Introduction

The enhancement of reliability and damage tolerance are the critical issues for the development of high performance ceramics, which are hard and wear-resistant, but, brittle in nature. The fracture resistance of ceramic materials is increased with crack extension by toughening mechanisms1 such as crack bridging2, microcracking, or phase transformation3,4. Materials with rising resistance-curve (R-curve) lead to an increase in the strength compared to a material with the same intrinsic toughness and a flat R-curve5. The R-curves can be measured by using specimens with macrocracks (mm size) or with microcracks (~100 μm size). R-curves depend on specimen geometry and they are not materials constants6. But, the early part of the R-curve, which is relatively insensitive to specimen geometry, provides the information on factors related to microscopic toughening mechanisms. The evaluation of R-curves with crack extension less than 10 μm is critical for the design of ceramic microstructures with both high strength and high toughness, because the allowable flaw size is small in ceramics7,8,9.

We propose a method to investigate R-curve behavior by using micro-cantilever beam, which has been originally used to measure fracture toughness of amorphous/glass10, thin films11, single crystals12 and grain boundaries13. The micro-cantilever beam technique is applied to study the microscopic crack shielding mechanisms of nanocrystalline stishovite ceramics, which exhibit a large fracture toughness due to fracture-induced amorphization14,15. Stishovite is a high-pressure phase of silicon dioxide (SiO2) stable at pressures above 9 GPa and metastable at ambient conditions16. While low-pressure phases, e.g., quartz and coesite, consist of networks of corner-sharing SiO4 tetrahedra, stishovite possesses the rutile structure and is described as chains of edge-sharing SiO6 octahedra. Stishovite is 60% more compact than quartz and has the highest hardness (33 GPa) of any stable/metastable oxide under ambient temperatures17. Only diamond and cubic boron nitride are industrially used materials that are harder than stishovite. Hard materials with limited ability of plastic deformation tend to be brittle, then, the fracture toughness K1C of a single crystal is 1.6 ± 0.3 MPa m1/2 by the indentation method18. Recently, Nishiyama14 found that a polycrystalline stishovite with submicron grain size had a fracture toughness of 7.9 MPa m1/2 by the indentation fracture method (IF method). Furthermore, a nanocrystalline stishovite with the average grain size of 127 nm had fracture toughness of 13 ± 3 MPa m1/2. The IF method is highly questionable for estimating the accurate fracture toughness value19, but, the results indicate the fracture toughness increases with decreasing grain size. This discovery shows that the nanocrystalline stishovite attains both excellent hardness and toughness which are vital requirements for structural materials.

Transformation of metastable stishovite with six-fold coordination to the stable phase with four-fold coordination often occurs through intermediate amorphous state, because the Gibbs free energy of stishovite is higher than that of amorphous SiO2 at any temperature above 0 K at ambient pressure20. The direct transition of crystal to amorphous state, which is analogous to melting, is triggered by heating at 1 bar, or decompression at room temperature. The terms, amorphization/vitrification and melting are used for the transition below and above the glass transition temperature. The amorphization accompanies a volume expansion up to about 100%. The amorphization is induced by fracture since the tensile stress, which is equivalent to negative pressure, can be very large at the crack tip. The formation of amorphous phase with the thickness of a few tens of nanometers was observed on the fracture surface by X-ray absorption near edge structure (XANES) spectroscopy15. In analogy to the transformation toughening of zirconia where metastable tetragonal phase transforms to stable monoclinic phase at crack tip3,4, the fracture-induced amorphization can be a toughening mechanism of stishovite. In order to understand why the nanometer-thick amorphous layer can increase the fracture resistance significantly, we have investigated R-curve behavior by using micro-cantilever beam specimens.

Results

The nanocrystalline stishovite with the average grain size of 128 nm was synthesized at 1473 K and at a pressure of 15 GPa by using a pure bulk silica glass as the starting material15. For comparison, we have also studied a pure silica (SiO2) glass, a submicron alumina (Al2O3) and 3 mol%-Y2O3 stabilized tetragonal zirconia polycrystals (ZrO2, 3Y-TZP). The full detail of materials and specimen preparations are included in the supplementary information. The micro-cantilever beam specimens with notch were used to measure R-curve behavior in microscopic scale (Fig. 1a). The resulting load (P) – displacement (u) curves are plotted in Fig. 1b. Unstable fracture occurs when the material has a flat R-curve. The principal mechanism of rising crack resistance in alumina is grain-localized bridging, which is more pronounced for coarse-grained materials than for fine-grained materials21, then, the R-curve of fine-grained alumina is almost flat. As expected, pure silica glass and the alumina with submicrometer grain size showed unstable fracture. The stress intensity factor K0 at the crack initiation was 0.8 MPa m1/2 for pure silica glass and 2.8 MPa m1/2 for the alumina. The measured values were in good agreement with the fracture toughness reported by macroscopic tests. In the materials which have rising R-curves, the crack starts propagation at K0 and grows stably and then, unstable fracture occurs at a critical crack extension5. The stable fracture was observed in 3Y-TZP and stishovite. The occurrence of unstable fracture is indicated by the “x” mark. The R-curves were calculated by the compliance method from P-u curves and plotted in Fig. 2a. The dimensions of each specimen and elastic constants used in the analysis are summarized in Supplementary table S1. The crack growth resistance of stishovite increased from K0 = 4 to 8 MPa m1/2 with crack extension about one micrometer. The initial slope ΔK/Δa was 7 MPa m1/2/μm at K0. In 3Y-TZP, the crack growth resistance increased from K0 = 2 MPa m1/2 with the initial slope of 0.2 MPa m1/2/μm. The initial steep rise in toughness has been found also in the silicon nitride (Si3N4) with MgO and Y2O3 as sintering aids by correcting the effect of notch root radius of macroscopic specimens8. The initial slope of stishovite was more than three times steeper than that of the silicon nitride toughened by bridging mechanisms9. The R-curves measured by micro-cantilever beam specimens show only the early part of rising R-curve and cannot be used to determine the plateau value. But, they are advantageous to determine K0 and the initial slope accurately. R-curve behaviors with crack extension of several tens of micrometers are shown for some ceramics in Fig. 2b. The extrapolation of R-curve of stishovite indicates that it can reach the stress intensity factor higher than 10 MPa m1/2, which is close to the fracture toughness measured by IF method. The plateau value of nanocrystalline stishovite is higher than that of the silicon nitride8 and 2 mol%-Y2O3 stabilized tetragonal zirconia polycrystals (2Y-TZP)22. The fracture toughness of nanocrystalline Y-TZP materials increases with increasing grain size and decreasing dopant content. The fracture resistance of 3Y-TZP measured in air was lower than that of 2Y-TZP measured in vacuum due to the susceptibility to subcritical crack growth under humid atmosphere.

Figure 1
figure 1

Micro-mechanical testing.

(a) Geometry of a micro-cantilever beam specimen. The side-grooves were cut to guide the crack. Lower parts show the side view of the notch. (b) Load-displacement curves (P – u curves).

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Figure 2
figure 2

R-curve measurements.

(a) Microscopic R-curve behavior of nanocrystalline stishovite and zirconia (Y-TZP). (b) Macroscopic R-curve behaviors.

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Figure 3 shows SEM micrographs of fracture surfaces of nanocrystalline stishovite (Fig. 3b) and Y-TZP (Fig. 3c). The fracture surface of the nanocrystalline stishovite showed a rough morphology accompanied with many worm-like textures scattered over the whole surface. The dimensions of a “worm” are several tens and hundreds of nanometers in diameter and length, respectively. This feature of nanocrystalline stishovite was quite different from that of the intergranular fracture of Y-TZP. The worm-like textures observed on a micro-cantilever beam specimen of nanocrystalline stishovite had been also observed on a surface of mechanically crushed sample15. The selected-area electron diffraction patters of the worm-like textures had a halo, then, it showed the presence of amorphous phase on the fracture surface15.

Figure 3
figure 3

Fracture surface of micro-cantilever beam specimen.

(a) Specimen geometry. (b) nanocrystalline stishovite. Arrows show some examples of “worms”. (c) Y-TZP.

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Discussion

The effect of extrinsic toughening mechanism is described by a stress intensity change ΔK between the applied stress intensity factor and the stress intensity factor at the crack tip, which is assumed to be equal to the intrinsic toughness K0 of the material. In the transformation toughening, the transformation zone develops upon crack extension by stress-induced transformation as illustrated in Fig. 43,4. The transformation zone width h depends on the critical stress σc for the phase transformation:

The transformation zone width increases with crack extension Δa and then, saturates at Δa* ≈ 5h. The extent of ΔK is proportional to and the dilatational strain εT accompanying transformation (i.e. the volume increase by the transformation):

where Vf is the volume fraction of transformed phase in the transformation zone. From equations (1) and (2), the toughness is expressed as:

The sharply rising R-curve indicates that the transformation zone width h of stishovite is much narrower than that of Y-TZP. This is the evidence that the toughening by fracture-induced amorphization acts in nano- and submicron- scales. The width h of Y-TZP is estimated from the monoclinic phase content measured by Raman microscopy: 4 μm for the grain size of 900 nm and 2 μm for the grain size of 140 nm22. The critical stress σc for transformation determines the transformation zone width h. σc is estimated to be about 1.3 GPa for tetragonal-monoclinic transition in 2Y-TZP23.

Figure 4
figure 4

R-curve behavior by transformation toughening.

The crack-tip stress field is altered by the formation of transformation zone at the critical stress σc. The stress intensity change ΔK by the presence of transformation zone is the origin of the transformation toughening. The amorphization of nanocrystalline stishovite is supposed to nucleate at surfaces, grain boundaries and dislocations near the crack tip.

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As well as stishovite, dense high pressure crystalline silicates, where silicon is in octahedral coordination, transform under tension to a low-density glass composed of tetrahedral silicon. The toughening by fracture-induced amorphization can occur in a number of such materials, for example, CaSiO3 and MgSiO3 perovskites. In the molecular dynamic simulation, high-pressure phases of CaSiO3 and MgSiO3 started amorphization at tensile stress of 18 GPa at 300 K24. This result suggests that the critical transformation stress of stishovite is more than 10 times higher than that of Y-TZP. From equation (1), the transformation zone width of stishovite is estimated to be a few tens of nanometers. This estimate agrees with the experimental observation by the surface-sensitive Si-K XANES measurement15.

The initial slope of R-curve ΔK/Δa is a function of parameter and increases linearly with α approximately25. While the fracture toughness of stishovite was about two times larger than that of Y-TZP, ΔK/Δa of stishovite was 30 times larger than that of Y-TZP. The slope of stishovite is very steep, because it is proportional to the product of εT and σc, both of which are about 10 times larger in stishovite than in Y-TZP. Steep initial slopes are desirable for R-curves because materials that achieve high toughness at small crack length also achieve high strength.

The increase of fracture toughness with decreasing grain size of stishovite is opposite to the behavior expected from the crack bridging effect and the results observed in transformation toughening of Y-TZP26. But, the grain size effect on fracture toughness cannot be separated from other factors such as internal microstrain and dislocation densities14. The microstrain arose during synthesis of stishovite which crystallized from bulk glass at 15 GPa. As the synthesis temperature decreases, the grain size decreases and the microstrain increases.

The amorphization of stishovite is dominantly a heterogeneous nucleation and growth controlled process27,28. The transformation proceeds by nucleation of amorphous at defects, such as grain boundaries, surfaces and dislocations27. Many dislocations were observed in fine stishovite grains by TEM observation11. The origin of dislocations is unknown. One possible explanation is that local deformation occurred during the phase transformation from glass to stishovite at the synthesis pressure29. Dislocation density decreased with increasing the synthesis temperature and then, grain size. It is possible that the fine grain size promotes the amorphization process due to high defect density. Indeed the amount of transformed phase on the fracture surface and the fracture toughness increased with decreasing grain size15. The high density of nucleation sites increases the volume fraction of amorphous phase in the transformation zone, which in turn, enhances the crack shielding effect ΔK in equation (3).

The relation between fracture strength and the critical transformation stress is illustrated in Fig. 5. When the strength is limited by failure from pre-existing flaws, the strength is proportional to fracture toughness. From equation (3), the toughness and then, strength increase as σc decreases. However, as the critical stress decreases, the strength is limited by σc due to the transformation induced deformation4,30. The achievement of peak strength by optimizing σc is the target in the material design of zirconia. In fracture-induced amorphization of stishovite, the volumetric transformation strain εT is from 60 to 95%, while it is about 4% in the tetragonal-monoclinic transition of zirconia. From equation (3), the increase of εT enhances the fracture toughness at a given σc as illustrated in Fig. 5. This effect shows that the peak strength of stishovite can be higher than that of zirconia ceramics. The very narrow transformation width and high critical stress are effective in toughening of stishovite due to large εT.

Figure 5
figure 5

Relation between strength and critical transformation stress σc.

The strength is limited by fracture toughness in the failure from pre-existing flaw region. The strength is limited by σc in the yield limited region.

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In summary, the fracture resistance measurement by using micro-cantilever beam specimens revealed that there exists a toughening mechanism which can operate at nano-scale. The narrow transformation zone in fracture-induced amorphization of nanocrystalline stishovite was very effective to increase the fracture resistance by a crack extension of less than one micrometer. This finding will provide a motivation to search for other nano-scale toughening mechanisms in many structural materials, such as ceramics, composites, nanocrystalline materials and also, synthetic materials with hierarchical architecture.

Methods

Material

Nanocrystalline stishovite samples were synthesized using a Kawai-type multi anvil apparatus15. The dimensions of the starting material (pure SiO2 glass) are 2.5 mm in diameter and 1.4 mm in height. Load was applied first up to 15 GPa under room temperature and the temperature was increased rapidly from ∼450 °C to 1473 K within 30 s at constant load. The temperature was held constant for 30 min. The decompression (3 h) was started when the temperature was decreased to ∼450 °C. The nanocrystalline stishovite contained numerous dislocations.

Mechanical testing

The loading of the cantilever beams is carried out in air using a mechanical testing machine designed for micro-sized specimen. The basic concept of this machine is described in ref. 10. The displacement was applied by a piezoelectric device at a displacement rate of 10 nm/sec. The load was applied by using a spherical diamond indenter with radius of 2.5 μm. The machine compliance was 0.023 μm/mN. Load and displacement data were acquired with the sampling interval of 0.1 second.

Stress intensity factor and compliance of micro-cantilever beam specimen

The stress intensity factor (mode I) KI of a side-grooved cantilever beam specimen in Fig. 1a was calculated by the extended finite element method (XFEM) using the commercial solver Abaqus 6.13. The stress intensity factors were determined by path-independent contour integral. Side grooves were introduced for straight crack propagation under the presence of KII component in cantilever beam test. Three-dimensional isotropic elastic model was employed to simulate the cantilever beam specimens with side grooves (H: L: W: B = 1:3:1:1, BN = 0.8B), where H was the distance between the notch and the root of the cantilever beam. The ratio KII/KI was less than 5%. The critical specimen thickness limit for plane-strain fracture toughness is given as12

The yield stress σy is estimated from Vickers hardness HV according to Tabor’s approximation . The critical specimen thickness is 1.25 μm for stishovite. We used specimens with the thickness B of 20 μm for reliable fracture toughness tests. Furthermore, side-grooves increases the level of constraint, then, promotes a more uniform stress state according to ASTM E399-90.

The stress intensity factor of cantilever beam specimen with side-grooves was calculated and expressed in the following equation:

where P is the applied force, L is the distance between the notch and the loading point, a is the crack length, W is the cantilever width, B is the thickness and BN is the minimum thickness measured at the root of the side grooves. The shape factor can be used for 0.2 ≤ a/W ≤ 0.7:

The compliance C ≡ u/P is expressed as:

where E is Young’s modulus and v is Poisson’s ratio.

The dimensionless shape factor for the compliance fc is given as:

The crack length is expressed as a function of :

The micro-cantilever beam test is carried out by controlling the displacement u′ of the actuator:

where u = CP is the displacement of the specimen and Cmachine is the machine compliance. The crack length is determined by the compliance method using equations (7) and (10).

Additional Information

How to cite this article: Yoshida, K. et al. Large increase in fracture resistance of stishovite with crack extension less than one micrometer. Sci. Rep. 5, 10993; doi: 10.1038/srep10993 (2015).