Indentation Studies on Y2O3-Stabilized ZrO2: II, Toughness Determination from Stable Growth of Indentation-Induced Cracks

Stable indentation cracks were grown in four-point bend tests to study the fracture toughness of two Y₂O₃-stabilized ZrO₂ ceramics containing 3 and 4 mol% Y₂O₃. By combining microscopic in situ stable crack growth observations at discrete stresses with crack profile measurements, the dependence of toughness on crack extension was determined from crack extension plots, which graphically separate the crack driving residual stress intensity and applied stress intensity factors. Both materials exhibit steeply rising R -curves, with a plateau toughness of 4.5 and 3.1 Mpa·m^1/2 for the 3- and 4-mol% materials, respectively. The magnitude of the plateau toughness reflects the fraction of tetragonal grains contributing to transformation toughening.     

Influence of Surface Stress on indentation Cracking

A simple, two-dimensional fracture mechanics analysis was used to determine the influence of nonuniform residual surface stresses on the formation of radial indentation cracks. The indentation behavior depends on the depth of the compressive stresses, such that the apparent fracture toughness passes through a maximum with increasing indentation load. The analysis was used to estimate the surface stress from indentation data for a zirconia-toughened ceramic and was compared to previous X-ray diffraction measurements of this stress. The comparison gives only fair agreement; the sources of possible error are discussed. Such surface stresses also influence the accuracy of K _{I C} measurements when an indentation crack length technique is used; surface preparation is a critical factor in the measurement. Finally, the K _{I C} values obtained from indentation crack sizes were compared with those obtained by the double-cantilever-beam technique.     

Effect of Precrack "Halos" on Fracture Toughness Determined by the Surface Crack in Flexure Method

The surface crack in flexure method, which is used to determine the fracture toughness of dense ceramics, necessitates the measurement of precrack sizes by fractographic examination. Stable crack extension may occur from flaws under ambient, room-temperature conditions, even in the relatively short time under load during fast fracture strength or fracture toughness testing. In this article, fractographic techniques are used to characterize evidence of stable crack extension, a "halo," around Knoop indentation surface cracks. Optical examination of the fracture surfaces of a high-purity Al₂O₃, an AlN, a glass-ceramic, and a MgF₂ reveal the presence of a halo around the periphery of each precrack. The halo in the AlN is merely an optical effect due to crack reorientation, whereas the halo in the MgF₂ is due to indentation-induced residual stresses initiating crack growth. However, for the Al₂O₃ and the glass-ceramic, environmentally assisted slow crack growth is the cause of the halo. In the latter two materials, this stable crack extension must be included as part of the critical crack size to determine the appropriate fracture toughness.     

Effect of Indenter Geometry on Controlled-Surface-Flaw Fracture Toughness

Fracture toughness values obtained using both Knoop and Vickers-indentation-produced controlled surface flaws were compared as a function of indentation load for a well-characterized glass-ceramic material. At the same indentation load, Knoop cracks were larger than Vickers. As-indented K_c values calculated from fracture mechanics expressions for surface flaws were higher for Knoop flaws than Vickers, but both types gave low K_c values due to indentation residual stress effects. Analysis suggested that theoretical formalisms for indentation residual stress effects based on fracture mechanics solutions for a center-loaded penny crack in an infinite medium should apply to both indentation types. K_c values calculated using the residual stress approach were identical for Knoop and Vickers controlled surface flaws when a "calibration" value for a constant term in the expression for K_c was used for both indentation types.     

Slow Crack Growth from Controlled Surface Flaws in Hot-Pressed Si3N4

The elevated-temperature slow-crack-growth behavior of HS-130 Si₃N₄ was studied by extending "controlled" surface cracks in bars loaded in 4-point bending. Several such nonin-teracting cracks were produced on the tensile surfaces of bend bars by Knoop microhardness indentation. The stress and dimensions of the subcritically growing cracks were used to calculate the stress-intensity factor, K₁ , from fracture-mechanics formulas for semielliptical surface cracks in bending. The crack-growth velocity, v, was obtained by dividing crack extension by loading time interval. The data indicated very large scatter in measured velocities for given K₁ values, which was interpreted as due to the interaction of the small cracks with local material heterogeneities. No simple functional relation between K _I and v could be established for HS-130 Si₃N ₄ from the v − K ₁ data.     

Damage resistance and R-curve behavior of multilayer Al2O3/SiC ceramics

Damage resistance and R-curve behavior of multilayer Al₂O₃/SiC ceramics were evaluated in bending by the indentation-strength and the single-edge-notched-beam methods. Due to the crack deflection at the Al₂O₃/SiC interfaces, a plateau indentation strength response was achieved, suggesting an exceptional resistance to contact-induced damage. Moreover, fracture toughness was observed to increase from 8.0 to 15.5 MPa m^1/2 with increasing notch depth from 0.5 to 2.0 mm, indicative of a strong R-curve behavior.     

Determination of Fracture Toughness at High Temperatures after Subcritical Crack Extension

As a consequence of R -curve behavior, ceramic materials may exhibit increased fracture toughness ( K _Ic) following slow crack extention. In this investigation, the effect of crack propagation on fracture toughness is studied in static bending tests. For the calculation of stress intensity factors ( K _I) the stress distribution must be known at the moment of fracture. As a consequence of creep, this stress distribution must deviate from the linear distribution. The corresponding stress intensity factors are computed using the fracture mechanical weight function. Experimental results for fracture toughness are communicated for a 2.5%-MgO-doped hot-pressed Si₃N₄ at 1300°.     

R-Curve Behavior of a Polycrystalline Graphite: Microcracking and Grain Bridging in the Wake Region

The contributions of nonlinear fracture processes both in the microcracking frontal process zone and in the following wake region and of grain bridging to crack-growth resistance parameters are discussed in terms of the R-curve behavior of an isotropic polycrystalline graphite. The R-curve behavior of the graphite is characterized by rapidly increasing values at the initial stage of crack extension (Δa≤1 to 2 mm) followed by a steady-state plateaulike region and then a distinct decrease when the primary crack tip approaches the end surface of the test specimen. Scanning electron microscopy of fracture mechanics specimens revealed a dominant role of grain bridging in the following wake regions on the rising R-curve behavior and confirmed the significant size effect of the large-scale microcracking process zone on the falling R-curve behavior. The stress-derived fracture toughness (K_R) and the energy fracture toughness (R_c) are discussed in relation to the micro-cracking residual strain.     

Mixed-Mode Fracture of Hot-Pressed Si3N4

The mixed-mode fracture of hot-pressed Si₃N₄ was investigated using inclined indentation surface flaws in bending and large crack geometries in combined tension/torsion. Non-coplanar fracture was observed in all cases. Values of K_Ic, K_IIc, and K_IIIc stress intensity factors were obtained, with ratios K_IIc/K_Ic= 0.79 and K_IIIc/K_Ic= 1.55 observed. For large cracks, mode II conditions had more of an effect on mode I fracture than mode III conditions. The mixed-mode I-II fracture of surface flaws was significantly different from that for large cracks, suggesting surface flaw shear resistance effects. A model describing these effects was derived, based on the ratio of the crack-opening displacement to the crack surface asperity height.     

Short-Crack Fracture Toughness of Silicon Carbide

The fracture toughness of four different silicon carbides was measured using single-edge precracked beam (SEPB) and indentation/strength techniques. Two were development grades with similar microstructures and chemistries, and yet exhibited different fracture modes. The grade that exhibited a predominantly intergranular fracture had an SEPB fracture toughness (6.4 MPa√m) 88% higher than the one that showed primarily a transgranular fracture (3.4 MPa√m). The higher fracture toughness was associated with a modest increase in average strength (25%), although there was a significant increase in the Weibull modulus (11–32). Fracture toughness at short crack lengths was assessed by an indentation method that used fracture strengths, crack lengths at fracture, and a new method of estimating the constant δ that characterizes the residual driving force of the plastic zones based on the stable growth of the indentation cracks from the initial ( c ₀) to the instability ( c ^*) lengths. The results showed a rising crack-growth-resistance behavior for the grade exhibiting intergranular fracture, while the grade showing transgranular fracture had a flat crack-growth resistance. Tests on two commercial grades of silicon carbide showed similar behaviors associated with the respective fracture modes.     

Transformation Driving Force for Indentation Cracking in Zirconia Ceramics

The transformation driving force for indentation cracking in phase-transformation-toughened ZrO₂ ceramics is confirmed with the direct crack measurement method. This driving force is produced by expansion of the plastic zone beneath the indenter due to stress-induced transformation, and it promotes the extension of the indentation cracks. The driving force cannot be neglected when evaluating the indentation fracture toughness of the materials.     

Evaluation of Bridging Stress from R-Curve Behavior for Nontransforming Ceramics

Bridging stresses at the crack interface behind the crack tip are calculated for nontransforming ceramics which show increasing toughness with crack extension (R-curve behavior). With this approach, bridging stresses can be related analytically to the experimental R curve. Sample calculations for SiC-whisker-reinforced Al₂O₃, with a bridging-zone length of >0.5 mm, are shown in the present study. The results indicate that the bridging stress has a maximum value within a short distance (<0.01 mm) behind the crack tip and then decreases to 0 or levels off to a finite value at the end of the bridging zone depending upon the nature of the R-curve behavior.     

Measurement of the Fracture Toughness of Ceramic Materials Using a Miniaturized Disk-Bend Test

The fracture toughness of several ceramic materials has been measured using a miniaturized disk-bend test apparatus and methodology based on small disk-shaped samples 3 mm in diameter. The method involves the Vickers indentation of specimens ranging in thickness from 300 to 700 μm, and testing them in a ring-on-ring bending mode. New experiments on a glass-ceramic (GC) and Si₃N₄ have been performed to demonstrate the validity of the technique, supplementing the original work on ZnS. The fracture resistances of these materials increase with increasing crack length ( R -curve behavior). The data are analyzed using a specific model for the relationship between fracture resistance and crack length; this model enables the R -curve behavior to be treated analytically, and the fracture resistance at "infinite" crack length to be evaluated using a straightforward graphical procedure. The resulting values of the fracture toughness for ZnS, GC, and Si₃N₄ are 0.74 ± 0.02, 2.18 ± 0.09, and 4.97 ± 0.07 MPa-m^1/2, respectively, which are all in very good agreement with values obtained from conventional fracture toughness tests on large specimens. The results verify the utility of the miniaturized diskbend method for measuring the fracture toughness of brittle materials.     

Indentation Damage and Residual Stress Field in Alumina-Y2O3-Stabilized Zirconia Composites

Fracture features, residual stresses, and zirconia transformation are studied in indentation strength specimens of alumina-Y₂O₃-stabilized zirconia (3% mol of Y₂O₃, 3YTZP) ceramics in order to analyze the extension of the indentation damage in the bulk of the specimens. Two compositions, 5 vol% 3YTZP (A5) and 40 vol% 3YTZP (A40), have been prepared by stacking tape-casted tapes and sintering. After indentation with loads ranging from 50 to 300 N, samples were fractured in four-point bending and the fracture surfaces were characterized by scanning electron microscopy. Raman and piezospectroscopic techniques were used to determine the monoclinic zirconia fraction and the residual stresses through the fracture surfaces. In the A5 composition, the indentation damage morphology was clearly half-penny, whereas the A40 composition presented Palmqvist crack formation. Zirconia transformation was only observed in the plastically deformed zones underneath the imprints whereas there were significant residual compressive stresses outside the plastic zones due to the indentation damage. The intensity of this residual compressive field was dependent on the level of zirconia transformation due to indentation damage because zirconia transformation induced tensile stress fields superimposed on the compressive stresses.     

Subcritical Crack Growth of Macrocracks in Alumina with R-Curve Behavior

Subcritical crack growth of macroscopic cracks in two Al₂O₃ ceramics is investigated with single-edge-notched bending specimens under constant load. The resulting v - K _I-curves are in complete contrast to the behavior of natural cracks. In spite of the monotonic increase of the externally applied stress intensity factor due to crack extension, the crack growth rates first decrease. This behavior is caused by crack shielding due to crack border interaction and can be described by a rising crack growth resistance. Two methods are applied to determine the R -curve under subcritical crack growth conditions.     

Grain-Size Dependence of Fracture Energy in Ceramics

A simple model incorporating thermal elastic anisotropy stresses is used to calculate the microcrack zone size around cracks in Al₂O₃. It is found that the ratio of microcrack zone size to grain size is almost constant for notched beam tests, but increases with grain size for double cantilever beam data. It is suggested that notched-beam ratios of fracture toughness are related to crack initiation, whereas double cantilever beam values are related to propagation and reflect R-curve behavior of the material.     

Indentation Fracture Response and Damage Resistance of Al2O3-ZrO2 Composites Strengthened by Transformation-Induced Residual Stresses

Indentation fracture behavior of three-layer Al₂O₃-ZrO₂ composites with substantial compressive residual stresses was compared with the behaviors of monolithic Al₂O₃ and Al₂O₃-ZrO₂ ceramics without intentionally introduced residual stresses. The indentation cracks were smaller in the three-layer specimens relative to the monolithic specimens in agreement with the predictions of indentation fracture mechanics theory. Indentation and strength testing were used to show that a residual compressive stress of approximately 500 MPa exists in the outer layers of the three-layer composites. The three-layer specimens showed excellent damage resistance in that the strength differential between the three-layer and monolithic indented specimens was maintained at indentation loads up to 1000 N, the maximum indentation load used in the experiments.     

Crack-Growth Resistance-Curve Behavior in Silicon Carbide: Small versus Long Cracks

Crack-growth resistance-curve (R-curve) behavior for small (<400 μm) surface cracks and long (>3 mm) through-thickness cracks is examined in two silicon carbide (SiC) ceramics that have sharply contrasting fracture properties. The first, an in-situ toughened material designated ABC-SiC, fails by intergranular fracture, whereas the second, a commercial SiC (Hexoloy SA), fails by transgranular cleavage. In the former microstructure, hot pressing with aluminum, boron, and carbon additives yields a network of plate-shaped grains, and the presence of an amorphous grain-boundary film that is ∼1 nm thick promotes debonding and crack deflection. The resultant grain bridging generates R-curve toughening; in contrast, no evidence of crack-tip shielding is observed in Hexoloy SA. R-curve behavior has been evaluated using two techniques for the different crack-length regimes: a small-crack R-curve has been deconvoluted from indentation-strength data and a long-crack R-curve has been directly measured using fatigue-precracked, disk-shaped compact-tension specimens. Although Hexoloy SA fails catastrophically at <3 MPa.m1/2, ABC-SiC exhibits much-improved flaw tolerance with significant rising R-curve behavior and a steady-state fracture toughness of ∼9 MPa.m1/2 after crack extension of ∼600 μm. In ABC-SiC, however, differences in the behavior of long and small cracks exist for crack sizes of less than ∼120 μm, with the small-crack measurements demonstrating much-reduced crack-growth resistance; this effect is not observed in Hexoloy SA. Microstructural sources of this behavior are discussed.     

Effect of Surface Flaw Size on Fracture Strength of Alumina Ceramics

Semielliptical surface flaws of different sizes were introduced into Al₂O₃ by Knoop microhardness indentation. The specimens were fractured by four-point bending and the profiles of the indentation flaws were determined by observing the fracture surfaces with a scanning electron microscope. The relation between the indentation flaw size and the fracture strength could be well explained by applying the fracture-mechanics analysis for semielliptical surface flaw in bending. The calculated values of the as-indented critical stress intensity factor, K_IC, were lower than previously reported presumably because of the influence of the residual stresses produced by the indenter.     

Mechanical Behavior of a Borosilicate Glass Under Aqueous Corrosion

In France, fission products are being vitrified for a possible final geological disposal. Under disposal conditions, corrosion of the glass by groundwater as well as stress corrosion because of stresses occurring at surface flaws cannot be excluded. Within this framework, the mechanical behavior of the French simulated nuclear waste glass SON68 was studied by Vickers indentation and fracture experiments in air and in a corrosive solution. The glass was corroded at 90°C in a solution enriched with Si, B, and Na. The results showed that the glass corrosion enhances the cracks propagation relative to experiments in air. The indentation fracture toughness ( K _{I C} ) obtained using a four-point bending test showed that the K _{I C} of the glass decreased with increasing corrosion time.