Strength And Toughness Of Nanocrystalline SiO Stishovite .

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Strength and toughness of nanocrystalline SiO2 stishovite toughenedby fracture-induced amorphizationKimiko Yoshida a, Norimasa Nishiyama b, Masato Sone a, and FumihiroWakai *aLaboratory for Materials and Structures, Institute of InnovativeResearch, Tokyo Institute of Technology, R3-23 4259 Nagatsuta, Midori,Yokohama, 226-8503, Japanb Deutsches Elektronen-Synchrotron (DESY), Notkestr. 85, 22607 Hamburg,GermanyaAbstractThe finding of “fracture-induced amorphization” innanocrystalline SiO2 stishovite lead to a proposal of a new type oftransformation toughening by the direct transition from crystal toamorphous state, which is different from the classical martensitictransformation of zirconia. Here, we investigated strength andtoughness of nanocrystalline stishovite by using micro-cantileverbeam specimens of different sizes. The maximum strength of 6.3 GPagave the estimate of the lower bound of critical stress foramorphization, which was much higher than the criticaltransformation stress of zirconia. The crack growth resistancecurve (R-curve) rose steeply with crack extension of only a few m,and reached to a plateau value of 10.9 MPa m1/2. We discussed theeffects of grain size, microstrain, and dislocation density on thecritical stress, the transformation zone width, and thereby, thefracture toughness.Keywords: Ceramics; Fracture mechanisms; Nanocrystalline material;1

Phase transformation;* Author to whom correspondence should be addressed.Tel.: 81-45-924-5361; fax: 81-45-924-5390.E-mail address: wakai.f.aa@m.titech.ac.jp (F. Wakai)2

1. IntroductionSilica (silicon dioxide, SiO2) is a common mineral found in manyrocks and sands. More than 90 % of the Earth’s crust is composed ofsilicate minerals. Among them, quartz and silica glass are widelyused because they are hard and transparent. However, they arebrittle and easily broken. Stishovite is a high-pressure polymorphof silica stable at pressures above 9 GPa, and metastable atambient conditions [1]. Stishovite has a denser structure thanquartz, and has the highest hardness (33 GPa) of anystable/metastable oxide under ambient temperatures [2]. Hardmaterials with limited ability of plastic deformation tend to bebrittle, then, the fracture toughness K IC of a single crystal is1.6 0.3 MPa m1/2 [3], which is not very high compared with that ofsilica glass (0.8 0.3 MPa m1/2) [4]. Recently, Nishiyama [5] foundthat a nanocrystalline SiO2 stishovite with the grain size of 100nm had a fracture toughness of 13 3 MPa m1/2 by indentationfracture method (IF method [6]). This nanocrystalline material wassynthesized by crystallization of silica glass at 15 GPa and 1473K, in other words, the brittle glass is transformed to the noveladvanced ceramics, which is tough and very hard, by the highpressure synthesis.At fixed synthesis pressure of 15 GPa, microstructures andmechanical properties of stishovite depend on the synthesistemperature. The average grain size increased with increasing thesynthesis temperature. Williamson-Hall analysis revealed the3

microstrain was 0.4 %in the sample synthesized at 1473 K, anddecreased with increasing the synthesis temperature. TEMobservation showed that dislocation density decreased withsynthesis temperature. The fracture toughness also decreased withsynthesis temperature, then, the fracture toughness ofnanocrystalline stishovite increased with decreasing the grain size[5]. This effect of grain size on fracture toughness of stishoviteis opposite to the behavior expected from the toughening mechanismby crack bridging [7], e.g., in alumina [8] and silicon nitride[7].The fracture toughness of zirconia (ZrO2)-based ceramics can beenhanced by martensitic transformation in the stress field ofpropagating cracks [9-11]. In analogy to the transformationtoughening [12-14], Nishiyama [15] proposed a toughening mechanismby fracture-induced amorphization. Transformation of metastablestishovite with six-fold coordination to the stable phase withfour-fold coordination often occurs through intermediate amorphousstate, because the Gibbs free energy of stishovite is higher thanthat of amorphous SiO2 at any temperature above 0 K at ambientpressure [16]. The direct transition of crystal to amorphous state,which is analogous to melting, is triggered by heating at 1 bar[17], or decompression at room temperature. Here, the termamorphization/vitrification is used below the glass transitiontemperature, and the term melting is used above it. Theamorphization is induced by fracture since the tensile stress,4

which is equivalent to negative pressure, can be very large at thecrack tip. The formation of amorphous phase with the thickness of afew tens of nanometers was observed on the fracture surface by Xray absorption near edge structure (XANES) spectroscopy.Furthermore, fracture toughness increased with the amount ofamorphous silica near the fracture surface [15].Brittle ceramics can be toughened by crack-tip shielding whichreduces the stress intensity factor experienced at crack tip. Thiseffect depends on crack size, then, crack growth resistanceincreases with crack extension [18, 19]. Yoshida et al. [20]developed a micro-mechanical test method using micro-cantileverbeam specimens to determine the very early part of resistance curve(R-curve) of nanocrystalline stishovite, and showed that crackgrowth resistance increased from 4 MPa m1/2 to 8 MPa m1/2 with crackextension of only one micrometer. The effect of tougheningmechanism is described by a stress intensity change K between theapplied stress intensity factor and the stress intensity factor atthe crack tip, which is assumed to be equal to the intrinsictoughness K 0 . In the transformation toughening, the extent of Kis given by [13] K 0.22EVf T h1 (1)where E is Young’s modulus, is Poisson’s ratio, V f is the volumefraction of transformed phase in the transformation zone, T is thedilatational strain accompanying transformation, and h is thetransformation zone width. From Eq. (1), fracture resistance can be5

increased significantly by the amorphous layer with the thicknessof 10–50 nm, because the volumetric strain associated with theamorphization of stishovite is from 60 to 90 %, which is muchlarger than that in the tetragonal to monoclinic transformation ofzirconia (4 %). The effect of crack shielding K increases withcrack extention a , and saturates to Eq. (1) at a certain cracklength a* 10h [12]. The sharply rising R-curve is the result ofvery narrow transformation zone width of nanocrystallinestishovite. Materials with rising R-curve lead to an increase inthe strength, in many cases, the steeper the initial R-curve, thehigher the strength [21].The objective of the present paper is to study strength andtoughness of nanocrystalline stishovite, so as to clarify theeffect of microstrain on R-curve behavior. We used a large microcantilever beam specimen to study how R-curve rises and attains toa steady-state (plateau) value. We show the crack growth resistancereaches to more than 11 MPa m1/2 with crack extension around 8 m.The lower bound of the critical stress for amorphization is alsodiscussed from the fracture strength.2. Experimental procedure2.1. MaterialsNanocrystalline stishovite sample was synthesized by a Kawaitype multi anvil high pressure apparatus (LPR 1000-400/50, MaxVoggenreiter GmbH, Germany). The starting material was pure bulk6

silica glass, whose dimension was 2.5 mm in diameter and 0.6 mm inheight. All the impurities were less than 0.1 ppm except OH (about800 ppm). The pure bulk silica glass was heated rapidly from 723 Kto 1473 K under high pressure, 15 GPa. After holding at 1473 Keither for0.5 h or 5 h, temperature was decreased to 723 K, anddecompression was started [5]. The average grain size of sample wasdetermined by TEM observation, and microstrain was evaluated by Xray diffraction pattern using Williamson-Hall method [22].3 mol% Y2O3-stabilized tetragonal zirconia polycrystals (3YTZP) and alumina (Al2O3) samples were sintered using a spark plasmasintering machine (SPS-515S, Fuji Electronic Industrial). Thetemperature was measured by a radiation thermometers at surface ofa graphite die. 3Y-TZP sample was sintered from commercial zirconiapowders stabilized with 3 mol% Y2O3 (TZ3Y, Tosoh Co. Ltd., Japan).As-received powder was heated directly to 1673 K under a uniaxialpressure of 50 MPa. The heating rate was 50 K/min to sinteringtemperature, and holding 5 min at the temperature. Alumina samplewas sintered from commercial α-alumina powder (TM-DAR, TaimeiChemicals Co. Ltd., Japan). As-received powder was heated under auniaxial pressure of 80 MPa. The heating rate was 25 K/min from 873K to 1273 K, and 8 K/min to 1423 K. After holding for 20 min at thesintering temperature, sample was annealed at 1273 K for 10 min inorder to reduce the residual stress [23].2.2. Fabrication of micro-cantilever beam specimens7

The micro-cantilever beam specimens (Fig.1 (a)) was machined bya focused ion beam (FIB) machining (HITACHI-FB2100) using a highcurrent Ga ion beam (40 keV, 32 nA), followed by fine machining atlow currents (6 nA). A notch was introduced by using an even finercurrent beam (300 pA) in the direction perpendicular to the notchlength, so that the contamination of Ga ion at the notch root isminimized (Fig.1 (b)). The notch-tip radius was 50 nm (Fig. 1 (c)).The side-grooves were cut to guide the crack (Fig. 1 (d)). Theposition-marks are made on the top surface and the side surface ofthe micro-cantilever beam specimens for easy positioning of theindenter (Fig. 1 (a)). All beam directions in the FIB machining areillustrated in Fig. 1 (e).The thickness of surface layer damaged by ion beam wasestimated by Monte Carlo simulation. When the 40 keV Ga ion beamhitting the stishovite target at a grazing angle of 89 degree, thethickness of damage was less than 20 nm. In this study, thespecimen size was large enough, so that the influence of the ionbeam machining can be neglected.2.3. Micro-sized bending testMicro-sized bending test were carried out in air using amechanical testing machine designed for micro-sized specimen. Thebasic concept of this machine is described in [24]. Thedisplacement was applied by a piezoelectric device at adisplacement rate of 10-50 nm/sec. The load was applied by using a8

spherical diamond indenter with radius of 2.5 m. Load anddisplacement data were acquired with the sampling interval of 0.1second.2.4. Calculation of stress intensity factor and specimen complianceThe stress intensity factor (mode I) K I of a notched microcantilever beam specimen was calculated by the extended finiteelement method (XFEM) using the commercial solver Abaqus 6.13 [20].The stress intensity factors were determined by path-independentcontour integral. Three-dimensional isotropic elastic model wasemployed to simulate the cantilever beam specimens with sidegrooves. The ratio K II K I was less than 5 %.The stress intensity factor of cantilever beam specimen withside-grooves was calculated, and expressed in the followingequationKI PLBBN W32f a W (2)where P is the applied force, L is the distance between the notchand the loading point, a is the crack length, W is the cantileverwidth, B is the thickness, and B N is the minimum thickness measuredat the root of the side grooves. The dimensionless shape factor canbe used in the range 0.2 a W 0.7 for the cantilever beam specimenswith side grooves ( H : L : W : B 1:3:1:1, B N 0.8 B ), where H is thedistance between the notch and the root of the cantilever beam9

af W a 2.2996 7.6061 W234 a a a 61.404 193 .33 229 .22 . W W W (3)The compliance C u P is expressed as2 a L C fC E BB N W W 8E E1 2(4)(5)where ν is Poisson’s ratio. The dimensionless shape factor for thecompliance f c is given as0.2112.0172 a f C 2.3235 .(1 a / W ) (1 a / W ) 2 W (6)The crack length is expressed as a function of b 1 /a 0.8866 0.9826b 18.357b 2 56.933b 3 68.099b 4 .WfC(7)The micro-sized bending test is carried out by controlling thedisplacement u of the actuatoru u C machine P(8)where u is the displacement of the specimen, and C machine is themachine compliance. The machine compliance was 0.023 μm/mN. Theinitial compliance C ini of notched specimen was obtained from themeasured displacement ( u CP ) and load. The theoretical complianceC calc of the notched specimen was calculated by Eqs. (4) and (5)using specimen dimensions, Young’s modulus of 531 9 GPa, andPoisson’s ratio of 0.21 0.01 [Supplementary data of [5]]. Thedifference between C ini and C calc was within 5 %. The compliancemeasured from the load-displacement curve was calibrated by the10

ratioCcalc Cini . The value of f c was obtained by substituting thecalibrated compliance to Eq. (4), then, the crack length wasdetermined by Eq.(7). For the initial notch length of a0 W 0.5 ,data were taken at the crack extension of a W 0.15 to construct Rcurves in most cases.2.5. Calculation of fracture strengthThe fracture strength of micro-cantilever beam specimenswithout notch were defined as a maximum flexural stress located onthe tensile side of fixed end. According to the simple Euler–Bernoulli beam theory, it is 6 PL BW 2(9)where L is the distance between the fixed end and the loadingpoint. Three types of specimens with width W of 5, 20, 60 mm wereused to study the effect of specimen size on the fracture strength.All specimen had self-similar shape: B W and L 4W .2.6. Effect of side-groove on R-curve testingThe straight crack propagation is necessary to analyze thestress intensity factor by using the compliance method. Fig.2 showsthe fractured micro-cantilever beam specimens with and without sidegrooves. The fracture surface of the specimen without side groovecurved toward the fixed end. On the other hand, the crackpropagated along side-grooves in the specimen with side groove11

depth of 20 % ( B N 0.8 B ), and the fracture surface wasmacroscopically flat. In this study, we used side-grooved specimenswith 20% depth. Furthermore, side-grooves enhance plane strainfracture, i.e., the situation where the crack front remainsstraight as it extends [25, 26].3. Results3.1. Microstructure of nanocrystalline stishoviteTwo nanocrystalline stishovite samples are prepared at 15 GPaand at 1473 K by holding either for 0.5 h or 5 h, which aredesignated as 0.5h sample and 5h sample, respectively. Themicrostructure were observed by transmission electron microscopy(TEM) (Fig.3). The average grain size of 0.5h sample was 128 59nm, and that of 5h sample was 164 58 nm. TEM micrographs showcomplex contrast suggesting the presence of microstrain in thesetwo samples.Themicrostrain was determined by Williamson-Hall method, andplotted as a function of synthesis temperature in Fig. 4. Nishiyamaet al. [5] showed that microstrain decreased with increasingsynthesis temperature. The present data showed similar trend. Atthe synthesis temperature of 1473 K, calculated microstrain was0.34 % and 0.24 % for 0.5h sample and 5h sample, respectively. Themicrostrain decreased 29 % with increasing the holding time, whilegrain size increased 28 %. The grain size and microstrain werealmost the same with the sample synthesized at 1873 K for 0.5 h by12

Nishiyama [Supplementary data of [5]]. However, the samplesynthesized at 1873 K showed heterogeneous microstructure due toabnormal grain growth. In the present study, we compare mechanicalproperties of 0.5h sample and 5h sample, both of which have uniformmicrostructure.3.2. R-curve of nanocrystalline stishoviteFig. 5 (a) shows load ( P )-displacement ( u ) curves of 0.5hsample measured by using notched specimens of different sizes. Thedimensions of specimens are summarized in Table 1. All specimensshowed stable fracture, and the occurrence of unstable fracture wasindicated by the “X” mark. An arrow at the P - u curve of thelargest specimen ( W 60 m) also shows an unstable fracture. TheR-curves were calculated by the compliance method from P - u curvesof stable fracture before “X” mark, and plotted in Fig. 5 (b).While P - u curves depend on the specimen size and the notch length,R-curves were similar in shape for all specimens. The crack growthresistance rose steeply from 4 MPa m1/2 to 8 MPa m1/2 with crackextension of only a few m, and reached to a plateau value of 10.9MPa m1/2. This value was comparable to the fracture toughness (13MPa m1/2) reported by Nishiyama [5].Unstable fracture occurs when the following conditions arefulfilled [21]KI KR(10)dK IdK R. dada(11)13

Stable fracture occurs at the beginning thanks to the very steep Rcurve of nanocrystalline stishovite. Since dK R da decreases to zeroas the crack extends to the plateau region, unstable fractureoccurs at a critical crack length. For a given a W and K I , Eq. (2)predicts that dK I da decreases with increasing the specimen size.Then, from Eq. (11), the region of stable crack growth is extendedby using larger specimens. As shown in Fig. 5 (b), we could observeR-curve behavior at crack extensions close to the plateau region.Fig.6 shows the comparison between R-curves of the 0.5h sampleand that of the 5h sample. For both materials the early part of theR-curves was relatively insensitive to specimen size. The initialR-curve was steeper in 0.5h sample with microstrain of 0.34 % thanin the 5h sample with microstrain of 0.24 %. The plateau value ofthe 5h sample was 9.9 MPa m1/2 which was 1 MPa m1/2 lower than thatof the 0.5h sample.The fracture toughness was also measured by the indentationfracture method (IF method [6]) with 30, 20 and 10 kg loads. Weused scanning electron microscopy to measure crack length preciselyfor comparison between 0.5h material and 5h material. The fracturetoughness was 8.9 0.40 MPa m1/2 and 8.0 0.49 MPa m1/2 for 0.5hsample and 5h sample, respectively. The average fracture toughnessof 0.5h sample was higher than that of 5h sample, although thedifference was small. The crack length was also measured by opticalmicroscope and CCD camera. The values of fracture toughnessmeasured by optical microscopy agreed with previous report [15],14

and was about 1 MPa m1/2 higher than that measured by scanningelectron microscopy.3.3. Strength of nano-crystalline stishoviteThe fracture strengths of nanocrystalline stishovite, 3Y-TZP,and alumina were measured by bending micro-cantilever beamspecimens without notch. The nanocrystalline stishovite specimensshowed brittle fracture. The load-displacement curves had no yieldpoint until fracture. Measured strengths are plotted as a functionof specimen volume in Fig.7 together with the data of singlecrystal [25-27] and polycrystalline [28] silicon measured by microsized test. The volume of a cantilever specimen was defined asV BWL . The strength increased with decreasing the size ofspecimens. This size effect can be explained by Weibull theory forbrittle fracture where the strength is controlled by the defect[29]. When fracture occurs from defects inside the specimen, andthe Weibull modulus m is assumed to be constant, the strengthincreases with decreasing the effective volume VE , which isproportional to the specimen volume V as long as specimens of selfsimilar shape are used f 1 VE 1 m .(12)The slopes of the lines fitted to the data of polycrystallinesilicon gave the Weibull modulus of 5.7, which was smaller than themeasured m-value of 7.5. The plots of stishovite data suggests thatthe Weibull modulus is larger than that of polycrystalline silicon.15

For a fixed specimen volume of 20 20 80 32000 m3, thestrength of nanocrystalline stishovite was higher than that of 3YTZP, alumina, and silica glass. The highest strength was 6.3 GPaand 6.1 GPa for the 0.5h sample and the 5h sample, respectively.The strength of the 0.5h sample was higher than that of the 5hsample, which may be explained by its steeper in

1 Strength and toughness of nanocrystalline SiO2 stishovite toughened by fracture-induced amorphization Kimiko Yoshida a, Norimasa Nishiyama b, Masato Sone a, and Fumihiro Wakai *a a Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, R3-23 4259 Nagatsuta, Midori,

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