and the evaluation of temperatureduring fatigue damage [28,29]. A review of these efforts can befound in Ref. [30].

(b)

(c) (d)

(a)

(d)

(c)

(b)

U-shape dimples

U-shape dimples

U-shape dimples

Fig. 5. Regions in fracture surface after static compression.

However, since the dimensions (w20 nm) and time scale(w1 ms) of a shear band and its formation are small compared withthe framing speed of IR cameras, direct measurement of the tem-perature of a shear band is not totally reliable. Consequently someheat evolution models have been proposed to complement exper-imental results. Hufnagel et al. [7] proposed a theory involvingshear band thickness, whereby the temperature rise in a BMG shearband can be derived, and concluded that adiabatic processes areunlikely in this type of material. Lewandowski and Greer [31]developed a novel method to improve the spatial and temporalresolution of temperature measurement by coating Vitreloy 1 witha thin layer of tin and analysing it after fracture; they found that thetemperature increase in a shear band could be in terms of thou-sands of degrees centigrade. Miracle et al. [32] established aframework to evaluate the size effect on the thermal profiles of avariety of BMGs, and also estimated the temperature rise within ashear band to be possibly around 2000 �C. These results point to avery significant temperature increase in shear bands at fracture.However, most of these studies focused on Zr-based BMG, andthere is little information on La-based amorphous alloys. Therefore,the present investigation seeks to provide more details by esti-mating the temperature profile in a shear bandwith the aid of high-speed IR thermography. It is generally accepted that a shear bandcan be considered a planar heat source [31]; a simple conclusion isthat the temperature gradient in a small region near the shear bandis normal to it e i.e. the x direction shown in Fig. 7(a). This enablessimplification of the heat conduction in a 3D sample to 1D analysis.Furthermore, symmetry of the shear band reduces the 1D model tohalf the geometry, starting from the mid-plane of the shear band,which has the highest temperature during evolution.

Hence, a two-stage 1D hierarchical multi-scale model of heatevolution is established, as shown in Fig. 7(b), in which ts1 and ts2are the time durations of Stages 1 and 2 respectively. lsb is the half-width of the shear band, lmeso is the meso scale length of this modeland l is the length of the whole sample. The governing heat con-duction equation for this analysis assumes the well-known form of:

rc _T ¼ kv2Tvx2

þ _r (1)

in the region x˛[0,L], where L is the length of the region. T repre-sents the temperature field and r,c and k are the material density,

Fig. 7. 1D hierarchical multi-scale model.

J. Liu, V.P.W. Shim / International Journal of Impact Engineering 60 (2013) 37e4340

specific heat capacity and thermal conductivity, respectively; _r isthe heat generation power of the system.

Stage 1 commences at the beginning of shear band initiation(t ¼ 0). During shear band evolution (t˛(0,tc), where tc is theshear band evolution time), the heat generation power term isdefined by _r ¼ bs _g, where s is the critical shear stress and _g theplastic shear strain rate. b is the TayloreQuinney coefficientrepresenting the ratio of mechanical work converted to heat,which is taken to be 1 for simplicity [33]. When catastrophicfracture occurs at t ¼ tc, further plastic dissipation ceases,resulting in _r ¼ 0 thereafter. A short settling time is then incor-porated for heat conduction to take place before proceeding tothe next stage. A settling time of tr ¼ 2 ms is prescribed, as this isof the same order as the shear band evolution time. Hence, thetotal time for Stage 1 is ts1 ¼ tc þ tr. The initial condition for thisstage is:

T jðx;t¼0Þ ¼ Te

where Te represents the room temperature, and the boundaryconditions are:

vTvx

����ðx¼0;tÞ

¼ 0

vTvx

����ðx¼ L;tÞ

¼ 0

In Stage 2, the initial sample temperature profile at t¼ 0 is takenas the sample temperature profile at the end of Stage 1 at the samematerial point. The natural boundary condition at the fracturesurface is

�kvTvx

����ðx¼0;tÞ

¼ h�T jðx¼0;tÞ � Te

�

This means that the fracture surface is exposed to the air, whereh is the heat transfer coefficient between the fracture surface andair, and

vTvx

����ðx¼ L;tÞ

¼ 0

Stage 2 has a much larger length and time scale, which allow theresults to be compared with experimental data. As a result, the totaltime for Stage 2 is taken to be ts2 ¼ 6 ms, which is long enough forthe high-speed IR camera to capture sufficient data, yet shortenough to be simulated with the assumption that heat loss to theenvironment is negligible. In some experiments, the fracturedportion rotated sufficiently to face the IR camera; this enabled thefracture surface temperature to be recorded. The temperatureprofile on the fracture surface was captured for the time period upto about 6 ms after fracture, at time intervals between images ofabout 0.3 ms. The maximum temperature values in these IR imagesare taken as representative of the fracture surface temperature,since they are least influenced by the external environment.

The material parameters are determined as follows: the densityr¼ 6000 kg/m3 is obtained directly frommeasurement of the massand volume of samples; the specific heat capacity c ¼ 424 J/(kg K)and thermal conductivity k ¼ 5.6 W/(K m) correspond to La-basedBMG in Ref. [34], while the failure shear stress is taken as half theaxial failure stress for static compression, which leads tos ¼ 300 MPa. The duration of the shear band formation and evo-lution is assumed to be 2 ms as a first-approximation; this is dis-cussed later. The shear band width is taken to have a nominal valueof 20 nm [1,35]; i.e. the half-width of the shear band in the model islsb ¼ 10 nm. The characteristic length in a heat conduction problemcan be evaluated by 2

ffiffiffiffiffiat

p, where a¼ k/rcp is the thermal diffusivity.

Hence, a meso length scale of lmeso ¼ 20 mm is adopted, which isseveral times the characteristic length. Applying the sameapproach, the total length of the shear band model is taken to bel¼ 1mm, which is sufficiently long tominimise the influence of thefar-end boundary, yet short enough to limit computational time. Afinite difference method with a FTCS (Forward-Time-Central-Space) scheme is used to discretise and solve the parabolic partialdifference equation (PDE). The only unknown parameter is theshear strain rate, which is difficult to measure directly. A value of_g ¼ 2:8� 109=s is selected to obtain a good fit with experimentaldata. The temperature evolution of the fracture surface is plotted inFig. 8(a) and (b) for Stage 1 and 2, respectively. They show that thehighest temperature within the shear band is roughly 5300 K whenfracture occurs at t ¼ 2 ms; this is a very high temperature.

The first stage encompasses the entire shear band evolutionprocess. Fig. 9 shows the temperature profile within the model as afunction of time. It indicates that that before fracture (t � 2 ms), thehighest temperature within the shear band increases rapidlybecause of plastic dissipation, and the peak value is around 5300 Kat fracture (t ¼ 2 ms). Thereafter, there is no heat source, so thesystem can be deemed to be a pure heat conduction problem. Fig. 9illustrates that the diffusion range is much larger than the shearband thickness. This is different from traditional adiabatic shearband theory for crystalline materials, which assumes that materialsoftening comes from thermal softening, since there is insufficienttime for heat to conduct away; hence, this thermal effect is themain reason for the strain softening [16]. In contrast, the presentresults support the occurrence of abrupt fracture that arises fromstructural instability generated by initiation of free volume andactivation of STZ caused by rearrangement of atoms. This leads tothe conclusion that shear banding in BMG cannot simply beconsidered as ‘adiabatic’, since heat conduction plays a significantrole during shear band evolution. Heat generation is the result ofrapid shear band propagation within a small region (which alsocontributes to local softening).

The heat source _r and shear band evolution duration are the keyparameters in the proposed model, and govern the final tempera-ture. As a result, the shear band evolution duration will determinethe maximum temperature reached. The optical images in Figs. 2and 3 indicate that the shear band evolution duration for

(a) (b)

Fig. 8. Temperature evolution on the fracture surface.

J. Liu, V.P.W. Shim / International Journal of Impact Engineering 60 (2013) 37e43 41

La62Al14Cu12Ni12 cannot exceed 7 ms. Hence, various shear bandevolution times smaller than this limit are examined to calculatethe corresponding maximum temperature rise. The results can befitted by the expression T¼ 11.936� t�0.465; this power law yields alinear relationship in logarithmic coordinate axes, and is plotted inFig.10. The figure shows that the relationship between temperaturedistribution and shear band duration, as well as the correspondingmaximum temperatures attained (2000 K w 8000 K). These esti-mated values are of the same order as those reported by Lew-andowski and Greer [31].

3.3. Effect of strain rate on BMG

It is generally recognised that strain rate affects the response ofcrystalline materials, and is possibly associated with dislocationmovement, twinning and adiabatic shear banding [36,37]. How-ever, because of the amorphous nature of BMG, there is yet noaccepted description of the mechanism for strain rate sensitivity onit mechanical response. There is discussion on strain rate effects atroom temperature, and it is accepted that this rate sensitivity varieswith chemical composition and microstructure. Therefore, experi-ments involving strain rate as a parameter is instructive inobtaining a better understanding of rate effects for different BMGalloys.

Fig. 11 summarises the static and dynamic compressive yieldstress for La62Al14Cu12Ni12 BMG alloy samples of 4 mm and 8 mmlength at different strain rates. For static loading, the yield stress is

Fig. 9. Temperature profile along the model at different time instant.

approximately constant, with only a small variation around650 MPa. The behaviour of the 4 mm samples is similar to that ofthe 8 mm ones, which indicates that no extrinsic size effect isevident. However, a detailed analysis shows that the yield stress of8 mm samples seems somewhat more consistent than that of the4 mm samples. This is because the 8 mm samples are less affectedby interfacial friction at their ends, whereas 4 mm samples, with anaspect ratio of 1:1, could possibly tend more to plane strain con-dition. For dynamic compression, the yield stress displays anobvious decrease with strain rate, which indicates that La62Al14-Cu12Ni12 BMG alloy has negative rate sensitivity. The mechanismfor this is now discussed.

4. Rate sensitivity characteristics

Some researchers have studied strain rate effects on BMGs ofdifferent compositions at room temperature [2e14]. The influencevaries for different BMG alloys, and the rate sensitivity could bepositive, negative, or neutral; details are listed in Table 1. Due to thelack of a crystalline structure in BMGs, common theories for ratesensitivity in crystalline materials cannot be applied to amorphousalloys, and several possible reasons to account for the influence ofstrain rate on the yield stress have been proposed.

Initially, it was found that Zr41.2Ti13.8Cu12.5Ni10Be22.5 BMG(Vitreloy 1) is rate insensitive at room temperature for a wide rangeof strain rates [2e4]. This conclusion was well accepted, since nomechanism that influences the yield strength of amorphous

Fig. 10. Maximum temperature within shear band for different evolution time.

10−4

10−3

10−2

10−1

100

0

100

200

300

400

500

600

700

800

Strain rate(s−1)

Yie

ld s

tres

s(M

Pa)

Static 4mmStatic 8mm

102

103

104

0

100

200

300

400

500

600

700

800

Strain rate(s−1)

Yie

ld s

tres

s(M

Pa)

Dynamic 4mmDynamic 8mm

Fig. 11. Yield stress at different strain rate.

J. Liu, V.P.W. Shim / International Journal of Impact Engineering 60 (2013) 37e4342

materials has been identified. This was the case until more BMGalloys were developed. Thereafter, BMG materials with differentcompositions have been tested and negative strain rate effectsobserved for most of the alloys [5e11]. However, details of thefailure mechanisms involved are different for these materials, eventhough they exhibit the same rate effect. For Zr-based materials, asin [7,8], serrated flow is found to be suppressed at high strain rates;this promotes the creation of a single shear band. Theories showthat catastrophic fracture happens when the critical plastic shearstrain exceeds a certain value. The creation of multiple shear bandscan accommodate the critical strain and delay the occurrence ofcatastrophic fracture. When the generation of multiple micro shearbands is reduced at high strain rates, major shear bands predomi-nate and rapidly reach the critical strain value, causingmuch earlierfailure; this results in a decrease in the yield stress from a macro-scopic perspective. For BMG materials other than Zr-based onesthat shows a negative rate effect [5,6,9e11], high strain rates pro-mote the creation of multiple shear bands. Micro shear bands havebeen found to initiate well below the static yield stress. These mi-nor shear bands do not propagate at low stress levels. However,under dynamic loading, the rapid creation of heat within shearbands becomes significant in shear band evolution, and a samplewill fail very soon after the initiation of minor shear bands; thisdecreases the yield stress at high strain rates and accounts for thenegative strain rate sensitivity.

With the development of BMG alloys, two types of Ti-basedBMG have been found to possess positive rate sensitivity [12,13].The researchers attributed this to the different cluster structure ofTi-based amorphous alloys. Locally ordered icosahedral nuclei havebeen found to be embedded in the amorphous matrix [38]; thisprovides a mechanism to improve the strength and ductility of Ti-based amorphous alloys significantly. The existence of a micro-crystalline structure is also a reason for the positive strain rate ef-fect of Ti-based BMG alloys. Another material that has been foundto have positive rate sensitivity is Nd60Fe20Co10Al10; this behaviouris also attributed to the cluster structure of this BMG alloy [14].

Table 1Published strain rate effect studies of BMG.

Negative rate effect Positive rate effect No effect

Pd40Ni40P20 [5,6] Ti45Zr16Ni9Cu10Be20 [12] Vitreloy 1 [2e4]Zr57Ti5Cu20Ni8Al10 [7] Ti40Zr25Ni8Cu9Be18 [13]Zr38Ti17Cu10.5Co12Be22.5 [8] Nd60Fe20Co10Al10 [14]Zr/Hf [9,10]Dy3Al2 [11]

In the present study, no micro shear band initiation before yieldis evident. The creation of several fragments at fracture indicatesthat multiple shear bands were generated within the sample atdynamic strain rates. At low strain rates, a single shear band canquickly accommodate the applied strain, which leads to the samplefracturing via only one major shear band. When the strain rate issufficiently high and exceeds a critical value, a single shear banddoes not have enough time to propagate and the strain energy alsodoes not have adequate time to dissipate. As a result, the samplewill deform continuously and a second or third shear band willinitiate, as shown in Figs. 3 and 4. Furthermore, inhomogeneousstress distribution inside the sample, associated with stress con-centration, contributes to the negative rate sensitivity. Under quasi-static compression, uniform axial stress is applied and the spec-imen is in equilibrium at all times, so the stress distribution isessentially homogeneous. As a result, the fracture surface in Fig. 5shows a uniform flow pattern. Under dynamic loading, the stresswithin a specimen may not be uniform, especially for brittle ma-terials which fail early. This non-equilibrium influences the stressdistribution, and generates stress concentration within the sample.The resulting heterogeneous stress distribution may be the reasonfor the arbitrary flow direction patterns on the fracture surfaceshown in Fig. 6. Moreover, impurities or defects inside a samplewillpromote stress non-uniformity, and thus result in early materialfailure compared to static loading. Differences in the fracture sur-face for quasi-static and dynamic loading, shown in Figs. 5 and 6,support this assertion. The randomly distributed vein pattern di-rections for dynamic loading indicates a non-uniform stress dis-tribution compared to static loading.

5. Conclusion

In this study, quasi-static and dynamic compression tests onamorphous alloy La62Al14Cu12Ni12 were undertaken to examine thefailure mechanism for this type of BMG. The material shows no ratesensitivity under quasi-static loading, and negative rate effects fordynamic compression. This negative rate sensitivity is attributed tothe occurrence of non-uniformity of stress, as well as stress con-centrations induced at high strain rates; these are aggravated byimpurities and defects within the amorphous material. Stressconcentrations reduce the macroscopic yield strength significantly,and generate heterogeneous stress distributions inside the mate-rial. For dynamic compression, the strain energy stored in thesample has no time to relax at fracture, and continued deformationafter initiation of fracture leads to multiple shear band formation.The temperatures within a shear band have also been estimated by

J. Liu, V.P.W. Shim / International Journal of Impact Engineering 60 (2013) 37e43 43

hierarchical multi-scale modelling, and the results indicate a rise tothe order of 103 K at fracture. The experimental and simulationresults also show that adiabatic shear banding is not the mainreason for the softening behaviour observed and failure.

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