Factors influencing the ductile-to-brittle transition

On factors in?uencing the ductile-to-brittle transition

in a bulk metallic glass

R.Raghavan a,b ,P.Murali a,c ,U.Ramamurty a,*

Department of Materials Engineering,Indian Institute of Science,Bangalore 560012,India

EMPA,Swiss Federal Laboratories for Materials Testing and Research,Feuerwerkerstrasse 39,CH-3602Thun,Switzerland

Large Scale Complex Systems Group,Institute of High Performance Computing,Singapore 138632,Singapore

Received 19December 2008;received in revised form 28February 2009;accepted 30March 2009

Available online 4May 2009

Abstract

An experimental study to ascertain the ductile-to-brittle transition (DBT)in a bulk metallic glass (BMG)was conducted.Results of the impact toughness tests conducted at various temperatures on as-cast and structurally relaxed Zr-based BMG show a sharp DBT.The DBT temperature was found to be sensitive to the free-volume content in the alloy.Possible factors that result in the DBT were critically examined.It was found that the postulate of a critical free volume required for the amorphous alloy to exhibit good toughness cannot rationalize the experimental trends.Likewise,the Poisson’s ratio–toughness correlations,which suggest a critical Poisson’s ratio above which all glasses are tough,were found not to hold good.Viscoplasticity theories,developed using the concept of shear transformation zones and which describe the temperature and strain rate dependence of the crack-tip plasticity in BMGs,appear to be capable of cap-turing the essence of the experiments.Our results highlight the need for a more generalized theory to understand the origins of toughness in BMGs.

Keywords:Metallic glass;Impact test;Toughness;Brittle-to-ductile transition;Free volume

1.Introduction

The mechanical behavior of amorphous alloys has attracted considerable attention in the recent past,after the discovery that they can be processed in bulk form and hence can be deployed in structural applications as they exhibit extraordinary strengths and yield strains.However,thorough understanding of their fracture and fatigue behavior is far from complete [1–3].For example,certain Zr-based bulk metallic glasses (BMGs)have frac-ture toughness comparable to that of conventional Al-alloys ($25–50MPa m 1/2),while Mg-and Fe-based BMGs are as brittle as silicate glasses ($1–2MPa m 1/2).The fun-damental understanding of reasons for such signi?cant dis-parity in the toughness of BMGs is not fully developed yet.

In particular,it would be highly desirable to know the prin-ciples of alloy design that would yield BMGs with high toughness.In crystalline metals and alloys,such knowledge is gained by systematic experiments which correlate micro-structure and properties.The lack of a ‘‘microstructure ”and the inability to conduct systematic parametric studies are the main impediments for gaining such knowledge in BMGs.

It is now well established that the fundamental carriers of plasticity in amorphous alloys are the shear transforma-tion zones (STZs),which are aided by the ‘‘free volume ”available in the material.Free volume also plays an impor-tant role in determining the fracture toughness,as it medi-ates the crack-tip plasticity via shear bands.For example,Ramamurty and co-workers [3,4]have shown that struc-tural relaxation during annealing below the glass transition temperature (T g )results in the decrease in the propensity of shear band formation and hence decreases the energy

Corresponding author.Tel.:+918022933241;fax:+918023600472.E-mail address:ramu@materials.iisc.ernet.in (U.Ramamurty).

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Acta Materialia 57(2009)

3332–3340

dissipation at the crack tip,thus imparting severe embrit-tlement to a Zr-based BMG,which is otherwise tough. The structural relaxation is also shown to be associated with a decrease in the excess free volume which rationalizes the decrease in shear band propensity of a glass.

In an earlier study[2],we have shown that the impact toughness of the as-cast BMG is sensitive to the testing temperature with the samples tested at low temperatures exhibiting relatively lower toughness values compared to the similar samples tested at high temperature.This is gen-erally consistent with a number of studies that report dependence of plasticity in BMGs on temperature,all of which indicate reduced propensity to shear banding at lower temperatures[1–6].However,the precise nature of toughness variation with temperature in BMGs is not known yet.Speci?cally,whether the toughness of BMG varies smoothly with temperature or exhibits a sharp tran-sition(as in semi-brittle body-centered cubic(bcc)metals and alloys,and other intermetallics)has not been clearly established yet.In this work,we conduct experiments that demonstrate the existence of a sharp brittle-to-ductile tran-sition in a Zr-based BMG.We then seek to?nd microme-chanical reasons for such dramatic changes in toughness through available theories in literature such as the existence of a critical Poisson’s ratio(m)$0.32that demarcate the brittle and ductile metallic glasses.

2.Material and experiments

The material used in this study is a commercially avail-able Zr-based BMG,Zr41.2Ti13.8Cu12.5Ni10.0Be22.5(at.%), referred to as Vitreloy-1(T g=625K),and is one of the most widely studied alloy.Relevant properties of Vitre-loy-1are listed in Table1.Charpy impact tests were con-ducted on3mm deep notched rectangular beams(30mm in length,6mm in width and3mm thick)that were elec-tric-discharge-machined from plates.Tests were conducted on both as-received and structurally relaxed specimens. The latter was performed by annealing the samples below the glass transition temperature at473,500and563K for2.5,12and24h each.The impact tests were conducted within the temperature range of123–523K,at intervals of 50K.For sub-ambient temperature toughness testing,the specimens were?rst soaked in liquid nitrogen for about 300s.For the above-ambient temperature testing,a fur-nace with good temperature control was utilized.In order to minimize the heat loss during the transfer of the samples from liquid nitrogen/furnace the samples were cooled/ heated to$10K lower/higher than the desired testing tem-perature?rst.They were then transferred to the impact testing jig,allowed to reach the temperature and tested immediately.The samples were directly connected with a Chromel/Alumel thermocouple to measure the exact test-ing temperatures at the time of testing.This procedure pro-vided an accuracy of about±5K at each temperature allowing for small temperature variations during testing time.At least three samples were tested for each case. The fracture surfaces were characterized using a scanning electron microscope.

The elastic properties of the as-cast and annealed speci-mens were measured using ultrasonic techniques.Plane parallel specimens with a10?10mm2cross-section and 3mm thickness were polished with a0.25l m diamond paste for the ultrasonic testing.

3.Results

Fig.1shows the impact toughness(C)of the as-cast and annealed BMGs as a function of testing temperature(T t). For the as-cast alloy C is$1.2J above200K,and,no sig-ni?cant correlation of C and T t is observed.However,for T t<200K,C decreases to$0.8J.While not a con?rma-tion of the existence of a DBT,these results indicate to a possible DBT.It is likely that the actual ductile–brittle transition temperature(T DB)of the as-cast glass is below the lowest testing temperatures we have conducted.Hence we have chosen samples which are brittle at room temper-ature(T R)and examined whether they exhibit high C at T t>T R.Interestingly,experiments on anneal-embrittled glasses give a de?nite indication of a DBT.For example,

Table1

Properties of Vitreloy-1

Property Value

Elastic strain limit,e el$2%

Tensile yield strength,r y 1.9GPa Young’s modulus,Y96GPa

Shear modulus,l34.3GPa Poisson’s ratio,m0.36

Vickers hardness,VHN534VHN Fracture toughness,K IC55–59MPa m1/2 Thermal expansion coe?cient,a10.1?10à6Kà1 Density,q 6.11g cmà

3Fig.1.Variation of impact toughness as a function of temperature in the as-cast and annealed states.

R.Raghavan et al./Acta Materialia57(2009)3332–33403333

samples annealed at563K for 2.5h are brittle for T t<400K(with C<0.4J).When T t>400K,the C increases to1.2J,a4-fold rise in toughness,clearly demon-strating a sharp brittle-to-ductile transition at around 400K.Samples annealed at473and500K exhibit a similar sharp transition at lower temperatures whereas the sample annealed at563K for12h remains brittle with(C<0.2J) for testing temperatures up to500K and recovers tough-ness(C$1.2J)thereafter.

Some additional points are noteworthy.With an exper-

imental scatter of±10%,the measured C values fall in two di?erent ranges.Irrespective of the annealing state,the upper shelf values appear to vary between1.0and1.2J, suggesting an upper limit to the toughness of BMG.The samples annealed at563K,2.5h and500K,12h exhibit a slight/moderate decrease in toughness with increasing temperature when tested beyond the T DB.The results unambiguously show that the T DB is a function of annealed state and increases with the severity of annealing(annealed at either high temperatures or for long durations).

Relative changes in the free volume due to structural relaxation were estimated by the exothermic enthalpy near the glass transition range utilizing the di?erential scanning calorimetry[3,7,8].The elastic constants of the as-cast and annealed BMGs,measured from ultrasonic techniques are listed in Table2.Annealing leads to reduction of free vol-ume and increase in density,which results in the increase of the elastic constants.However,the changes in elastic prop-erties are only marginal(with a maximum di?erence of less than3%between the m values of the as-cast and563K,12h annealed samples,the latter being the severest of the relax-ation treatments imparted in this study).The increase in the bulk modulus(j)is relatively small,compared to the increase in the shear modulus(l),which results in a mar-ginal increase of m.In all,no dramatic changes in elastic properties are noted.

Earlier studies have shown that the vein patterns found on the fracture surfaces of metallic glasses are similar to those found by breaking two surfaces held together by a thin layer of a highly viscous?uid such as grease or wax [9].Based on this observation,the fracture toughness,K c, of the specimens was estimated by measuring the widths of the vein patterns(w).In this study,the K c of the as-cast and severely embrittled specimens tested below and above the transition temperature(T DB)was calculated using the Dugdale approximation(discussed later).The values for the plastic zone size were obtained from w estimated from fractography of the specimens(Table3).The annealed BMG exhibits a signi?cant increase in the calculated K c in the ductile regime,while the as-cast specimen does not show any change in the testing temperature regime.

4.Discussion

In an earlier work[2],we have established,through experiments on as-cast and structurally relaxed Vitreloy-1,a one-to-one correspondence between the impact tough-ness and free-volume content of Vitreloy-1.The BMG annealed below the T g loses its ability to deform as a result of free-volume annihilation during the annealing process. This correlation,as well as earlier works by Wu and Spae-pen[10],implies that free volume is the intrinsic state parameter that determines whether a BMG is tough or not.Results presented in the present paper demonstrate that toughness of a metallic glass is also sensitive to the temperature in addition to the free-volume content.(Note that,by virtue of the thermal expansion,the free-volume content itself increases with temperature.However,DBT suggests an explicit dependence on temperature,1as we shall discuss later.)It is to be noted here that temperature and strain rate,etc.,play an important role in determining the mechanical properties of most classes of materials. However,and in the context of the amorphous alloys,the changes in toughness with temperature is not gradual but has a sharp transition.The as-cast Vit-1resides in the tough space for all practical purposes(i.e.,except at tem-peratures much below100K or extremely high strain rates).Therefore,its fracture toughness values are high and hence it is a potential candidate for structural applica-tions.On the other hand,Fe-based multi-component BMGs are extremely brittle,possibly because room tem-perature corresponds to the lower shelf.The latter could be due to two reasons:(i)the T g of these BMGs are rela-

Table2

Elastic parameters of the as-cast and annealed BMGs.

Condition Poisson’s ratio,m Shear modulus,l(GPa)Young’s modulus,Y(GPa)Bulk modulus,j(GPa) As-cast0.35436.197.7111.7

Annealed563K,2.5h0.35136.999.8111.8

Annealed563K,12h0.35037.2100.6112.1

Table3

Fracture toughness,estimated using the ridge spacing measured through

fractography.

State Testing temperature

(K)w

(l m)

K1c

(MPa m1/2)

Annealed(563K,12h)2980.11 2.7

573 3.9816.8

As-cast123 5.8220.3

423$520.0

1By extension and given the viscoplastic nature of BMGs,strain rate is

also likely to play a similar role.However,we shall restrict ourselves to the

temperature–free-volume space in this paper.

3334R.Raghavan et al./Acta Materialia57(2009)3332–3340

tively high vis-a`-vis those of the tough BMGs(Zr-,Pd-,Pt-based BMGs,for example);(ii)the free-volume content in the as-cast alloy itself is very low.It may be possible that the Fe-based BMGs exhibits high toughness at high tem-peratures and low strain rates.

If tough and brittle regimes exist in the3D space of tem-perature–free-volume strain rate space,it would be desir-able to identify the factors that make a glass go from one region to another,as it would facilitate the design of tough BMGs.In this work,we con?ne ourselves to the2D space of free volume and temperature and see if some general principles that are available in the literature can be used to rationalize the experimental results of this study.

4.1.Critical free volume

Wu and Spaepen[10]demonstrated for the?rst time that metallic glasses can undergo DBT when tested at dif-ferent temperatures.In their experiments of bending on Fe-based metallic glass ribbon samples,they observed that T DB varies linearly with the fractional free-volume change (D t/t0).The D t/t0can be expressed as a function of an annealing parameter v which is a single-valued function of annealing temperature,T A and time,t A.According to Wu and Spaepen’s model,

D t t0?

veT A;t AT

ct?=v0tveT A;t AT

;e1T

where c is a geometric factor$0.5–1,t*is the critical free-volume?uctuation.The function v is expressed as follows:

veT A;t AT?ln1tAe0Texp

RT A

t A

e2T

where A(0)is a prefactor that depends on the initial con?g-

urational state(given by_g0=ge0T

0,the ratio of rate of viscos-

ity relaxation to the viscosity of the as-cast glass)and~Q is the apparent activation energy.The annealing state v is also determined by enthalpy changes D H measured from di?erential scanning calorimetry.~Q is obtained from the slope of the constant–D H curves in the plot of1=T A vs. log t A.By choosing appropriate values,Wu and Spaepen have observed that T DB varies linearly with D t/t0.In order to connect the T DB with D t/t0,they assumed that the brit-tleness/ductility depends on the free volume being below or above a critical value.The free volume of a particular con-?guration varies as a function of temperature according to teTT?teT RTtaeTàT RTXe3Twhere a is the coe?cient of thermal expansion and X is the atomic volume.Based on the critical free-volume assump-tion,T DB can be obtained as

T DB?t0

D t

tT as-cast

e4T

While the above free-volume model successfully captures the qualitative trends on DBT temperatures,it leaves a num-ber of questions open.For example,what determines the critical free volume for ductile-to-brittle transition?Is this critical free volume universal to all the glasses?Also the detailed atomistic mechanisms assumed by free-volume the-orists are largely in debate now[1].While the Wu and Spae-pen’s theory is rigorous and requires considerable amount of experimental data for validation,we take the essence of it from Eq.(4),and compare it with our experimental data after reasonable approximations and assumptions.An important assumption that we make is that the fractional free-volume change D t/t0is proportional to the fractional enthalpy change D H/H0that can be computed from a DSC thermogram.This assumption is well supported by the experimental results of Slipenyuk and Eckert[8],who measured density changes of a metallic glass and showed that D t/D H.

In Fig.2the T DB observed in our experiments on Vitreloy-1are plotted against the annihilated free-volume change.A linear?t of the data shows a rise of D T DB/D U$11K per 1%change of free-volume.Extrapolation of this data results in a T DB of$à700K for the as-cast glass,i.e.no DBT for the as-cast at all.In Fig1,the toughness of the as-cast glass starts decreasing at temperatures close to123K and T DB of this glass can also be anticipated close to this temperature.Data in Fig.2indicates that glasses annealed to various degrees (473K,24h;500K,12h;and563K,12h)show similar val-ues of free-volume changes as indicated by D H/H0.However their T DB values range from123K to500K.These results clearly indicate that quantitative theories based on free vol-ume fail to validate experimental results in all situations. The key factors that control brittleness of a metallic glass can be more complicated than free volume alone and should also be a function of intrinsic parameters that are related to the elastic constants,viscosity,strain rate,etc.,which again could be inter-related to each other.We now examine these factors to rationalize the DBT in metallic glasses.

4.2.Poisson’s ratio

Recently,there has been considerable interest in under-standing the toughness of BMGs in terms of their m[11–13]

. Fig.2.Variation of T DB as a function of normalized-exothermic enthalpy.

R.Raghavan et al./Acta Materialia57(2009)3332–33403335

This is after Schroers and Johnson [12]have synthesized a Pt-rich BMG,showed that it exhibits large ductility as well as high fracture toughness ($80MPa p m)and suggested that these properties are due to that particular BMG’s large m of 0.42.Subsequently,Lewandowski et al.[13]correlated the fracture energy of a number of di?erent glasses (includ-ing silicate glasses)with m and report a sharp brittle to tough transition at m =0.31–32.Gu et al.[14]claim to have successfully designed Fe-based BMGs based on this.Although the precise reasons for the criticality of these val-ues are not known yet,there has been considerable subse-quent activity to process BMGs having high m values.It is to be noted here that such correlations between global elastic properties and plasticity and toughness were also proposed for crystalline materials earlier by Pugh [15]and Kelly et al.[16].They point out that metals with a high l /j ratio or equivalently low m are relatively brittle.In the following,we examine if such a critical m theory would be able to rationalize the DBT observed in the Vit-1BMG.Zhang et al.[17]extended a model proposed by Varshni [18],which discusses the temperature dependence of elastic constants in amorphous materials.According to Varshni,the elastic constant C (T )of a solid varies with temperature T according to

C eT T?C 0às

e t =T

à1e5Twhere C 0is the elastic constant at absolute zero tempera-ture,s and t are ?tting parameters.Zhang et al.eliminated the ?tting parameters by assuming t =h D which is the De-bye temperature and using the observation that of a solid near melting is $55%of the value at 0K.Thus,s ?

C eT R T1

e h D =T R à1

à1n G

ee h D =T m à1Te6T

where T m is the melting temperature,and n G is a dimen-sionless parameter de?ned as n G ?

C eT m TàC 0

C 0

e7T

Thus,the full temperature dependence of C (T )can be ex-pressed as:C eT T?C eT R Tt

s e h D =T R à1

s e h D =T à1

e8T

Using the above equation Zhang et al.[17]were able to predict the variation of l ,j and longitudinal modulus for various BMGs as a function of temperature using only the room temperature data,which showed an excellent agreement with experiments.Hence,we used the above equation to predict l (T )for the BMG used in the present study.The variation l and j for both the as-cast and annealed alloys is shown in Fig.3a and b.Then,m is obtained using m ?12à

2ej =l t1=3T

:e9T

The variation of m with temperature for two cases,one in the as-cast condition and the other in a fully annealed con-dition (563K,12h),is shown in Fig.3b.As expected the m increases with increasing temperature indicating the rise in C with increasing temperature.

Note that m >m c (0.31–0.32)for both the as-cast and the annealed alloys at all testing temperatures.However,the impact toughness measurements as well as SEM fracto-graphs (for example see Fig.2of Ref.[3])clearly indicate the embrittlement of BMGs due to annealing.Impact toughness measurements indicate that T DB $550K for a sample annealed for 12h at 563K.These observations sug-gest that the m –C correlation observed by Lewandowski et al.[13]cannot explain the DBT observed in BMGs.We examine an alternative and what appears to be a physically more meaningful method to see if the critical m theory works.On annealing a metallic glass below T g ,l increases,because of the densi?cation during annealing (Fig.3a).However,the slope of l vs.T does not change.Lind et al.[19]have shown that l is a strong function of the con?gurational state of the system,which is in?uenced by annealing the as-cast alloy.Also,the relative change in

Fig.3.(a)Variation of shear modulus l and bulk modulus j as a function

of temperature for both the as-cast and annealed alloys.(b)Variation of m with temperature,for two samples one in the as-cast condition and the other in a fully annealed condition (563K,12h).

3336R.Raghavan et al./Acta Materialia 57(2009)3332–3340

is much larger than that in j.But the linear relationship of l–T is an extrapolation of the Debye–Gruneisen lattice expansion,which has a much lower e?ect on the tempera-ture dependence than the con?gurational contribution. Thus,the annealing state dependence of any annealed/ relaxed alloy can be expressed as follows:

l R?l0

R tl1

àl0

àá

?expà

t A

e10T

s?A expàB T A

e11T

where l R is the shear modulus of the metallic glass(at room temperature)annealed at a temperature T A for time t A,s is the characteristic relaxation time which depends

on temperature of annealing as given in Eq.(11),l0

R and

l1 R are the shear moduli of the as-cast and fully annealed

BMGs at room temperatures respectively,and A and B are?tting parameters.

DBT in the as-cast BMG occurs because of a decrease in the shear modulus of the as-cast state below a critical(com-position-speci?c)value(l c)at temperatures greater than T DB.By extrapolating l c to the shear modulus-temperature dependence of the annealed/relaxed state,the T DB of an annealed/relaxed state is obtained as follows:

T DB?el Ràl cT

h d l=dT i

tT Re12T

where h d l=dT i is the average rate of change of shear mod-ulus with temperature,and T R is the room temperature. Though both the o?set in modulus due to relaxation, (l Ràl c),and slope h d l=dT i)are small,the predicted T DB of the annealed state is higher due to the ratio of the two being higher.In a similar fashion,the T DB for any gi-ven con?gurational state can be predicted from the m dependence on temperature of the as-cast and annealed states.By assuming m c=0.353,the T DB for an annealed state can be modeled and compared with the experimen-tally observed T DB(Fig.3).Following are the observations from the comparison:

(1)The theory predicts a T DB(as-cast)not only much

higher than that predicted by experiments,but also close to room temperature,which is not possible. (2)A weak dependence of T DB on the annealed state,as

opposed to an expected strong dependence as exhib-ited by experiments.All these observations indicate that the DBT observed as a function of temperature in the present study cannot be explained with the empirical Poisson’s ratio–fracture energy correlation.

Fig.1shows that anneal specimens undergo a DBT only to attain the toughness of the as-cast state.This tempera-ture-aided‘‘memory”of the anneal-embrittled BMG emphasizes the fact that BMGs are viscoplastic in nature. The invariance of hardness(and hence?ow stress) observed as a function of temperature across the T DB also suggests that a‘‘viscoplasticity”model may capture the features of DBT,which are discussed in the next section.

4.3.Viscoplasticity

Falk and Langer[20,21]studied the factors a?ecting the ductile/brittle fracture in amorphous solids utilizing molec-ular dynamics simulations and developed a theory of visco-plastic deformation in them.The theory seeks to identify, from the dynamic fracture mechanics,the key parameters that govern brittle fracture in amorphous solids under the conditions of very high strain rates.At such rates,the con-stitutive equation of?ow of materials is proposed by Fre-und and Hutchinson[22]as follows:

_e pl

?_e tt_e0er sàr flowT=le13T

where_e pl

is the plastic?ow rate,_e t is the?ow rate at yield, r s is the applied shear stress,r flow is the?ow stress and_e0 characterizes the strain-rate sensitivity.Note that_e0can be

expressed as l j@_e pl

=@r s j

r flow

which is same as the ratio of shear modulus to viscosity.Incorporating the above consti-tutive model,Freund and Hutchinson have shown that the minimum energy release rate,G min,required to propagate a crack in dynamic loading conditions,is given by

G min

G c

tip

%1tC

_e0

flow

e14T

where G c

tip

is the bare fracture toughness near the tip and C is proportionality constant.Falk[20],in his study of molec-ular dynamics simulations,?nds that change in the?ow stress does not contribute to the brittleness and the chief contribution comes from_e0.An expression for_e0is also de-rived using the STZ-based viscoplasticity theory and the key governing parameters are ascertained.While these parameters are related to the speci?cs of inter-atomic po-tential which are material dependent,an important out-come from this theory is the parameter_e0itself.The_e0 can be approximated to l=g where g is the viscosity.Falk shows that_e0is sensitive to the activation volume.He has also clearly demonstrated that by conducting molecular dy-namic simulations on two systems of Lennard–Jones atoms,one with a lower activation volume(compressed Lennard–Jones system,described in Ref.[15])undergoes a brittle fracture.Recently,Torre et al.[23,24]have exper-imentally measured the activation volume of Zr52.5Ti5-Cu17.9Ni14.6Al10BMG by conducting the variable strain-rate experiments at di?erent temperatures.They observed an increase in the apparent activation volume with increas-ing temperature.From these?ndings the hitherto much-less studied‘‘activation volume”emerges as a new impor-tant parameter in determining the brittleness/ductility of BMGs.The increase in the activation volume with temper-ature,similar to the increase in toughness with tempera-ture,suggests a correlation between toughness and activation volume in BMGs.Further experimental probing is necessary to establish this correlation.It is worth noting

R.Raghavan et al./Acta Materialia57(2009)3332–33403337

here that the pressure sensitivity of plastic?ow,exhibited by amorphous alloys[25,26],may also have a role to play in determining the toughness as considerable levels of hydrostatic tension exists ahead of a loaded crack-tip.In fact,detailed?nite element analysis by Tandaiya et al.

[27]show considerably increasing notch blunting with pres-sure sensitivity,implying pressure sensitivity has a role to play in determining the toughness of a metallic glass.

4.4.Energy dissipating mechanisms

Fractography is an excellent methodology to under-stand whether a material is intrinsically brittle or ductile. Brittle materials exhibit a sequential mirror–mist–hackle morphology on their fracture surfaces[28].Numerous investigations of energy dissipation mechanisms of brittle materials in terms of the fracture surface morphologies have provided signi?cant insights into the dynamic fracture behavior of materials.Similar studies on the fracture energy dissipation process have been conducted on brittle and tough BMGs in terms of dynamic fracture mechanics and crack-tip instability[29–32].

Figs.4and5illustrate the energy dissipation mechanism in an anneal-embrittled specimen(563K,12h)across the T DB.Interestingly,below the T DB and at low magni?cations, a perfectly planar fracture morphology was seen,and sug-gests a classical‘‘mirror–mist–hackle”sequence(Fig.4a). Similar fracture surface morphology was observed in a brit-tle Mg-based BMG,which was fractured by quasi-static and notched3-point bending[32].In addition,high-resolution SEM of the apparent‘‘mirror-like”region reveals extensive corrugation to form shallow ridges with spacings of$50nm (Fig.4d).Initially interpreted as surface roughening due to void growth and/or coalescence[30],these nanoscale corru-gations are now explained in terms of Argon and Salama’s ?uid-meniscus instability model[31].In particular,Jiang et al.[29]conjecture that the quasi-cleavage fracture features observed in BMGs are a result of rupturing of tension trans-formation zones(TTZs),which are local atomic clusters sim-ilar in size to STZs but with smaller relaxations timescales.In other words,these TTZs are less viscoplastic than STZs and are more amenable to fracture than?ow when subjected to stress.This point is of paramount importance in the present context of DBT.We postulate that across the T DB(of

an Fig.4.SEM of the optically mirror-re?ecting fracture surface of the brittle state specimen annealed at563K for12h:(a)micrograph showing apparently smooth crack-initiation site(inset);(b–d)higher magni?cation SEM micrographs of region inset in(a);and(d)high-resolution SEM micrograph exhibiting shallow nm-sized vein patterns.

3338R.Raghavan et al./Acta Materialia57(2009)3332–3340

anneal-embrittled BMG),the relaxation timescales of TTZs increase and the TTZs can no longer be distinguished from the STZs.Fig.6is a schematic illustration of the conjecture of a transition in the nature of the zones from TTZs to STZs across the T DB .This allows the BMG to accommodate plas-tic strains by shearing and exhibit a ductile response.Inter-estingly,above the T DB ,the fracture morphology is that of shearing and formation of deep ridges of $5l m lateral dimensions (Fig.5).The increase in the relaxation timescales of TTZs occurs as a result of the drastic increase in strain-rate sensitivity,which is expected for reasons discussed in the pre-vious section.

Thus,the BDT occurs as a result of a change in the frac-ture mechanism as a function of temperature,which is pos-tulated from a microstructural point of view and supported by mechanistic reasons of change in strain-rate sensitivity.It is interesting to note that a similar change in the micro-scopic fracture mode in?uenced by temperature has been observed by Pampillo and Polk [33].Similar plastic zone size toughness correlations were suggested by Nagendra et al.[34]and used to estimate the fracture toughness by Xi et al.[35].Furthermore,Argon and Salama [31]have been able to make quantitative estimates of the fracture

toughness of amorphous alloys using the spacing of the vein patterns,assuming fracture of metallic glasses to be a variant of the Taylor’s meniscus instability theory for ?u-ids.Hence,the ridge spacing (w )found near the notch-tip was used to calculate the fracture toughness (K c )using the Dugdale approximation (Table 3).

w ?

16p K c

r y 2e15TThe anneal-embrittled specimens exhibit low values of $3MPa m 1/2,while at high temperatures,toughness values of $20MPa m 1/2,which are similar to those found in the as-cast state,are observed.The negligible di?erence in the values at room and the lowest workable temperature in the as-cast state recon?rm that embrittlement of the as-cast state might require much lower temperatures.5.Summary

The experimental results on impact toughness measure-ments made on as-cast and annealed BMG at various tem-peratures reported in this work clearly demonstrate

that

Fig.5.SEM micrographs of the fracture surface in the ductile state in the annealed state (563K,12h):(a)low magni?cation micrograph of the notch tip region showing that crack initiates by Mode II shearing;(b–d)higher magni?cation SEM micrographs and high-resolution SEM micrograph exhibiting deep micron-sized vein patterns in the ductile state.

R.Raghavan et al./Acta Materialia 57(2009)3332–33403339

amorphous alloys are susceptible to ductile-to-brittle tran-sition.Results also show that the DBT temperature is sen-sitive to the free-volume content in the alloy.Existing theories of deformation and fracture in amorphous alloys cannot satisfactorily rationalize the experimental trends,indicating that the dynamics of crack-tip plasticity of visco-plastic materials like BMGs cannot be captured by conven-tional theories of plasticity and fracture.Falk and Langer’s extended theory of viscoplasticity appears capable of cap-turing the temperature dependence of the crack-tip plastic-ity of BMGs,although it requires detailed experimental veri?cation.The brittle-to-ductile transition in anneal-embrittled BMGs is conjectured to occur because of a tran-sition in the strain-rate sensitivity.Acknowledgement

The authors wish to thank Prof.Vincent Keryvin (Uni-versity of Rennes,France)for useful discussions and comments.References

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Fig.6.Schematic illustration of the change in the nature of the transformation zones from TTZs to STZs across the T DB .

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