Method to Estimate Crack-Tip Toughness from Bending Tests on Prenotched Bars

A strain-gauge procedure that enables determination of the crack-tip toughness ( K _I0) from bending-strength tests is described. The procedure is applied to coarse-grained alumina and yields an average K _I0 value of 2.51 MPa·m^1/2, with a standard deviation of 0.16 MPa·m^1/2.     

Error Propagation Biases in the Calculation of Indentation Fracture Toughness for Ceramics

Indentation fracture toughness models generally share the derived parameter Pc ^−3/2, where P is the indentation load and c the measured crack length. Biases, inherent to error propagation through this nonlinear transformation ( c to c ^3/2), can be introduced into calculated values for K _{I C} , depending upon the amount of averaging of crack length data performed prior to the transformation. This work utilizes Monte Carlo simulations to evaluate the bias in K _{I C} calculated using both mean and linear regression methods. Significant positive biases were demonstrated when using mean-based calculations where coefficients of variation (cv) in c exceeded 10%. Regression methods produced significantly less bias. With cv < 10% or when c is averaged per load, both methods produce essentially unbiased estimates for K _{I C} .     

Effect of Alumina on the Strength, Fracture Toughness, and Crystal Structure of Fluorcanasite Glass-Ceramics

The influence of alumina content (0-15 wt% Al₂O₃) on the indentation strength, fracture toughness ( K _{I c} ), and crystal structure of fluorcanasite (Al₂O₃-CaO-F-K₂O-Na₂O-SiO₂) glass-ceramics was analyzed. Increasing the Al₂O₃ content from 0 wt% (CAN0) to 8 wt% (CAN8) caused the mean indentation strength and K _{I c} values to decrease from 213 ± 14 MPa and 2.7 ± 0.1 MPa·m^1/2, respectively, for the CAN0 glass-ceramic to 78 ± 16 MPa and 1.3 ± 0.2 MPa·m^1/2, respectively, for the CAN8 glass-ceramic. Increased Al₂O₃ concentrations (0-15 wt%) significantly affected the crystal size, crystal shape, aspect ratio, and crystal aggregation characteristics of the fluorcanasite glass-ceramics. The addition of greaterthan equal to8 wt% of Al₂O₃ to fluorcanasite glass caused a transformation from canasite to leucite.     

Mixed-Mode Fracture of Ceramics in Asymmetric Four-Point Bending: Effect of Crack-Face Grain Interlocking/Bridging

The mixed-mode fracture of a large-grain-size alumina ceramic and a soda-lime glass is investigated. These ceramics are tested using straight-through precracked or notched specimens. The straight-through precrack is introduced by the single-edge-precracked beam method. Precracked or notched specimens are subjected to combined mode I/II or pure mode II fracture, under asymmetric four-point bending, and pure mode I fracture, under symmetric four-point bending. A pure mode II fracture is never achieved in the precracked polycrystalline alumina by the crack-face friction inevitably induced by grain interlocking/bridging. The crack-face friction in sliding mode reduces the local mode II stress intensity factor in the crack-tip region and produces a sizable amount of mode I deformation. Accounting for the contribution of the crack-face friction to the crack-tip local stress intensity factors, K _I and K _II, in mixed-mode fracture tests, the experimental results of the K _I/ K _{I c} versus K _II/ K _{I c} envelope and the initial angle of noncoplanar crack extension are in good agreement with the theoretical predictions of the maximum hoop-stress theory.     

Effects of an Electric Field on the Fracture Toughness of Poled Lead Zirconate Titanate Ceramics

Compact tension tests and indentation-fracture tests have been conducted to study the effects of an applied electric field on the fracture toughness ( K _{I C} ) of poled commercial lead zirconate titanate (PZT) ceramics. The experimental results show that an applied electric field, either parallel or antiparallel to the poling direction, considerably reduces the K _{I C} value of the PZT ceramics. The reduction in K _{I C} for a negative field is larger than that for a positive field of the same strength. The failure mode in the PZT ceramics is basically transgranular, insensitive to the applied electric field.     

Fracture Toughness of Dental Porcelains Evaluated by IF, SCF, and SEPB Methods

Fracture toughness of six dental porcelains with leucite content ranging from 0 to 22 vol% was evaluated by indentation fracture (IF), surface crack in flexure (SCF), and single edge pre-cracked beam (SEPB) methods. The results of the IF method were similar to those of the SCF method for all the porcelains investigated. The results of the SEPB were similar to those of the other two methods only for the glassy porcelains, but for leucite-based porcelains this method resulted in higher values of K _{I c} . Based on microstructure, fractographic analysis, and an additional single edge V-notched beam test, it was concluded that the pre-crack size influences the value of K _{I c} for porcelains reinforced by leucite. For design and failure analysis purposes, the K _{I c} determined by SCF method should be preferred, since fracture of dental restorations usually starts from small surface cracks.     

Effects of Residual Stress and Loading Geometry on Single-Edge Precracked-Beam (SEPB) Fracture-Toughness Test Results

The single-edge precracked-beam (SEPB) specimen test, using the "bridge indentation" method, is one of the standard test methods in the new ASTM standard for the determination of the fracture toughness of ceramics. In support of this effort, the effect of several test parameters on the fracture-toughness ( K _{I C} ) values was established. The effect of the residual stress, because of the indent and the alignment in three- and four-point bending, on the K _{I C} values was determined using aluminum nitride specimens. The results show that indent loads should be kept below 10 kgf, and the crack-plane angle should be <5°, to prevent artificially high K _{I C} values.     

Enhanced Mechanical Properties of Alumina by Dispersed Titanium Diboride Particulate Inclusions

The mechanical properties of composite ceramics composed of 0 to 20 vol% of titanium diboride particles dispersed in an α-alumina matrix were investigated. The alumina–titanium diboride composite powder was hot-pressed at 1470°C for 20 min to achieve over 98.8% of the theoretical composite density. The strength and fracture toughness of the twophase, hot-pressed composite were both significantly improved compared to the single-phase alumina. Results from different methods of measuring the stress intensity factor, ( K _{I c} ) are compared and discussed.     

Mode I Fracture Toughness of a Small-Grained Silicon Nitride: Orientation, Temperature, and Crack Length Effects

The Mode I fracture toughness ( K _{I C} ) of a small-grained Si₃N₄ was determined as a function of hot-pressing orientation, temperature, testing atmosphere, and crack length using the single-edge precracked beam method. The diameter of the Si₃N₄ grains was <0.4 µm, with aspect ratios of 2–8. K _{I C} at 25°C was 6.6 ± 0.2 and 5.9 ± 0.1 MPa·m^1/2 for the T–S and T–L orientations, respectively. This difference was attributed to the amount of elongated grains in the plane of crack growth. For both orientations, a continual decrease in K _IC was observed through 1200°C, to ∼4.1 MPa·m^1/2, before increasing rapidly to 7.5–8 MPa·m^1/2 at 1300°C. The decrease in K _IC through 1200°C was a result of grain-boundary glassy phase softening. At 1300°C, reorientation of elongated grains in the direction of the applied load was suggested to explain the large increase in K _IC. Crack healing was observed in specimens annealed in air. No R -curve behavior was observed for crack lengths as short as 300 µm at either 25° or 1000°C.     

Stoichiometry Effects on the Fracture of TiO2−x

Fracture characteristics of TiO_{2− x} were studied as a function of Stoichiometry. With increasing x , the fracture toughness K _{I e} and the fracture surface energy γ _f decrease and the amount of transgranular cleavage increases, corresponding to the increased concentration of planar defects within the grains. Increasing nonstoichiometry also shifted the ( K _I- V ) diagram to lower K _I values, commensurate with the K_{I e} decrease. Water accelerated stress corrosion by promoting intergranular failure during subcritical crack growth.     

Toughening of SiC with Ti3SiC2 Particles

Composites in the SiC–TiC–Ti₃SiC₂ system were synthesized using reactive hot pressing at 1600°C. The results indicate that addition of Ti₃SiC₂ to SiC leads to improved fracture toughness. In addition, high microhardness can be retained if TiC is added to the material. The best combination of properties obtained in this study is K _{I c} =8.3 MPa·m^1/2 and H _v=17.6 GPa. The composition can be tailored in situ using the decomposition of Ti₃SiC₂. Ti₃SiC₂ decomposed rapidly at temperatures above 1800°C, but the decomposition could be conducted in a controlled manner at 1750°C. This can be used for synthesis of fully dense composites with improved properties by first consolidating to full density a softer Ti₃SiC₂-rich initial composition, and then using controlled decomposition of Ti₃SiC₂ to achieve the desired combination of microhardness and fracture toughness.     

R-Curve for a Lead Zirconate Titanate Ceramic Obtained from Tensile Strength Tests with Knoop-Damaged Specimens

A procedure was used that made it possible to determine the R -curve for piezoelectric ceramics from tensile strength tests conducted with Knoop-damaged specimens. The resulting crack-tip toughness K _I0 was 0.6 MPa·m^1/2, and the R -curve starting from this value increased to 1.4 MPa·m^1/2 within a 0.7 mm crack extension.     

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.     

Influence of ZrO2 Grain Size and Content on the Transformation Response in the Al2O3─ZrO2 (12 mol% CeO2) System

Based on experimental and modeling studies, the rate of increase in the martensite start temperature M _s for the tetragonal-to-monoclinic transformation with increase in zirconia grain size is found to rise with decrease in ZrO₂ content in the zirconia-toughened alumina ZTA system. The observed grain size dependence of M _s can be related to the thermal expansion mismatch tensile (internal) stresses which increase with decrease in zirconia content. The result is that finer zirconia grain sizes are required to retain the tetragonal phase as less zirconia is incorporated into the alumina, in agreement with the experimental observations. At the same time, both the predicted and observed applied stress required to induce the transformation are reduced with increase in the ZrO₂ grain size. In addition, the transformation-toughening contribution at temperature T increases with increase in the M _s temperature brought about by the increase in the ZrO₂ grain size, when T > M _s. In alumina containing 20 vol% ZrO₂ (12 mol% CeO₂), a toughness of ∼10 MPa. √m can be achieved for a ZrO₂ grain size of ∼2 μm ( M _s∼ 225 K). However, at a grain size of ∼2 μm, the alumina–40 vol% ZrO₂ (12 mol% CeO₂) has a toughness of only 8.5 MPa. √m ( M _s∼ 150 K) but reaches 12.3 MPa. ∼m ( M _s∼ 260 K) at a grain size of ∼3 μm. These findings show that composition (and matrix properties) play critical roles in determining the ZrO₂ grain size to optimize the transformation toughening in ZrO₂-toughened ceramics.     

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.     

Microstructure and Mechanical Properties of Hot-Pressed α-Al2O3-Seeded γ-Alumina Ceramics

High-quality alumina ceramics were fabricated by a hot pressing with MgO and SiO₂ as additives using α-Al₂O₃-seeded nanocrystalline γ-Al₂O₃ powders as the raw material. Densification behavior, microstructure evolution, and mechanical properties of alumina were investigated from 1250°C to 1450°C. The seeded γ-Al₂O₃ sintered to 98% relative density at 1300°C. Obvious grain growth was observed at 1400°C and plate-like grains formed at 1450°C. For the 1350°C hot-pressed alumina ceramics, the grain boundary regions were generally clean. Spinel and mullite formed in the triple-grain junction regions. The bending strength and fracture toughness were 565 MPa and 4.5 MPa·m^1/2, respectively. For the 1300°C sintered alumina ceramics, the corresponding values were 492 MPa and 4.9 MPa·m^1/2.     

Effects of Gadolinia and Alumina Addition on the Densification and Toughening of Silicon Carbide

SiC with mixtures of A1₂O₃ and Gd₂O₃ additions were effective in densifying SiC. The density of 98% of theoretical density was achieved with the Gd₂O₃ and A1₂O₃ eutectic composition. It is suggested that the improvement in density is due to liquid phase formed between A1₂O₃ and Gd₂O₃. The sintered bodies have an improved fracture toughness due to the crack deflection mechanism.     

Effect of Crystallinity on Strength and Fracture Toughness of Li2O-Al2O3-CaO-SiO2 Glass-Ceramics

The influence of crystal volume fraction on fracture toughness ( K _{I C} ) and indentation strength was analyzed for Li₂O-Al₂O₃-CaO-SiO₂ (LACS) and LACS glass-ceramics containing 0.58 mmol% AgNO₃ (LACS-0.58Ag) or 0.78 mmol% AgNO₃ (LACS-0.78Ag). The mean flexure strength, indentation strength, and K_{I C} values of the LACS-0.78Ag groups increased with volume fraction of crystallinity. To achieve the greatest strength and K_{I C} in LACS-Ag specimens, a high volume fraction of crystallinity (95%) had to be produced. However, the relationship between volume fraction of crystal phase and translucency had to be analyzed to determine the influence of crystallization on the potential esthetic results that are essential for dental applications. Addition of AgNO₃ to LACS glass produced a change from surface crystallization to bulk crystallization.     

Grain Growth in CaO-Stabilized ZrO2 in the Presence of a Liquid Phase

Calcia-stabilized zirconia, CSZ (7.5 wt% CaO), with impurities of A1₂O₃, SiO₂, MgO, Fe₂O₃, and TiO₂, was sintered in air at 1783 K for times (t) up to 230 h. The microstructure consisted of grains of CSZ with small amounts of pores and a CaO-Al₂O₃-SiO₂ eutectic. Grain diameters grew in proportion to t^1/3. The results are consistent with a mechanism in which grain growth is limited by diffusion of Zr⁴⁺ ions through the liquid eutectic.     

A Novel Technique for Producing Fine Metal Fibers for Enhancing Mechanical Properties of Glass-Matrix Composites

Micrometer-sized refractory metal fibers of Nb were produced by an unconventional method of mechanically reducing arc-cast ingots of Nb-Cu in which the original microstructure contains ductile Nb precipitates. During mechanical reduction the precipitates were elongated into fibers, which were extracted by chemically dissolving the Cu matrix. Composite specimens of Nb fibers in a glass matrix were fabricated by dry-blending a mixture of fibers and powdered glass, then hot-pressing into disks. Fracture toughness, K _{I C} , was measured using microin-dentation and three-point bending methods. The fracture toughness increased with increasing volume fraction of fibers with the greatest improvement noted at 0.10≤ v_f ≤0.20. The values of K _{I C} increased as the interfiber spacing and the fiber diameter decreased. Both the effective fracture surface energy and the fracture strength were enhanced by increasing v_f . The small fibers embedded in the brittle matrix showed virtually no evidence of microcracking; Nb fibers and glass matrices also demonstrated good interfacial adhesion. Fractographs suggested that the fibers were very effective in resisting crack propagation. Experimental observations were explained using the concept of crack-front bowing and fiber bridging.