Fracture Toughness Determination of A12O3 Using Four-Point-Bend Specimens with Straight-Through and Chevron Notches

Fracture toughness of a sintered A1₂O₃ was determined with four-point-bend specimens having either straight-through or chevron notches. For the straight-through notched specimens, measured K _Ic decreased with decreasing notch width. For the smallest notch width (66 μm) K _Ic= 3.42±0.13 MN m^−¾. For specimens with chevron notches, a crack initiates and extends from the tip of the notch under increasing load. K _Ic is calculated from the maximum load without measuring crack length, under the assumption that the derivative of the compliance is the same as that for a specimen with a straight-through crack. A refined calculation accounts for the truncated chevron crack shape at maximum load using Bluhm's slice model. For the chevronnotch configuration, a value of K _Ic= 3.49±0.11 MN m^−¾ was measured, which appears to be independent of the initial notch length a ₀ (distance from the crack mouth to the tip of the triangular notch). An effect of a ₁ (length of the chevron notch at the surface) on K _Ic was observed, independent of whether the calculation of K _Ic was based on the straight-through crack assumption or on the slice model.     

Toughness Anisotropy in Textured Ceramic Composites

In this investigation, a model predicting toughness anisotropy in textured ceramics containing elongated grains and in composites reinforced with rod-shaped particles is presented. The model predictions are based on the assumption that crack deflection is the only toughening mechanism. In the model, toughness anisotropy is calculated as a function of texture degree. For composite materials, the volume fraction of the reinforcement phase is also an input parameter. Correspondence between model and experiment was established by comparing measured toughness anisotropies in β-Si₃N₄ and Al₂O₃/SiC whisker composites to model predictions. In these model predictions, measured orientation distributions from hot-pressed and hot-forged specimens were employed. The potential for relating other toughening mechanisms in a similar format is also addressed, since the model and experimental measurements give different results. The crack deflection model simultaneously overpredicts the toughening enhancement and underpredicts the toughening anisotropy observed in the experiments.     

High-Temperature Crack Growth in Monolithic and SiCw-Reinforced Silicon Nitride under Static and Cyclic Loads

Experimental results are presented on subcritical crack growth under sustained and cyclic loads in a HIPed Si₃N₄ at 1450°C and a hot–pressed Si₃N₄–10 vol% SiC_w composite in the temperature range 1300°–1400°C. Static and cyclic crack growth rates are obtained from the threshold for the onset of stable fracture with different cyclic frequencies and load ratios. Fatigue crack growth rates for both the monolithic and SiC_w-reinforced Si₃N₄ are generally higher than the crack growth velocities predicted using static crack growth data. However, the threshold stress intensity factor ranges for the onset of crack growth are always higher under cyclic loads than for sustained load fracture. Electron microscopy of crack wake contact and crack–tip damage illustrate the mechanisms of subcritical crack growth under static and cyclic loading. Critical experiments have been conducted systematically to measure the fracture initiation toughness at room temperature, after advancing the crack subcritically by a controlled amount under static or cyclic loads at elevated temperatures. Results of these experiments quantify the extent of degradation in crack–wake bridging due to cyclically varying loads. The effects of preexisting glass phase on elevated temperature fatigue and fracture are examined, and the creep crack growth behavior of Si₃N₄–based ceramics is compared with that of oxide-based ceramics.     

Theoretical Analysis of Chemical Vapor Deposition of Ceramics in an Impinging Jet Reactor

A mathematical model for chemical vapor deposition in an impinging jet reactor is extended to consider growth of materials that are nonstoichiometric or that contain multiple solid phases. The model treats the fluid flow of the reactant gas mixture, multicomponent heat and mass transfer, and simultaneous gas-phase and surface reactions. For a given system, insight into the rate-limiting steps can be obtained by identifying a set of reaction rate constants that gives a match between theoretical results and experimental data. The calculations also provide quantitative information on the relationships between operating conditions, deposition rate, and deposit composition. Results for production of boron carbide from BCI ₃, CH₄, and H₂ are presented as an example. Under typical processing conditions, deposition of B_y C is found to be controlled primarily by the rate of CH₄ decomposition and the extent of surface coverage by CH₄ Theoretical calculations are presented for different sets of operating conditions to illustrate the predictive capability of the model. Also, the sensitivity of results to various reaction mechanisms and to values for solid-phase activities is evaluated. Analogies are drawn between the boron carbide process and deposition of other ceramics in which a carbon-containing reactant is used.     

Nonstoichiometry and Mixed Conduction in α-Ta2O5

Electrical conductivity of single-crystal and polycrystalline Ta₂O₅ was measured as a function of composition, temperature, and oxygen partial pressure ( P _O2) by both dc and ac complex impedance methods. A defect model based on the assumption of predominant disorder on the oxygen sublattice is proposed to explain the observed nonstoichiometry of α-Ta₂O₅. The defect model is consistent with the observed P _O2-independent ionic conductivity and the P ^−1/4_O2-dependent electronic conductivity. Blocking of the ionic component was observed at low P _O2. Both the electronic and ionic components of conductivity were found to decrease with time. This aging phenomena is related to destabilization of the a phase.     

Tribological Behavior of Si3N4 and Si3N4/Carbon Fiber Composites Against Stainless Steel Under Water Lubrication for a Thrust-Bearing Application

The tribological behavior of Si₃N₄ ceramics and Si₃N₄/carbon fiber composites sliding against stainless steel under water lubrication was investigated using a thrust-bearing-type test method with normal applied loads varying from 0 to 1000 N in 100 N increments. In the case of the monolithic Si₃N₄, the friction coefficient was found to increase up to 0.4 the first time the applied load was increased from 100 to 200 N, and sudden failure of the ceramic ring specimen occurred. In the case of the Si₃N₄/carbon fiber composite, a low friction coefficient was maintained up to the maximum normal load of 1000 N. The addition of the carbon fibers to the silicon nitride ceramics effectively restricts material transfer from the stainless steel to the Si₃N₄ worn surface due to reduction of solid–solid contact through the solid lubricating effect of the carbon fibers.     

Modeling Optical Changes in Perovskite Capacitor Materials Due to dc-Field Degradation

The depth sensitivity of spectroscopic ellipsometry (SE) to the presence of oxygen vacancies (V_O^••), in perovskite titanates, was examined over the wavelength range from 250 to 750 nm. To determine the effect of oxygen vacancy concentration, reference optical properties of barium titanate (BaTiO₃) and Fe-doped SrTiO₃ were determined for oxidized and reduced samples. These reference data were used to model the sensitivity of SE to changes due to degradation. Using these models, it was found that SE could detect reduced layers of 4 Å for BaTiO₃ and an 8 Å layer for Fe-doped SrTiO₃. From the models, concentration gradients were resolvable by SE with an average diffusion depth (√ Dt ) of 10 Å for BaTiO₃ and 50 Å for Fe-doped SrTiO₃. These models also predict that SE should be able to discern different degradation mechanisms through the way the optical properties change during degradation.     

Influence of Thermal History on the Crystallization Behavior and Hardness of a Glass-Ceramic

The glass system SiO₂─Al₂O₃─Li₂O─TiO₂ was examined to determine the dependence of hardness on heat-treatment temperature. In addition to hardness measurements, X-ray diffraction (XRD) was used to determine the type and amount of phases present and to relate this to the hardness results. Hardness increased with heat-treatment temperature. This correlated with the amounts of crystals present, as determined by XRD. For a particular heat-treatment temperature, when hardness was plotted versus load on the indenter, there was a load dependence. There was at first a rapid decrease as the load on the indenter increased, with a constant value being approached at higher loads.     

Surface Area Reduction During Isothermal Sintering

A kinetic model for the reduction in specific surface area during isothermal sintering is examined in detail. Experimental data for a variety of materials including A1₂O₃, B, Ni, Cu, ZnO, TiO₂, Fe₂O₃, and As-Se-S glasses are analyzed by the technique provided. The results of this technique agree well with those for previously identified sintering mechanisms for each material. The kinetic model is based on sintering driven by the curvature gradient in the interparticle neck region associated with initial-stage sintering. At the intermediate stage of sintering, a diminished curvature gradient shifts the sintering driving force to the excess surface free energy.     

TESTING FOR CYCLICAL NON-STATIONARITY IN AUTOREGRESSIVE PROCESSES

This paper deals with the distributions evolving from the likelihood-ratio test for the factor 1 − B ⁿ in the lag polynomial Φ( B ) under the basic assumption that the data series is generated by the autoregressive model Φ( B ) X _t = ε _t where {ε _t } denotes Gaussian white noise. A characterization of the statistic and its asymptotic properties is given. Asymptotic and finite-sample significance points are tabulated. The test procedure is illustrated by an economics example.     

Thermodynamic Modeling of Alkali Metal Oxide-Silica Binary Melts

The evaluation of the thermodynamic properties as well as the phase diagrams for the binary Na₂O–SiO₂, K₂O–SiO₂, and Li₂O–SiO₂ systems are carried out with a structural model for silicate melts and glasses. This thermodynamic model is based on the assumption that each metallic oxide produces the depolymerization reaction of silica network with a characteristic free-energy change. A least squares optimization program permits all available thermodynamic and phase diagram data to be optimized simultaneously. In this manner, data for these binary systems have been analyzed and represented with a small number of parameters. The resulting equations represent the thermodynamic and phase diagram data for these alkali metal oxide–silica systems within experimental error limits. In particular, the measured limiting liquidus slope at     is well reproduced.     

In-Plane Fracture Resistance of a Crossply Fibrous Monolith

The in-plane fracture resistance of a crossply Si₃N₄/BN fibrous monolith in the 0°/90° and ±45° orientations is examined through tests on notched flexure specimens. The measurements and observations demonstrate the importance of fiber pullout following fiber fracture. The mechanical response is modeled using a crack-bridging approach. Two complementary approaches to evaluating the bridging law are developed: one based on a micromechanical model of fiber pullout and the other based on the load versus crack mouth opening displacement response of the flexure specimens following fracture of all fibers. Both approaches indicate that the bridging law follows an exponential form, characterized by a bridging strength and an effective pullout length. An assessment of the bridging model is made through comparisons of simulations of the load–displacement response with those measured experimentally.     

Behavior of Cyclic Fatigue Cracks in Monolithic Silicon Nitride

Cyclic fatigue-crack propagation behavior in monolithic silicon nitride is characterized in light of current fatiguecrack growth models for ceramics toughened by grainbridging mechanisms, with specific emphasis on the role of load ratio. Such models are based on diminished cracktip shielding in the crack wake under cyclic loads due to frictional-wear degradation of the grain-bridging zone. The notion of cyclic crack growth promoted by diminished shielding is seen to be consistent with measured (long-crack) growth rates, fractography, in situ crack-profile analyses, and measurements of back-face strain compliance. Growth rates are found to display a much larger dependence on the maximum applied stress intensity, K _max than on the applied stress-intensity range, Δ K , with behavior described by the relationship da/dN ∞ K²⁹_maxΔK^1.3. Fatigue thresholds similarly exhibit a marked dependence on the load ratio, R = K _min/ K _max; such effects are shown to be inconsistent with traditional models of fatigue-crack closure. In particular, when characterized in terms of K _max growth rates below ∼10⁻⁹ m/cycle exhibit an inverse dependence on load ratio, an observation which is consistent with the grain-bridging phenomenon; specifically, with increasing R, the sliding disance between the grain bridges is decreased, leading to less frictional wear, and hence less degradation in shielding, per loading cycle. The microstructural origins of such behavior are discussed.     

Thermal Oxidation Kinetics of MoSi2-Based Powders

The oxidation process of MoSi₂ is very complex, and controversial results have been reported, especially for the early-stage oxidation before the formation of passive SiO₂ film. Most oxidation studies have been carried out on bulk consolidated samples, and the early stage of oxidation has not been studied. In this investigation, very fine MoSi₂ powder with an average particle size of 1.6 μm was used. Such a fine particle size makes it easier to study the early stages of oxidation since a significant portion of the powder is oxidized before the formation of passive SiO₂ film. The oxidation kinetics of commercial MoSi₂-SiC and MoSi₂-Si₃N₄ powder mixtures were also studied for comparison. Weight changes were measured at discrete time intervals at 500° to 1100°C in 0.14 atm of oxygen. X-ray diffraction was used to identify the phases formed during oxidation. Our results show the formation of MoO₃ phase and an associated weight gain at low temperatures (500° and 600°C). At temperatures higher than 900°C, Mo₅Si₃ phase formed first and was subsequently oxidized to solid SiO₂ and volatile MoO₃, resulting in an initial weight gain followed by subsequent weight loss. A model based on the assumption that oxidation kinetics of both MoSi₂ and Mo₅Si₃ are proportional to their fractions in the system describes the experimental data well.     

Controlled Crystallization in Self-Reinforced Silicon Nitride with Y2O3, SrO, and CaO: Crystallization Behavior

The controlled crystallization of the amorphous grain boundary phase has been examined in a series of self-reinforced Si₃N₄ materials with added Y₂O₃, SrO, and CaO. The effects of time, temperature, atmosphere, glass content, glass chemistry, and matrix Si₃N₄ on the crystallization have been investigated. The stability of the crystallized product, the crystallization kinetics ( T-T-T curve), and crystallization mechanisms have also been examined. Crystallization produced an oxynitroapatite containing Y, Sr, and Ca over a broad range of heat-treatment conditions and glass compositions. The oxynitroapatite was compatible with Si₃N₄ and remained stable up to 1600°C. At low temperatures (<1350°C), the rate-limiting crystallization mechanism was oxygen diffuson in the glass, and at higher temperatures (>1350°C) the rate-limiting crystallization step changed to either the formation of new Si₃N₄ grains or solute diffusion in the glass.     

Two-Dimensional Modeling of Self-Propagating High-Temperature Synthesis of Strontium-Doped Lanthanum Manganate

A two-dimensional finite element model is developed to study the reaction kinetics and heat transfer during the self-propagating high-temperature synthesis of La_0.6Sr_0.4MnO₃, a cathode and interconnect material used in solid oxide fuel cells. The activation energy of La_0.6Sr_0.4MnO₃ formation was calculated from experimental temperature history. The calculated spatial-temporal temperature profile, heat generation rate, reaction conversion, and flow pattern of surrounding gas during the reaction are reported in this work. Hot spots are found at the corner near the ignition point shortly after the ignition. The model provided a simple and reliable way to design a large-scale production of La_0.6Sr_0.4MnO₃.     

High-Temperature Failure of an Alumina-Silicon Carbide Composite under Cyclic loads: Mechanisms of Fatigue Crack-Tip Damage

Experimental results are presented on the mechanisms of tensile cyclic fatigue crack growth in an A1₂0₃-33-vol%-SiC-whisker composite at 1400°C. The ceramic composite exhibits subcritical fatigue crack propagation at stress-intensity-fator values far below the fracture toughness. The fatigue characterized by the stressintensity-factor range, ΔK, and crack propagation rates are found to be strongly sensitive to the mean stress (load ratio) and the frequency of the fatigue cycle. Detailed transmission electron microscopy of the fatigue crack-tip region, in conjunction with optical microscopy, reveals that the principal mechanism of permanent damage ahead of the advancing crack is the nucleation and growth of interfacial flaws. The oxidation of Sic whiskers in the crack-tip region leads to the formation of a silica-glass phase in the 1400°C air environment. The viscous flow of glass causes debonding of the whisker-matrix interface; the nucleation, growth, and coalescence of interfacial cavities aids in developing a diffuse microcrack zone at the fatigue crack tip. The shielding effect and periodic crack branching promoted by the microcracks result in an apparently benefcial fatigue crack-growth resistance in the A1₂0₃—SiC composite, as compared with the unreinforced alumina with a comparable grain size. A comparison of static and cyclic load crack velocities is provided to gain insight into the mechanisms of elevated temperature fatigue in ceramic composites.     

Initial Sintering of Submicrometer Titania Anatase Powder

Measurements of surface area reduction of TiO₂ anatase powder (of initially 100 m²· g⁻¹) were carried out for various partial pressures of water and oxygen at 823 K. The kinetic equation obtained for the experimental rates has the formulation r = k[P _H2O]^1/α [ P _O2]^1/β where α and β are equal to 2 and -12, respectively. A mechanistic model involving six consecutive elementary steps was developed, in which hydroxyl species play a dominant role. No geometrical assumption is required. The general expression of the deduced theoretical rates has the same form as previously given. The comparison between the experimental and the predicted rates points out that the rate-limiting step is the surface diffusion of hydroxyl species. This model can easily be used for any other compounds, for particle growth, and for porosity elimination.     

Wear Mechanisms of TiB2 and TiB2–TiSi2 at Fretting Contacts with Steel and WC–6 wt% Co

Unlubricated fretting wear tests on TiB₂ and TiB₂–5 wt% TiSi₂ ceramics against two different mating materials (bearing grade steel and WC–6 wt% Co balls) were performed with a view to understand the counterbody-dependent difference in friction and wear properties. The fretting experiments were conducted systematically by varying load (2–10 N) at an oscillating frequency of 4 Hz and 100 μm linear stroke, for a duration of 100,000 cycles. Adhesion, abrasion, and three-body wear have been observed as mechanisms of material damage for both the TiB₂/steel and TiB₂/WC–Co tribosystems. The third body is predominantly characterized as tribochemical layer for TiB₂/steel and loose wear debris particles for TiB₂/WC–Co tribocouple. An explanation on differences in tribological properties has been provided in reference to the counterbody material as well as microstructure and mechanical properties of flat materials.     

Magnetic Properties of a Novel Ceramic Ferroelectric–Ferromagnetic Composite

A series of [0.8Pb(Ni_1/3Nb_2/3)O₃–0.2PbTiO₃]/[(Ni_0.2Cu_0.2 Zn_0.6)Fe₂O₄] (PNNT/NiCuZn) ferroelectric–ferromagnetic composites were prepared by the conventional solid-state route. The composites show good co-firing behaviors. X-ray diffraction and scanning electron microscope studies confirmed the coexistence of ferroelectric PNNT phase and ferromagnetic NiCuZn phase in the composites. No significant chemical interaction has occurred between PNNT phase and NiCuZn phase. All sintered samples exhibit typical magnetic hysteresis loops at room temperature. The saturation magnetization of composites rises linearly with the increase in NiCuZn content. Frequency dependence of initial permeability was also measured. With an increase in NiCuZn, the initial permeability increases and the cutoff frequency tends to decrease. The Maxwell–Garnett (MG) effective medium theory was used to model the magnetic properties of composites. Although the MG equation cannot give an accurate prediction for the initial permeability of composites because of the oversimplified assumption, it gives upper and lower limits for the initial permeability of compositions.