Fracture of A12O3 in Combined Tension/Torsion: I, Experiments

Combined tension/torsion tests were performed on solid A1₂O₃ rods at principal stress ratios σ₂/σ₁ of 0 (pure tension), -0.17, -0.38, -0.78, and -1.0 (pure torsion). The tensile principal stress at fracture σ₁ increased with increasing compressive principal stress σ₂, resulting in a higher strength in torsion than uniaxial tension. The ratio σ₁ (torsion)σ₁ (tension) was 1.31 for A1₂O₃, in general agreement with limited torsional data for brittle materials in the literature. Brittle fracture data in the tension-compression quadrant of principal stress space show an interesting dichotomy since strengthening is observed in torsional investigations, whereas weakening is observed for pressurized-tube studies. This difference may be either a pressurized-tube test artifact or a real effect due to the presence of stress gradients.     

Residual Stress in a Soft-Buffer-Inserted Metal/Ceramic Joint

Residual stresses in a soft buffer layer developing during cooling of a metal/buffer/ceramic joint were analyzed. It is shown that there is a parabolic distribution for normal stress and a cubic parabola for shear stress in the buffer. The maximum shear stress, τ₁₂ or τ₁₃, is approximately proportional to the ratio of length to thickness of the buffer, and it is far more than the normal stress σ₁, σ₂ or σ₃. With increasing thickness of the soft buffer, the maximum shear stress will decrease, but the normal stress will change little. A new physics parameter m is suggested in this paper to describe the beneficial role of the buffer, and the influence factors of m are also discussed.     

Use of Fracture Mirrors to Interpret Impact Fractures in Brittle Materials

The impact resistances and fracture mirror radii ( r_m ) of rods of several ceramic materials were measured. The fracture stresses (σ _f ) were determined from σ _f vs r_m^−1/2 curves obtained from fiexural strength tests. An analysis, based on the assumption that the principal factor contributing to the impact energy absorbed is the energy ( U_e ) required to deflect the specimen to the fracture stress, indicated that the impact energy absorbed ( U ) per unit of specimen cross-sectional area ( A ) increased in proportion to the square of the maximum stress. The analysis also indicated that the slopes of the curves of U/A vs σ _f ² are proportional to the reciprocal of Young's modulus. Experimental data for several materials are consistent with this analysis.     

Enhancement of Fracture Properties of Wustite by Precipitation

Both the fracture-initiation energy, γ_i, and the fracture strength, σ _f , of 99.5% dense wustite (grain size 23 μm) were substantially increased by (1) precipitating coherent-coplanar Fe₃O₄, and (2) decomposing the wustite eutectoidally to α-Fe+Fe₃O₄, forming a continuous α-Fe network at the former wustite grain boundaries. The increase in γ_i, and σ_f resulting from the presence of 13 vol% Fe₃O₄ in wustite was attributed to the difference in cleavage habits between the precipitates and matrix and to crack-front pinning. The continuous α-Fe network increased the fracture stability in that fracture was not catastrophic but progressed in steps. The improvement in γ _i and σ _f was attributed mainly to the plastic work in fracturing the α-Fe.     

ON THE CONSISTENCY OF LEAST SQUARES ESTIMATORS FOR A THRESHOLD AR(1) MODEL

Abstract. For the SETAR (2; 1,1) model

where {a_t(i)} are i.i.d. random variables with mean 0 and variance σ²(i), i = 1,2, and {a_t(l)} is independent of {a_t(2)}, we consider estimators of φ₁, φ ₂ and r which minimize weighted sums of the sum of squares functions for σ²(1) and σ²(2). These include as a special case the usual least squares estimators. It is shown that the usual least squares estimators of φ₁, φ₂ and r are consistent. If σ²(1) ≠σ²(2) conditions on the weights are found under which the estimators of r and φ₁ or φ₂ are not consistent.     

Relation Between Power and Exponential Laws of Slow Crack Growth

The coefficients ₀, and N of the power law of slow crack growth, =₀ exp [–/(RT)](K/K_C)^N, are evaluated in terms of the fundamental parameters V₀. Q₀. and B of the exponential law, V=V₀ exp [(-Q₀+BK)/(RT)]. It is shown that N =θ(BK_C)/(RT),=₀−θBK_C, and ₀=V₀θ^−N, where θ is a dimensionless coefficient with a value ranging from 0.2858 to 1.0, depending on the ratio of stress intensity at the fatigue limit to the critical stress intensity factor.     

Fracture of Al2O3 in Combined Tension/Torsion: II, Weibull Theory

The Weibull statistical fracture theory for multiaxial stresses has been extended to conditions of combined tension/torsion loading. At fracture, a tensile principal stress ratio σ₁ (tension/torsion) σ₁ (uniaxial tension) greater than one is predicted which is dependent on stress state, Weibull modulus, and fracture location. Comparison to experimental tension/torsion data for Al₂O₃ shows that the Weibull theory, although predicting correct trends, generally underestimates strengthening effects of the compressive principal stress, thus providing a conservative failure prediction. This discrepancy may be related to influences of stress state on crack-tip "process zone" behavior.     

Influence of Impurity Particles on the Fracture of UO2

Three types of second-phase precipitates were identified by scanning electron microscopy of helical specimens of nominally pure UO₂, i.e. (1) bonded or weakly bonded complex Si particles precipitated during sintering from impurities in the starting material, (2) more strongly bonded Al₂O₃-UO₂ surface particles that formed on the external surfaces during sintering, and (3) metallic Fe or U phases. The influence of these particles on the room-temperature fracture stress, σ _f , was investigated. Particles of types (1) and (2) were as large as 300 μm and caused up to 100% reduction in σ _f , whereas the metallic phases had no significant effect. The critical-strain-energy-release rate, G_c , determined from the measured flaw sizes and associated fracture stresses, was ∼3600 ergs/cm². Purification procedures that reduced the impurity particle sizes and number density improved the strength significantly.     

Fracture Properties of Polycrystalline Lithia-Stabilized β"- Alumina

The critical stress-intensity factor, K_1C , and the fracture strength, σ _f , have been investigated on both hot-pressed and sintered lithia-stabilized β "-alumina. The hot-pressed material possessed a strong preferred orientation with many of the basal planes aligned perpendicular to the direction of hot-pressing. Both K_1C and σ _f were found to be orientation-dependent. Two regimes of fracture were identified. In fine-grained material (<120 μm), the strength was slightly dependent on grain size.
For larger grain sizes, the strength decreased rapidly with increasing grain size and the fracture mode was almost entirely transgranular. The K_1C values for sintered β "-alumina were in the same range as those obtained on the hot-pressed material.     

Machining-Induced Surface Residual Stress Behavior in Al2O3–SiC Nanocomposites

The machining and subsequent annealing behavior of an Al₂O₃-SiC nanocomposite (A1₂O₃+ 5 vol% 0.2 μm SiC particles) was compared to that of single-phase A1₂O₃. The machining-induced residual line force was determined by measuring the extent of elastic bending in thin disk specimens, and the surface roughness was evaluated by profilometry. The results showed that, when the two materials were subjected to the same grinding conditions, they developed compressive residual stresses and surface roughness values of similar magnitude. The maximum thickness of the residual stress layers was estimated to be ∼ 10 μm for the A1₂O₃ and ∼12 μm for the nanocomposite. A direct linear correlation was observed between the residual force and the surface roughness for different machining treatments. Annealing of the machined samples produced complete relaxation of residual stresses in the single-phase Al₂O₃, whereas only partial stress relaxation occurred for the nanocomposite.     

ON LINEAR PROCESSES WITH GIVEN MOMENTS

Abstract. Let X _t = c ₀ Y _t + c ₁ Y _{t -1}+… be a linear process with known coefficients c _k , where Y _t is a strict white noise. Let m ₁, …, m _2r be given numbers. A method is presented to determine whether there exists a distribution of Y _t such that EX ^k _t = m _k for k = 1, …, 2 r . In the positive case, such a distribution of Y _t is described. Some explicit formulas for AR(1) and AR(2) models are derived. The results can be used for simulating a process with given moments of its stationary distribution. The procedure also enables proof that some stationary distributions cannot belong to the given linear process.     

Kinking of a Crack out of an Interface: Role of In-Plane Stress

A crack lying in the interface between two brittle elastic solids can advance either by continued growth in the interface or by kinking out of the interface into one of the adjoining materials. This competition can be assessed by comparing the ratio of the energy release rates for interface cracking and for kinking out of the interface to the ratio of interface toughness to substrate toughness. The stress parallel to the interface, σ₀, influences the energy release rate of the kinked crack and can significantly alter the conditions for interface cracking over substrate cracking if sufficiently large. This paper provides the dependence of the energy release rate ratio on the in-plane stress. The nondimensional stress parameter which emerges is, σ₀( a / E _* T_i)^1/2, where a is the initial length of the kink into the substrate, E _* is a modulus quantity, and T_i is the fracture energy of the interface. An experimental observation of the cracking of reaction product layers in bonds between Ti(Ta) and Al₂O₃ is rationalized by the theory.     

Optical Properties of Dysprosium-Doped Low-Phonon-Energy Glasses for a Potential 1.3 μm Optical Amplifier

Dysprosium-doped glasses were prepared in the system of gallium-based sulfide, tellurite, zirconium-baed and indium-based fluorides and their optical properties were studied. From the absorption cross sections of five f-f bands, three Judd-Ofelt parameters, ω _t ( t = 2, 4, 6), of Dy³⁺ ion were determined. The compositional variaton of the ω₂value showed the order sulfide > tellurite > fluorozirconate > fluoroindate, whereas the ω₆ value showed the opposite tendency. Compositional variaton of the fluorescence intensity ratio of the (⁴F_9/2⁶H_13/2)/(⁴F_9/2)→⁶H_15/2) is explained by the ratio of ω₂/ω₆ of doped Dy³⁺. The emission probabilities A and the branching ratio β from ⁶H_9/2 and ⁶F_11/2 levels, which are the doublet initial level of the 1.3 μm luminescence, were calculated for the glasses, and it was found that both values showed a tendency similar to that of ω₂ against the glass composition. In the sulfide glass, A was 2.6 × 10³S^-1 and β was 93%, both the highest in all of the glasses investigated. By 1.06 μm pumping of a Nd: YAG laser, the sulfide glass showed strong 1.3 μm emission and the lifetime was 25 μs, resulting in a quantum efficiency of 7%. This value is higher than that of the Pr³⁺:¹G₄ level in ZBLAN glass with β= 60%.     

Kinetics of Enthalpy Relaxation at the Glass Transition in Ternary Tellurite Glasses

The kinetics of enthalpy relaxation (recovery) at the glass transition in x K₂O·(20− x )MgO·80TeO₂ glasses has been examined from heat capacity measurements using differential scanning calorimetry to clarify the features of the structural relaxation in ternary TeO₂-based glasses. Ternary glasses such as 10K₂O·10MgO·80TeO₂ show high thermal resistance against crystallization compared with binary glasses. The degree of fragility m estimated from the activation energy for viscous flow E _η and the glass transition temperature T _g is m = 55–62, indicating a fragile character in TeO₂-based glasses. Large heat capacity changes of 43.1–48.2 J·mol⁻¹·K⁻¹ are also observed at the glass transition. The activation energy for enthalpy relaxation Δ H is evaluated from the cooling rate dependence of the limiting fictive temperature, and values of Δ H = 897–1268 kJ·mol⁻¹ are obtained. Negative deviation from additivity in Δ H is also observed. Values of the Kovacs–Aklonis–Huchinson–Ramos (KAHR) parameter θ estimated from Δ H and T _g are 0.33–0.42 K⁻¹. It has been proposed that ternary glasses have more homogeneous and constrained glass structure compared with binary glasses.     

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.     

Reactive-Templated Grain Growth of Bi1/2(Na,K)1/2TiO3: Effects of Formulation on Texture Development

In this paper we report the effects of formulation on texture development for the "reactive-templated grain growth" (RTGG) of Bi_1/2(Na,K)_1/2TiO₃ (BNKT). The solids formulation for BNKT was systematically varied by prereacting to well—defined alkali and bismuth titanates (Na₂Ti₃O₇ (N₂T₃), K₂Ti₂O₅ (K₂T₂), and Bi₂Ti₄O₁₁ (B₂T₄)). Use of these precursors in different BNKT formulations determined that the amount of expansion associated with reacting dry-pressed compacts at 600−800°C could be influenced by formulation. Lotgering factors ( F _{00 l} ) derived from Θ/2Θ X-ray diffraction scans indicated that the formulation route strongly affected the {00 l } texture development in tape-cast and sintered specimens. Prereacting alkali carbonates with TiO₂ to form N₂T₃ and K₂T₂ inhibited texture development in RTGG-processsed BNKT. However, when Bi₂O₃ was prereacted to form B₂T₄, the measured F _{00 l} increased from 0.5 to 0.7.     

Consolidation of Participate Layers in the Fabrication of Optical Fiber Preforms

Viscous sintering is experimentally identified through electron microscopy as the mechanism of consolidation of thin particulate layers in the fabrication of optical fibers. The rate of consolidation is primarily a function of the capillary number, C=[νl₀(1 -ε₀)^1/3/(σ t _s)], where ν is the glass viscosity, l ₀ the size of the initial void regions, ε₀ the initial void fraction, σ the surface tension, and t_s the sintering time. Numerical results indicate a sensitivity of the sintering rate to temperature, chemical composition of the particles, and gas thermal properties, primarily through the strong dependence of glass viscosity on these variables. These results are fully supported by the available experimental evidence. Under the conditions of the experiments, gas bubbles were occasionally produced; the causes are discussed.     

K/Na Ratio Dependence of the Electrical Properties of [(KxNa1−x)0.95Li0.05](Nb0.95Ta0.05)O3 Lead-Free Ceramics

[(K _x Na_{1− x} )_0.95Li_0.05](Nb_0.95Ta_0.05)O₃ (K _x NLNT) ( x= 0.40–0.60) lead-free piezoelectric ceramics were prepared by conventional solid-state sintering. The effects of K/Na ratio on the dielectric, piezoelectric, and ferroelectric properties of the K _x NLNT ceramics were studied. The experimental results show that the electrical properties strongly depend on the K/Na ratio in the K _x NLNT ceramics. The K _x NLNT ( x =0.42) ceramics exhibit enhanced properties ( d ₃₃∼242 pC/N, k _p∼45.7%, k _t∼47%, T _c∼432°C, T _o−t =48°C, ɛ_r∼1040, tanδ∼2.0%, P _r∼26.4 μC/cm², E _c∼10.3 kV/cm). Enhanced electrical properties of the K _x NLNT ( x =0.42) ceramics could be attributed to the polymorphic phase transition near room temperature. These results show that the K _x NLNT ( x =0.42) ceramic is a promising lead-free piezoelectric material.     

Deformation of UO2 at High Temperatures

The effects of temperature, strain rate, and grain size on the mechanical properties of UO₂ were investigated using the four-point bending technique. Strain rates were varied by two orders of magnitude, and test temperatures up to 1800°C were used. Data are presented on the ultimate tensile stress, yield stress, and plastic strain-to-fracture. Below the brittle-to-ductile transition temperature, T_c , the material fractured in a brittle manner, with no macroscopic plastic deformation. Between T_c and a second transition at a higher temperature, T_t , a small amount of plastic deformation was measured before fracture. Beyond T_t , the strength of UO₂ decreased continuously, and extensive plasticity was observed. This high-temperature plasticity was characterized by a thermally activated rate-controlling process; this behavior is consistent with observations of creep behavior under high stresses. The following phenomenological equations for the strain rate fit the data for the material with 8-μm grain size above T_t :
and
where σ_p and σ_88f are the proportional limit and steady-state flow stress, respectively, and temperature T is in °K.     

Particle Size Dependence of the Electrical Conductivity of NaCl

The ac and dc conductivities of single-crystal and polycrystalline NaCl were measured as a function of both temperature and particle size. The ac conductivity results for single-crystal NaCl agreed well with the literature: intrinsic activation energy = 1.86 ev; extrinsic, impurity-controlled range = 0.74 ev; extrinsic, association range = 1.16 ev; and the intrinsic-extrinsic knee in the curve was at 10³/ T ∼ 1.4°K⁻¹ and σ₀∼ 6 × 10⁻⁸ ohm⁻¹ cm⁻¹. In the intrinsic range, however, the total conductivity (σ₀) was the sum of two ionic contributions: a steady state, nonblocked contribution (σ_θ and a blocked contribution (σ₀—σ_θ). The activation energy for the dc steady state conductivity was 1.6 ev. When the extrinsic, impurity-controlled contribution to the total conductivity was made insignificant by anion doping, the same 1.6 ev was the activation energy for the intrinsic ac conductivity at low temperatures. The data for the polycrystalline samples showed that ac conductivity increased inversely with particle size and dc steady state conductivity increased only slightly, if any, with decreasing particle size. It is postulated that the steady state conductivity is the result of the nonblocked ionic transport of sodium ions and that the ac portion of the total conductivity is due to the movement of chlorine ions which are blocked, giving rise to the polarization phenomenon. The increase in the ac conductivity with decreasing particle size is correlated with the enhanced movement of Cl⁻ in the subgrain boundary region, as has been previously shown by diffusion measurements.