Materials Science and Engineering A · 2020. 11. 16. · INSTRON3384withastrainrateof1×10−4 s−1. The Zr acoustic velocities of bulk MGs were measured using a MATEC 6600 ultrasonic

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Materials Science and Engineering A 532 (2012) 430– 434

Contents lists available at SciVerse ScienceDirect

Materials Science and Engineering A

journa l h o me pa ge: www.elsev ier .com/ locate /msea

nderstanding the correlation of plastic zone size with characteristic dimpleattern length scale on the fracture surface of a bulk metallic glass

.C. Yuan, J. Ma, X.K. Xi ∗

nstitute of Physics, Chinese Academy of Sciences, Beijing 100190, China

r t i c l e i n f o

rticle history:eceived 19 September 2011eceived in revised form 28 October 2011ccepted 3 November 2011

a b s t r a c t

Fatigue pre-crack toughness measurements following standard procedures for a modelZr61Cu17.3Ni12.8Al7.9Sn1 glass in as-cast and annealed states were performed. Plastic zone size wasfound to be very sensitive to the internal states of this glass and be correlated with the characteristicdimple pattern length on fracture surfaces. Effect of plastic work energy dissipation on two characteristic

vailable online 9 November 2011

eywords:etallic glasses

racture toughnessnnealinglasticity

length scales in the vicinity of a crack tip was discussed, in addition to the analyses of excess freevolumes and Poisson’s ratio.

© 2011 Elsevier B.V. All rights reserved.

. Introduction

Metallic glasses (MGs) have great potential applications astructural and functional materials due to their high specifictrength, corrosion resistance, soft magnetic properties and uniqueet-shape formability [1]. For typical MGs, however, limited plas-icity and fracture toughness under ambient temperature severelylock their wide applications as structural materials [2,3]. It haseen shown that improved toughness can be achieved in mono-

ithic MGs by tuning compositions under the guidance of Poisson’satio [4] (or equivalently, the ratio of G/B, where G, shear modu-us; B, bulk modulus) or free volumes. Fracture toughness of MGsan be practically evaluated from the averaged dimple patternize on fracture surface where fractured in pure opening modemode I) since the characteristic size was found to be correlatedo the plastic zone size in the vicinity of crack tip. This correla-ion is fundamentally important for the understanding of cracktructure and fracture mechanics of metallic glasses. The forma-ion of dimple structures can be explained due to massive flowf softened material at the crack tip [4–8]. However, such corre-ation is not always straightforward when MGs fractured under

lane stress condition rather than plane strain condition. As crackropagates in mixed opening and shearing modes rather than purepening mode, it leaves various types of patterns on fracture sur-

∗ Corresponding author. Fax: +86 1082640223.E-mail address: [email protected] (X.K. Xi).

921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2011.11.008

faces, corresponding to the observed significant scatter of measuredfracture toughness values. Since the toughness of typical MGs issensitive to structural relaxation [9–11], the relaxation effect onthis correlation might provide another rigorous way, in additionto alloying, toward better understanding this correlation in termsof plastic work dissipation within the plastic process zone. How-ever, the relevant investigation from this point of view is stilllacking.

In this work, we measured quasistatic fatigue precrack frac-ture toughness under plain strain condition for both as-castand annealed samples in aim of determining quantitatively thecorrelation between plastic zone size and characteristic dimplesize on fracture surface. Zr61Cu17.3Ni12.8Al7.9Sn1 monolithic MGwas selected since it shows improved plasticity at room tem-perature upon 1 at.% Sn addition in Zr–Cu–Ni–Al system [12].Poisson’s ratio and excess free volumes for both as-cast andannealed samples were also measured and discussed to gaininsight of this correlation. We report that plastic work is themain source of energy dissipation that determines plastic zonesize and the length scale of structural features on fracture sur-faces.

2. Experimental procedure

ZrCuNiAlSn bulk glassy plates of the dimensions of2.2 mm × 10 mm × 70 mm and 3.1 mm × 8 mm × 70 mm (thick-ness × width × length) were prepared from a master alloy withnominal composition Zr 61 at.%, Cu 17.3 at.%, Ni 12.8 at.%, Al

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and Engineering A 532 (2012) 430– 434 431

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(b)Heating rate: 10 K/min

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Temperature (K )

Fig. 1. (a) XRD patterns taken from the cross-sectional surface, and (b) DSC

g

difference in mechanical response indicates their distinct inher-ent structures. For MGs fractured under plane strain condition,the plastic zone size “C” can be calculated by the equation [25],

C.C. Yuan et al. / Materials Science

.9 at.% and Sn 1 at.% by a conventional water cooled copper mouldasting process. Annealing below glass transition temperatureas performed at 623 K (∼0.95 glass transition temperature, Tg)

or 24 h. This annealing temperature and time was chosen tonsure the glass will be fully relaxed into another quasiequilibriumtate while preventing crystallization [13]. This annealing times much longer than the estimated relaxation time (�) (∼1000 s)or Zr-based MGs when isothermally annealed at 0.95Tg basedn Vogel–Fulcher–Tammann relation [14,15], thus a relativelytable relaxation state can be achieved. The amorphous naturef the as-cast and structurally relaxed samples was ascertainedy X-ray diffraction (XRD) with Cu K� radiation and differentialcanning calorimetry (DSC). Fracture toughness was measuredhrough three-point bending (3PB) tests on electromechanicalNSTRON 3384 and SANS 5104 equipments. The quasi-static load-ng rate is 0.5 mm min−1. Single edge notched (SENB) specimens

ere firstly sectioned from as cast plates, then notched usingn electro-discharge machine, and finally polished by hand. Theatigue pre-crack was conducted on a GZ-100c high-frequencyesonant vibration test equipment at a resonant frequency of61–164 Hz, under a constant load ratio of 0.2. The specimens withimensions of 2 mm × 4 mm × 16 mm and 3 mm × 6 mm × 24 mmthickness × width × span), a notch root radius of ∼100 �m andatigue pre-crack length 0.4–0.7 times of the specimen width weremployed for toughness testing. The crack opening displacementsCOD) was tested under standard condition [16,17]. A monitoringlip gage across the crack mouth was mounted between knifedges and affixed to the front of notch of fatigue pre-crackedample, seen in the inset A of Fig. 2. Yield and fracture strengthas measured under uni-axial compression test using cylindersith a diameter of 2 mm and a length-diameter ratio 2:1 on an

lectromechanical INSTRON 3384 with a strain rate of 1 × 10−4 s−1.he acoustic velocities of bulk MGs were measured using a MATEC600 ultrasonic system. The bulk density, � was measured byhe Archimedean technique within an accuracy of 0.1%. Young’s

odulus E, shear modulus G, bulk modulus B and Poisson’satio � were derived from acoustic velocities and bulk density18].

. Results and discussion

Fig. 1 presents X-ray diffraction and DSC analyses verifying themorphous structure of both as-cast and structurally relaxed orged samples. The clear glass transition feature and crystalliza-ion event(s) of two glasses are characterized in DSC traces at aeating rate of 10 K/min. Thermal parameters such as crystalliza-ion enthalpy and glass transition temperature (Tg) summarizedn Table 1. It can be seen these parameters are not significantlyffected by structural relaxation except the observable reductionf recovery enthalpy (�Hrel) [19], as shown in the inset of Fig. 1b.imilar observations have been reported for other Zr-based metalliclasses [9].

Fig. 2 plots applied load against COD under 3PB test. It cane seen that mechanical response to the structural relaxation isramatic. The as-cast sample displays serrated load-displacementurves, while the relaxed one exhibits more directly broken.t has been reported that the toughness is liable to be influ-nced by different sample geometries [20,21] and the radiusf crack tip [21,22], thus two pre-fatigue SENB specimens withimensions 2 mm × 4 mm × 16 mm and 3 mm × 6 mm × 24 mmthickness × width × span) are tested. Fracture toughness or crit-

cal stress intensity factor (KIC) monitored under 3PB experimentsollowing ASTM 399E procedures [23–25] with SENB specimenimensions conformed to plane strain condition [26]. The as-castamples show larger KIC ∼21 MPa m1/2 and the value decreases to

scans (at a heating rate of 10 K/min) of the as-cast and aged samples forZr61Cu17.3Ni12.8Al7.9Sn1 glass. The inset in (b) shows enthalpy recovery measure-ments for both samples.

∼12 MPa m1/2 after annealing at 623 K for 24 h. It can be seen theaged sample still remains a high fraction of fracture toughness, incontrast to the observations of significant drop of this quantity evenunder short time sub-T annealing of ZrTiCuNiBe glasses [9,27]. This

Fig. 2. The applied load and crack opening displacement (COD) of the as-cast andaged samples for Zr61Cu17.3Ni12.8Al7.9Sn1 under 3PB. Inset A shows a standard 3PBspecimen; inset B displays a typical fatigue pre-crack extending from the notch root.

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432 C.C. Yuan et al. / Materials Science and Engineering A 532 (2012) 430– 434

Table 1Tg , Tx and crystallization enthalpy (�Hx) measured by DSC, yield strength (�y) and fracture strength (�f) measured by compression, and elastic moduli, Poisson’s ratio (�)and bulk density (�) measured by ultrasonic method for Zr61Cu17.3Ni12.8Al7.9Sn1 glass in its as-cast and aged states, respectively.

Zr61Cu17.3Ni12.8Al7.9Sn1 Tg (K) Tx (K) �Hx (kJ mol−1) �y (GPa) �f (GPa) E (GPa) B (GPa) G (GPa) � � (g cm−3)

Cs∼

afaeritAds[p

FZi

As-cast 657 733 3.755 1.68

Aged (623 K, 24 h) 660 732 3.741 1.80

= (1/4�)(KIC/�0)2[(1 − 2�)2 + (3/2)], where �0 refers to fracturetrength [12]. The calculated C is ∼20 �m for as-cast MGs and6 �m for the aged one, respectively.

Fig. 3 displays typical fracture morphologies of as-cast andnnealed samples. Zone A (fatigue surface), B (bend fracture sur-ace) and the interface between two zones can be distinguishedlong the rough fracture surface, seen in Fig. 3a and b. It is inter-sting to note that Suh et al. observed a smooth featureless shearegion between Zones A and B, the distinct thin interface in Fig. 3ndicates the fatigue pre-crack specimens used in our study frac-ure in a pure opening mode, rather than in a mixed mode [28].t the fatigue stage, the cracks propagate along a ripple-like route

ue to cyclic crack-tip blunting and resharpening and the fatigueurfaces exhibit peak-to-valley striation patterns (Fig. 3c and d)29–31]. While at the overload stage, the fracture surfaces dis-lay characteristic peak-to-peak dimple patterns (Fig. 3e and f),

ig. 3. The fatigue striations and overload crack surfaces under 3PB test for as-cast (a, c,

one “B” marks overload fracture surfaces (e and f). The distinct thin interface between Zn our study fracture in a pure opening mode rather than in mixed modes.

1.77 77.4 102.6 28.2 0.374 6.8011.90 83.9 98.9 30.9 0.358 6.852

indicating two samples both fracture under the same mechanismthough the aged one displays much smoother overload fracturesurface. This dimple morphology is formed by massive flow ofsoftened material at the crack tip originating from Taylor’s menis-cus instability [5]. The size of dimple-like structures on fracturesurface can be defined as “w” which can be derived from the sta-tistical average spacing between ridges of dimples surroundingthe center of each dimple zone. It can be seen the value of wfor the as-cast sample is ∼16 �m, while it is ∼5 �m for the agedone, only 1/3 of the as-cast one. It is important to note here thatthe ratio is almost the same as that of the calculated plastic zonesize. The correlation suggests these two length scales of dimple

pattern size and plastic zone size originate from a common mech-anism. In addition, the effects of structural relaxation on fracturebehaviors can be demonstrated by the drastic change of character-istic size of dimple patterns on fracture surfaces.

e); for sub-Tg aged (b, d, f) samples. Zone “A” marks fatigue surfaces (c and d) andone “A” and Zone “B” demonstrates that the samples with sharp fatigue pre-crack

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[31] B.C. Menzel, R.H. Dauskardt, Acta Mater. 54 (2006) 935–943.[32] �p is usually around 1000 times �s or 3 orders of magnitude larger than the

C.C. Yuan et al. / Materials Science

To understand the underlying physics of this correlation, frac-ure energy and free volumes were calculated based on fractureoughness and recovery enthalpy measurements. It is well knownhat fracture energy can be dissipated via crack branching, multi-le shear banding, local plastic deformation, sound emission ando on. A clear observation of dimple pattern features is usuallyampered by mixed stress states and fracture energy dissipationechanisms. The exact dominant energy dissipation mechanism

uring crack propagation in steady state depends on given stresstates (including sample geometry) and intrinsic material prop-rties. For quasi-brittle BMGs showing marginal plastic strain,racture toughness under plane strain condition can be simplifieds [32]: KIC ≈

√E�p, where KIC mainly depends on plastic work

�p) which is much larger than �s (here �s refers to fracture sur-ace energy) under quasistatic condition. Thus, the plastic work is:p ≈ K2

IC/E. The calculated �p is 5.7 kJ m−2 and 1.7 kJ m−2 for thenvestigated as-cast and aged samples, respectively, orders of mag-itude larger than typical surface energy (∼1 J m−2) for metalliclloys. This large difference indicates local plastic deformation ishe dominant energy dissipation mechanism as MG breaks. Moremportantly, the ratio of �p is ∼3 for as-cast and aged samples. Recallhe value of w for the as-cast sample is 3 times of the relaxed one.his is the clear evidence that �p determines the length scale ofimple-like structures on crack surface fractured in mode I for aiven MG.

The fracture process has been described as a series of bondeconfiguration events related to Poisson’s ratio and the produc-ion of free volumes at the crack tip [2,33]. The excess free volume�x) frozen in glass can be indirectly measured by following equa-ion [34]: �x ∝ �Hrel =

∫(dQ/dt)dT , where �Hrel is the relaxation

nthalpy change on DSC curves. The visible reduction of free volumender structural relaxation manifested as �Hrel can be observed

n the inset of Fig. 1b and in Table 1. The free volume reduc-ion corresponds to the increase of bulk density from 6.801 to.852 g cm−3, as shown in Table 1. Recent investigations suggesthat amorphous structure of MGs be made up of weakly bondednd strongly bonded regions [35,36], which introduces the fluc-uations of inherent atomic density [37] and relates them to thenhomogeneity properties of the material. The fluctuations of den-ity will provide a chance for cavities nucleation, and plentiful freeolumes will improve this probability. More free volumes can beggregated in as-cast glass by the growth and coalescence of cav-ties, which produces larger dimple size on fracture surfaces andissipates more energy through local plastic deformation. Struc-ural relaxation will reduce excess free volumes due to the collapsef the weakly bonded regions into a denser packing, the nucle-tion and growth of void-like features at crack tip will be limitedor the aged glass, which causes the decrease of the characteristicimple pattern size as well as the plastic zone size, as observed

n experiments on metallic glasses. On the other hand, among thearious microscopic and fundamental properties of materials, G/Br � provides a measure of the ability of growth and coalescencef cavities by competition of shear flow and dilation [4]. A higheroisson’s ratio promotes the plastic zone size in the vicinity of crackip as evidenced by finite element analysis [38]. This is comparedell with our experimental observations. It can be seen in Table 1,

increases from 28.18 GPa to 31.01 GPa after annealing while Beduces from 102.55 GPa to 98.91 GPa, which leads to the increasef G/B from 0.274 to 0.314 and decrease of Poisson’s ratio � from.374 to 0.358. Similar observations have been recorded in otheretallic glasses [4,9,39]. The relaxed structure prevents shear plas-

ic flow by decreasing Poisson’s ratio, which explains the observededuction of fracture energy and plastic zone size since local shearill dissipate much more fracture energy and produce larger dim-

le patterns through more degree of local necking in the vicinity ofrack tip. [

ngineering A 532 (2012) 430– 434 433

4. Conclusion

In summary, we demonstrate that the mechanical length scaleor plastic zone size of bulk MGs can be conveniently and quantita-tively evaluated by the size of the dimple patterns on pure mode Icrack surfaces. The underlying mechanism can be understood thatplastic work energy scales with plastic zone size through cavitiesnucleation and growth mechanism at the crack tip of glass materialsand this size correlates with structural feature size on the fracturesurface of a MG. This mechanism was further verified by changingthe amount of plastic work energy dissipation during facture bystructural relaxation.

Acknowledgements

We thank W.H. Wang, D.Q. Zhao, M.X. Pan, H.Y. Bai, P. Wen fordiscussions, H.B. Ke for DSC, K.H. Jiang and X. X. Xia for tough-ness measurements. Support from the Hundred Talents Programof the Chinese Academy of Sciences, the NSFC (No. 51071171), andthe 973 programs (Nos. 2010CB731603 and 2011CB012806) areacknowledged.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.msea.2011.11.008.

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