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Acta Materialia 115 (2016) 468e474

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Acta Materialia

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Time-resolved measurement of shear-band temperature duringserrated flow in a Zr-based metallic glass

P. Thurnheer, F. Haag, J.F. L€offler*

Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland

a r t i c l e i n f o

Article history:Received 20 October 2015Received in revised form1 May 2016Accepted 4 May 2016Available online 7 June 2016

Keywords:Metallic glassesIR thermographySerrated flowShear bandsMechanical properties

* Corresponding author.E-mail address: joerg.loeffler@mat.ethz.ch (J.F. L€of

http://dx.doi.org/10.1016/j.actamat.2016.05.0081359-6454/© 2016 Acta Materialia Inc. Published by

a b s t r a c t

Severe localization of plastic flow into shear bands is typically accompanied by local heating. In metallicglasses, the small lateral extension of shear bands, the short duration of their intermittent plastic slips,and the unpredictable position of their initiation make in-situ investigations of local changes in tem-perature during shear banding difficult. An alternative is to estimate shear-band temperature usingcalculations for a given assumed deformation model, which generates predictions of temperaturechanges from 5 �C to more than 1000 �C. In this study we review four models of plastic slip accumulationand present first results on temporally resolved shear-band heating in metallic glasses via infraredthermography. We find that the heat evolution in a shear band during plastic slip is best modelled byshear that occurs simultaneously within serration time scales. This illustrates clearly that temperaturechanges within shear bands are less than 6 �C during stable plastic flow.

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1. Introduction

At temperatures well below their glass transition, the plasticdeformation of metallic glasses is manifested by shear steps on thesample surface. These steps are caused by plastic flow, which islocalized within narrow regions of weakened material called shearbands [1e6]. Because shear bands are as thin as 10 nm [7], initiateat locations which are difficult to predict, and operate intermit-tently for short durations only [8,9], in-situ investigation of theaccumulation of plastic strain in metallic glasses (MGs) is a chal-lenging task. It is thus not surprising that since the first reports onthe mechanical behaviour of MGs [10], different perceptions haveemerged regarding the exact mechanism by which shear steps aregenerated. This is not trivial, because the choice of a specific modelhas immediate consequences for the estimate of shear-bandproperties that are not directly measured experimentally, such asthe speed at which the shear step is generated (the shear-bandvelocity v), the shear-band viscosity h and the temperature riseduring shear-band operation DT. The latter parameter is of partic-ular interest, since a critical temperature jump is the core elementin at least two theoretical studies attempting to understand size-and compliance-induced MG embrittlement [11,12]. While both of

fler).

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these studies state that the degradation of mechanical properties iscaused by shear-band temperature exceeding a critical value, theydisagree on how a shear step is generated, and thus derive differenttemperatures within a shear band. Such unconformities are wide-spread in literature and indicate the necessity of the present work.

The aim of this work is twofold: (1) to give an overview of thedifferent perceptions regarding shear-step generation found inliterature, and (2) to test their agreement with new experimentalresults regarding time-resolved shear-band heating during inho-mogeneous MG flow. Both (1) and (2) will contribute to a detailedunderstanding of the shear-step generation mechanism indeforming MGs.

2. Models of shear-step generation during inhomogeneousplastic flow

Fig. 1a illustrates the four most important models of shear-stepgeneration. These models are labelled as (1) phonon-shear-frontpropagation, (2) serration-shear-front propagation, (3) serration-transient behaviour, and (4) serration-simultaneous shear.

A first means of distinguishing between these models is theirapproach to flow curves obtained by instrumented mechanicaltesting. In these curves, plastic flow is characterized by stick-slipdiscontinuities called serrations. A sequence of three serrations isschematically depicted in Fig. 1b, where each consists of a slowloading phase (stick, light grey) and a fast unloading phase (slip,

Fig. 1. a) Four scenarios of shear-step generation in MGs: (1) phonon-shear-frontpropagation, (2) serration-shear-front propagation, (3) serration-transient behaviour,and (4) serration-simultaneous shear. b) Schematic of the load- and displacement-signal of three serrations during MG plastic deformation. The serration parametersload drop DF, event duration Dt, and apparent displacement jump Du0 are indicated.Slow “stick” phases are shaded in light grey and fast “slip” phases in darker grey.

P. Thurnheer et al. / Acta Materialia 115 (2016) 468e474 469

darker grey). The slip phases appear simultaneously in the load anddisplacement signal, and are characterized by the size of the loaddrop DF, the apparent displacement jump Du0, and the serrationduration Dt. For better illustration, these serration parameters aretaken as positive quantities. While models (2)e(4) assume that theserration parameters correctly reflect the increment size of theshear step and the duration over which it is established, thephonon-shear-front propagation model (1) does not take suchserrations into account.

2.1. Phonon-shear-front propagation model

Georgarakis et al. [13] followed the approach that if the shear-step increment was calculated from each serration, then the sumof all these increments should add up to the total plastic strain.Finding that the sum of apparent displacement jumps Du0 stronglyunderestimates the true total size of the shear steps, the authorsinferred that the time scales must also be compromised, andconcluded that the stress serrations measured by instrumentedmechanical testing are measurement artefacts rather than a directprobe of shear-step size and shear-band dynamics. Acknowledgingthat a shear band cannot be formed instantaneously, they attrib-uted both the generation of the shear band and the formation of theshear step to the propagation of a dilating shear wave that travelsthrough the sample at a fraction of the speed of sound.When takinginto account the presence of a stress-redistribution field around theshear front, the time for the generation of a shear step of 1 mm sizethen accounts to 10�8 s. This led the authors to predict temperature

rises of thousands of �C within the shear band [13]. Such highvalues would explain reports of the establishment of a micron-sized heat-affected zone around the shear band [14] and of shearbanding which causes the melting of fusible tin coatings on top ofan emerging shear step [15]. This scenario is an integral part of themodel of Miracle et al. regarding the size effect in MG ductility [12].However, a recent study [16] has revealed that melting of a tincoating is not universally observed inMG deformation, but is rathera function of alloy and stress state. This eliminates the conditionthat shear bands must “necessarily” be hot.

2.2. Models (2), (3) and (4), using serration time scales

In contrast to this phonon-based model, various studies report adirect correlation between shear steps and the features of serratedflow curves from instrumented mechanical testing [17,18] (Fig. 1a,(2)e(4)). These models assume that the time scale for a singleserration corresponds to the time scale of the coincident shear-stepformation, and that the shear step of a given amplitude Dupl can becalculated via [19]

Dupl ¼ffiffiffi2

pðDu0 þ DFCSÞ: (1)

According to Equation (1), the shear step consists of the apparentdisplacement jump Du0, measured via strain gauges, plus a termaccounting for the elastic recovery of the sample during theserration, where CS is the sample compliance. The factor

ffiffiffi2

pcon-

verts uniaxial displacement to displacement on the shear plane,which is oriented z45� to the load axis. It is noted that the secondterm in Equation (1) was neglected by Georgarakis et al. [13] andthat its omission may be the true cause of the above-mentionedmismatch between the sum of flow-curve strain increments andthe total shear-step sizes. The apparent displacement jump Du0 canfurther be related to the compliance of the testing setup CM viaDu0 ¼ DFCM, leading us to an alternative formulation of Eq. (1),which is Dupl ¼

ffiffiffi2

pDFðCM þ CSÞ [20].

Although models (2)e(4) agree on serration time scales, theydiffer in their understanding of howplastic strain is accumulated bya shear band. Model (2) assumes that the shear step forms via apropagating front [19]. In other words, the full shear step isestablished behind the shear front, while the material ahead of thefront remains undeformed. In this case, the shear-band velocity, i.e.the speed at which the shear step is generated, can be calculated asthe ratio of the fully established shear band across the sample ofdiameter d and the serration time Dt, i.e. v ¼

ffiffiffi2

pd=Dt. In contrast,

model (4) assumes that the shear step is established simulta-neously along the shear plane [21]. In that case, it is the shear steponly that is divided by the event duration in the calculation of theshear-band velocity, i.e., v ¼ Dupl/Dt, with Dupl given by Equation(1). These calculations provide shear-band velocities that aresmaller by a factor of 103 compared to those calculated frommodel(2) for a sample of a few millimetres in diameter. Note, however,that the velocities calculated frommodel (2) are still three orders ofmagnitude smaller than those obtained frommodel (1). With high-speed imaging methods, Song et al. [22] and Wright et al. [23]directly observed the scenario of model (4) down to time scalesof about 0.2 ms, i.e. a simultaneous deformation on the shear planewithin their temporal resolution. They also did not resolve anydelayed onset of shear banding on either side of the sample. Theperception of sub-resolution intermittency, a necessity for recon-ciling the above mentioned experimental finding with model (2),was also made unlikely by recent Acoustic Emission (AE) mea-surements [24], which revealed only one shear-band initiationsignal per serration. From that perspective, scenario (2) may be

Table 1Event duration t, shear-band velocity v, temperature jump DT, minimum viscosity h,and references for the four different models.

t (s) v (m/s) DT (K) h (Pa s) Refs.

Model 1 10�8 103 1000 10�2 [12,13]Model 2 10�3 1 90 10 [19]Model 3 10�3 10�3 3 104 [25]Model 4 10�3 10�3 3 104 [6,22]

h calculated using h ¼ syw/(2v) with sy z 2 GPa and w z 10 nm.

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discarded. Most recently, Joo et al. [25] carried out experimentsusing digital image correlation (DIC) on MGs under compression.The authors observed a transition from front-propagating behav-iour of the shear band in the early stage of deformation (associatedwith small strain increments only) to simultaneous shear in thesubsequent stage, during which the major part of the total shearstep was generated [25]. This is the scenario (3) presented in Fig. 1a.Similar results regarding a transition from a propagating to asimultaneous flow mode were obtained in a recent study by Quet al. [26]. These authors report on shear steps that form via apropagating flow mode in the early regime of “apparent strainhardening”, i.e. prior to reaching peak stress, and a transition tosimultaneous shearing once a major shear band has formed. In apurely strain-weakening material, such as a metallic glass, eventsprior to reaching peak stress cannot be system-spanning and mustthus be associated with local geometric constraints. From thatperspective, wemay deduce that scenario (4) is an idealized case ofscenario (3) and shows an almost perfect elastic-to-plastic transi-tion, devoid of geometrically-induced artefacts that would give riseto apparent front-propagating shear banding at pre-peak plasticstrains. Initial apparent propagation thus appears to be related tostress-inhomogeneities within the MG samples rather than to adeformation mechanism according to model (2) in Fig. 1a.

Despite the fact that shear steps can be derived from serrations,there remains the necessity of an elastic wave that travels at afraction of the speed of sound and effectively generates the shearband. According to current understanding there is no need for thetime scale associated with shear-band initiation to be identical tothat of shear-step generation. In fact, a two-stage mechanism hasbeen proposed, which consists of a fast, front-propagating, phonon-controlled initiation phase, generating only a small step but causingthe structural rejuvenation of the whole band (which was alsodescribed as a stress-induced glass transition [24,27]), followed bya slow, simultaneous shearing phase on the now weakened bandthat creates themajor part of the step (Fig. 2) [6,9]. The implicationsof the four different models for event duration t, temperature jumpDT, shear-band velocity v, and viscosity h are summarized in Table 1.

3. Shear-band temperature

After this review of shear-step generation models, we will nowdiscuss possible temperature changes within a shear band uponinhomogeneous deformation. A direct assessment of shear-bandtemperature has so far been impeded by the small size of theshear band and the short time scale of its operation, which both liesignificantly below the resolution limits of standard experimentssuch as IR thermography which are normally used to resolve issuesof local heating in materials science [28e30]. Preliminary IR studiesof MG deformation [31e33] focused on fatigue and tension, and

Fig. 2. Idealized shear-band dynamics. A shear band is initiated within microsecondsby a front-dilating shear wave (aec). In this stage, only minor amounts of plasticdeformation are accumulated. In the subsequent propagation phase (def), macroscopicplasticity is obtained within the shear band via simultaneous shear occurring withinmilliseconds.

reported temperature jumps of 3 �C within regions of shear-bandactivity. While this method enables measurement of the totalamount of released heat, the true shear-band temperature can onlybe reconstructed by calculations that are highly dependent on thechoice of the deformation model (Fig. 1a), as outlined above. Wanget al. [33], for example, assumed instantaneous heating, which ledthem to estimate a temperature rise within the shear band of about1200 �C.

In this study, we present the results of high-acquisition rate IRthermography on stable serrated flow in Zr57.1Co28.6Al14.3 MG. Withthis method we have been able to probe an experimental time scalewhich lies between the time scales postulated bymodels 1 (phonontime scale) and 4 (serration time scale). Such improved resolutionwas obtained firstly by using cutting-edge IR technology, and sec-ondly by choosing a ZreCoeAl alloy, which is expected to haveparticularly slow shear-band dynamics [34].

4. Experimental procedure

Zr57.1Co28.6Al14.3 metallic glass [35] was produced using anEdmund Bühler arc melter by alloying the high-purity startingmaterials within a 6N Ar atmosphere and subsequent suctioncasting to rods with a diameter of 2 mm. Coplanar samples with anaspect ratio of 2:1 were produced by grinding and polishing. Thesamples were equipped with a small notch by Electric DischargeMachining (EDM) [36] in order to initiate the shear band at a free,lateral surface rather than at the contact points of sample andcross-heads. By this means the probability that the shear band willbe geometrically arrested shortly after its initiation can be stronglyreduced. Compression tests at a rate of 10�3 s�1 were carried outusing a screw-driven Schenck mechanical testing machine. A 60 kNpiezo-cell from Kistler recorded the load signal at a rate of 20 kHz,and a strain gauge from Sandner was used to measure thedisplacement. The compression tests were monitored using a high-speed infrared camera (IRCAM Equus 81k SM) equipped with anInSb detector, which is sensitive to a wavelength interval from 2 to5 mm. A fixed frame size of 64 � 32 pixels was chosen because itallows a maximum framerate of 3750 frames per second (fps). Toensure precise temperature measurement, the specimens werecovered with a thin high-emissivity carbon coating. The tempera-ture measured by the camera was also calibrated using type Kthermocouples before testing. Synchronisation of load- and IRsignal was established by triggered data acquisition using a cus-tomised LabView routine.

5. Experimental results

Fig. 3 illustrates the localized heating and subsequent cooling ofa line-shaped region, extending from the notch at an angle ofz45�,that appeared in the IR thermographs during stable serrated flow.The frame number for each snapshot (framerate 2500 fps ¼ 0.4 msper frame) is indicated. An improvement of contrast was achievedby subtracting a background image, which was obtained by anaverage of the last ten images prior to the onset of heating. Two

Fig. 3. Localized heating during serrated flow. a) Instantaneous appearance of theshear band, and b) propagating heat front; f indicates the frame number, whereby 1frame is measured within 0.4 ms.

Fig. 4. Serrated flow curve and temperature of the apparent shear band as a functionof time. a) Throughout the experiment, each temperature jump corresponds to asingle serration. b) Close-up of an individual serration. In the stress signal, thedifferent stages (I) slow loading, (II) transition to unloading, (III) fast unloading, (IV)arrest and (V) reloading (¼I) are indicated. A significant temperature rise is onlyobserved in stage III.

P. Thurnheer et al. / Acta Materialia 115 (2016) 468e474 471

different sequences of events are observed in Fig. 3. For most of theserrations (approx. 70%, Fig. 3a), the line-shaped heat source ap-pears within a single frame (f¼ 1e2). Within the course of the nextmilliseconds, the band widens and the temperature in the centreincreases (f ¼ 3e10, heating rate 260 K/s). Thereafter, the temper-ature peaks (f ¼ 14, DTz 2 �C) and the apparent band starts to cooldown slowly, as heat is conducted away towards the anvils. Forother serrations (Fig. 3b), the line shape is established via anapparent propagating front over up to 4 subsequent frames(f ¼ 1e4). The temperature difference across the front amounts toabout 0.15 �C, and the heating rate on the established part of theapparent band is about 50 K/s. Once it reaches the other side of thesample, the temperature of the apparent band simultaneously in-creases further along the band (f¼ 5e10, heating rate 230 K/s), untilit reaches a peak temperature of DT z 2 �C (f ¼ 14) at a delay ofabout 10 frames (¼ 4 ms). Afterwards cooling occurs analogous tothe event shown in Fig. 3a. Almost all heat created by an event isconducted away prior to the onset of a subsequent event. In otherwords, the sample temperature prior to a subsequent heating eventis constant. The observed temperature rises involves some degreesCelsius, agreeing well with literature [33].

The sample-spanning line of pixels at which heating wasinitially observed is assumed to contain the major shear band. Byaveraging over these pixels, i.e. the apparent shear band, we canquantify the evolution of the apparent shear-band temperatureover time. Fig. 4a shows the temporally synchronized signals ofstress (black) and apparent shear-band temperature (magenta).The plot is divided into three parts. The first part shows that thefirst major temperature increase correlates with the first majorserration, i.e. with the reaching of peak stress. The few minorevents that can be identified before reaching peak stress areattributed to diffuse, non-system spanning events which, webelieve, are due to a slight inhomogeneity of the stress state. Apartfrom the temperature jumps DTjump, a temperature increase dur-ing the first serration events causes a background temperaturerise DTonset z 0.2 �C, which also remains at larger strains. Themiddle part of Fig. 4a demonstrates clearly that each serrationcoincides with one temperature jump. The third part finally gives

the remaining flow curve for the sake of completion. The tem-perature jumps are largest in the intermediate time regime, whichis equal to an intermediate strain regime of about 5e15% becauseof the constant strain rate.

Fig. 4b resolves the correlation of a single flow serration withthe apparent shear-band temperature during an “instantaneouslyappearing” event (Fig. 3a). Five stages can be distinguished duringthe course of a flow serration. Stage (I) represents the end of theelastic loading, i.e. the “stick” part of the serration cycle. In asecond stage, (II), stress starts to drop at a moderate rate withoutinducing a resolvable temperature increase (it is noted that theapparent heat front appearing in the other type of serrations(Fig. 3b) occurs here, causing a minor temperature increase ofbelow 0.2 �C). In stage (III), the stress drop rate increases suddenlyand coincides with the onset of the temperature jump, which isresolved within at least 8 frames. Reaching the bottom stress level(IV), the drop rate is reduced and transits towards the slowreloading phase (V). On average, temperature jumps DTjump are on

P. Thurnheer et al. / Acta Materialia 115 (2016) 468e474472

the order of 1.1 �C and maximum temperature jumps are about1.9 �C. The onset temperature difference, i.e. the temperaturedifference at the coordinates of the apparent band prior to aserration event, is about 0.2 �C, which is around 10% of the peakvalue.

6. Discussion

Shear-band heating is observed to start either simultaneouslyon the apparent shear plane or, with less probability, to form over apropagating front. It is found that front propagation, which causesonly a small temperature increase, coincides with stage II in thestress serration, i.e. with a transient state between the slow stickstage (I) and fast slip phase (III). In serrations of the “instantaneous”type, no temperature rise is monitored in stage II. For both types ofserrations, significant heating starts only upon entering stage (III),i.e., the stage at which the AE shear-band initiation signal is alsolocated [24]. We may thus differentiate between some diffuse pre-initiation phase (II) and the pronounced, fast shearing phase (III). Inthe following, we will focus on the latter.

The fact that the temperature of the apparent major shear bandpeaks only towards the end of a serration strongly supports the ideathat the time scale for temperature rises equals that of the serra-tions. However, there remains the issue of limited spatial resolu-tion, because we do not directly measure the temperature of theshear band, but the temperature of an apparent band whosethickness is equal to the resolution of the IR thermographs. Natu-rally, it takes some time for the heat to diffuse from the true shearplane over the distance of the method’s resolution, which isw ¼ 80 mm for our setup. Thus only a comparison between themeasured data and the predictions of the different models willallow us to make a strong statement regarding the time scalesinvolved in heating and thus regarding the mode of shear-stepformation and shear-band temperature. With model (2) havingbeen discarded (see introductory part) and model (3) having beenidentified as the result of geometrically-induced artefacts, werestrict ourselves to comparing the experimental results with thepredictions of models (1) and (4), i.e. the phonon-shear-frontpropagation model (1) and the serration-simultaneous shearingmodel (4); see Fig. 1a.

In our modelling of shear-band temperature, the true shearband is approximated by an infinitely large plane with zero thick-ness. According to Ref. [13], the time- and coordinate-dependenttemperature jump caused by a constant heat source over anevent duration Dt is given by

DTconstðx; t; qsÞ ¼ qs2cpa

ffiffiffiffiffiffiffiffi4atp

rexp

��x2

4at

�� x erfc

�xffiffiffiffiffiffiffiffi4at

p�!

;

(2)

where DT is the temperature jump, cp z 3 � 106 J m�3 K�1 is thespecific volume heat capacity, a z 2 � 10�6 m2s�1 is the thermaldiffusivity, t is the time, x is the distance from the heat source and qsis the heat flux density, which is given as qs ¼ H/Dt, i.e. the amountof released heatH per area divided byDt. The released heat per areais [12,37]

H ¼ 0:5syDupl; (3)

where sy is the yield strength.In the case of model (1), the time scale of observation (milli-

seconds) is much greater than the time scale of assumed eventduration (nano- to microseconds). Therefore, the time-dependenttemperature jumps at the time scale of observation can be

approximated well by instantaneous heating [12]:

DTinstðx; tÞ ¼

H2cp

ffiffiffiffiffiffipa

p!

1ffiffit

p exp��x2

4at

�: (4)

For model (4), with an input time scale on the same order ofmagnitude as the time scale of observation Dt, Equation (2) is usedas a direct starting point which we will refer to as model (4a). Thismodel has two limitations, however, which we account for in thefollowing to obtain an improved model (4b). First, Equation (2) isonly valid as long as the heating source is active. It can therefore notbe used to model temperature evolution for times longer than Dt.This limitation can be overcome by calculating the temperatureevolution once the heating source is switched off, which gives

DToff�x; toff ;Hi

�¼Zd

x¼0

DTinst�x� x; toff ;Hiðx� x;Dt; qsÞ

�dx;

(5)

where x is a space variable, d is the distance at which the temper-ature rise becomes insignificant (in our case d ¼ 500 mm), toff is thetime elapsed since the source was switched off, and

Hiðx; t0; qsÞ ¼RxþDx

x

DTconstðx;Dt; qsÞcpdx, i.e. the heat content just

prior to switch-off, is discretized in spaces Dx. In other words, thethermal profile just before switch-off is converted into a discreteheat profile, and the components are then treated as instantaneousheat sources according to Equation (4), which, added together, willprovide the total temperature at a given coordinate and time. Thesecond limitation of Equation (2) is that constant heating rate hasthe tendency to oversimplify the problem, as acknowledged inRef. [13]. Having recorded stress drops with high acquisition rates,we are, however, also able to overcome this limitation and todirectly calculate a time-dependent heating rate from the deriva-tive of the stress signal during a serration. This is achieved bycombining Equation (1) and Equation (3), which gives

qsðtÞ ¼ 12sðtÞds

dtAðCM þ CSÞ; (6)

where A is the sample cross-section, and the yield stress sy in Eq.(3) has been substituted by the time-dependent stress during aserration, s(t). Equation (6) allows us to predict a temperatureevolution proportional to the decrease in potential energy of themachine-sample assembly. The time- and space-dependent tem-perature jump for model (4b), which we call “proportional heat-ing”, thus becomes

DTpropðx; tÞ ¼Zt

t¼0

DToff ðx; t� Dt;Hðx;Dt; qsðtÞÞÞdt; (7)

where Dt is the discrete time step of the numerical integration.Equation (7) thus represents the sum of all contributions to thetotal temperature jump caused by the heat sources qs that wereactive for durations Dt at times t � t, each of which can be calcu-latedwith Equation (5), i.e. with the above-mentioned switched-offsource method.

Models (1), (4a), and (4b) are now tested during stages III and IVof the serration displayed in Fig. 5a. The time-dependent heatingrate per area, i.e. heat flux density qs (Equation (6)), is shown inFig. 5b. For the calculations we used an effective heating rate whichis set to zero except for serration stages III and IV. The time at which

Fig. 5. a) Raw and smoothened stress-drop data. b) Raw and effective heating rate perarea (heat flux density) as a function of time. c) Comparison of the experimentaltemperature trace (circles) with the predictions of model (1) (phonon-shear-frontpropagation, magenta), model (4a) (serration-simultaneous shear with a constantheating rate, cyan), and model (4b) (serration-simultaneous shear with a heating rateproportional to the elastic-energy release, blue). (For interpretation of the references tocolour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Histograms of shear-band temperatures. (a) Experimentally measured tem-perature jumps of the apparent shear band (which has the size of a pixel); (b) tem-perature jumps simulated by model (1) for the apparent band (open columns) and forthe shear plane (solid columns); and (c) temperature jumps simulated by model (4b)for the apparent band (open columns) and for the shear plane (solid columns).

P. Thurnheer et al. / Acta Materialia 115 (2016) 468e474 473

stage III starts will also be used as a time reference for the posi-tioning of the curve obtained for models (1) and (4a).

Fig. 5c shows how the experimentally determined shear-bandtemperature compares with the various model predictions evalu-ated at x ¼ 80 mm. Shear-step generation according to model (1)(magenta) generates a rapid temperature increase upon shear-bandinitiation when entering stage III. Here, the maximum of the tem-perature jump (2.6 �C) is reached within 1.6 ms. Thus model (1) notonly overestimates the temperature jump but also the time-dependent heating rate (slope). Converse behaviour is observedfor shear-band heating at a constant rate (model (4a), cyan), wherethe heating rate is underestimated at the beginning of the serrationand slightly overestimated towards the end of the event. Thus,whilemodel (4a) provides realistic values for the temperature jump

it fails to match the time-dependent heating of the apparent band.Clearly, model (4b), which describes heating to be proportional tothe elastic-energy release, matches the experimental data best.Both the time-dependent heating rate (slope) and the peak tem-perature are reproduced very accurately by the simulation. This isobserved throughout the set of 80 serrations. Having nowaccounted for thermal diffusion from the shear plane to theapparent band, which has the thickness of one pixel, we can thusconclude that the temperature trace observed cannot be caused bythe process described by model (1). Instead, Fig. 5 provides strongevidence that the shear step is mostly caused by a process ofsimultaneous shear (Fig. 1a, model (4)), which occurs at the timescales obtained by high-acquisition rate instrumented mechanicaltesting.

Fig. 6 now addresses the emerging question of true shear-bandtemperature. To this end, Fig. 6a shows the histograms of theexperimentally recorded temperature jumps. The apparent bandtemperatures simulated by models (1) and (4b) are shown by theopen columns in Fig. 6b and c, whereas the solid columns in thesefigures refer to the temperatures obtained when the models areevaluated at x¼ 0, i.e. right at the position of the shear plane. In thecurrent calculation, Equation (2) with t ¼ Dt ¼ 10�8 s was used formodel (1). While model (1) predicts shear-band temperature risesof 2000e4000 �C, model (4b) predicts only moderate rises of2e6 �C for the actual shear plane. Because model (4b) was found toagree best with the experimental data in terms of the heating timeof the apparent band (Fig. 5c), we can clearly conclude that tem-perature rises during shear banding are very moderate. These re-sults may conclude the long-standing debate about the dynamics ofshear banding and the resulting temperature increase.

P. Thurnheer et al. / Acta Materialia 115 (2016) 468e474474

7. Conclusions

In summary, we have reviewed the current models of shear-stepgeneration during inhomogeneous deformation and carried outtime-resolved shear-band heating experiments on ZreCoeAl MGsduring compressive stable, serrated flow. We measured maximumtemperature jumps of 1e2 �C for an apparent band of 80 mmthickness and were able to show clearly that each temperature risecoincides with the end of the slip phase in a flow serration. Ac-counting for thermal diffusion and comparing the experimentalresults with two of the reviewed deformation models, namelyshear-band heating at time scales of elastic wave propagation(model (1): phonon-shear-front propagation) and shear-bandheating at time scales of flow serrations (model (4): serration-simultaneous shear), we find strong evidence for the validity ofmodel (4). Using this model, our results then provide evidence thatshear-band heating in metallic glasses is less than 2e6 �C duringstable serrated flow. More pronounced shear-band temperaturejumps may be expected for larger samples with higher stress levelsand increased shear-band dynamics, as can be concluded from anevaluation of Equation (6). In general, however, model (4)adequately describes shear-band dynamics in metallic glasses, andtemperature rises during shear banding are very moderate. Ourfindings may conclude a long-standing debate in this area ofresearch.

Acknowledgments

The authors gratefully acknowledge funding by the Swiss Na-tional Science Foundation (SNF Grant No. 200020-153103) and theEU Initial Training Network VitriMetTech (FP7-PEOPLE-2013-ITN-607080). They also thank Josef Hecht for setting up the LabViewroutine for synchronized recording of stress and IR camera signals.

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