Cavitational Strain Contribution to Tensile Creep in Vitreous Bonded Ceramics

Analysis of the role of cavitation during uniaxial creep deformation in vitreous bonded ceramics reveals that the cavity volume contributes only to the strain in the direction parallel to the tensile stress regardless of the shape and orientation of cavities. Creep asymmetry results from the fact that cavitation preferentially contributes to axial tensile strain while the strain observed under the same conditions in compression is produced only by volume-conserving mechanisms. The contribution of cavitational strain in the axial tensile strain is equal to the volume fraction of cavities and proportional to the difference between tensile and compressive strains in the axial direction. The density change method and a newly proposed method based on the difference in the axial strains were used for separating the cavitational from the true tensile strain in self-reinforced silicon nitride. Both methods consistently revealed more than 90% contribution of cavitation to the total tensile strain. Cavitation is concluded to be the dominant mechanism of tensile creep deformation in vitreous bonded ceramics because the reported volume fractions of cavities during their deformation are usually in the range of 70–90% of tensile strain.     

Comparison of Tensile and Compressive Creep Behavior in Silicon Nitride

The creep behavior of a commercial grade of Si₃N₄ was studied at 1350° and 1400°C. Stresses ranged from 10 to 200 MPa in tension and from 30 to 300 MPa in compression. In tension, the creep rate increased linearly with stress at low stresses and exponentially at high stresses. By contrast, the creep rate in compression increased linearly with stress over the entire stress range. Although compressive and tensile data exhibited an Arrhenius dependence on temperature, the activation energies for creep in tension, 715.3 ± 22.9 kJ/mol, and compression, 489.2 ± 62.0 kJ/mol, were not the same. These differences in creep behavior suggests that mechanisms of creep in tension and compression are different. Creep in tension is controlled by the formation of cavities. The cavity volume fraction increased linearly with increased tensile creep strain with a slope of unity. A cavitation model of creep, developed for materials that contain a triple-junction network of second phase, rationalizes the observed creep behavior at high and low stresses. In compression, cavitation plays a less important role in the creep process. The volume fraction of cavities in compression was ∼18% of that in tension at 1.8% axial strain and approached zero at strains <1%. The linear dependence of creep rate on applied stress is consistent with a model for compressive creep involving solution–precipitation of Si₃N₄. Although the tensile and compressive creep rates overlapped at the lowest stresses, cavity volume fraction measurements showed that solution–precipitation creep of Si₃N₄ did not contribute substantially to the tensile creep rate. Instead, cavitation creep dominated at high and low stresses.     

Cavitation Contributes Substantially to Tensile Creep in Silicon Nitride

During tensile creep of a hot isostatically pressed (HIPed) silicon nitride, the volume fraction of cavities increases linearly with strain; these cavities produce nearly all of the measured strain. In contrast, compressive creep in the same stress and temperature range produces very little cavitation. A stress exponent that increases with stress (ε∞σ ⁿ , 2 < n < 7) characterizes the tensile creep response, while the compressive creep response exhibits a stress dependence of unity. Furthermore, under the same stress and temperature, the material creeps nearly 100 times faster in tension than in compression. Transmission electron microscopy (TEM) indicates that the cavities formed during tensile creep occur in pockets of residual crystalline silicate phase located at silicon nitride multigrain junctions. Small-angle X-ray scattering (SAXS) from crept material quantifies the size distribution of cavities observed in TEM and demonstrates that cavity addition, rather than cavity growth, dominates the cavitation process. These observations are in accord with a model for creep based on the deformation of granular materials in which the microstructure must dilate for individual grains to slide past one another. During tensile creep the silicon nitride grains remain rigid; cavitation in the multigrain junctions allows the silicate to flow from cavities to surrounding silicate pockets, allowing the dilatation of the microstructure and deformation of the material. Silicon nitride grain boundary sliding accommodates this expansion and leads to extension of the specimen. In compression, where cavitation is suppressed, deformation occurs by solution—reprecipitation of silicon nitride.     

Evidence of Grain-Boundary-Sliding-Induced Cavitation in Ceramics under Compression

Detailed microscopy of two crept aluminas, one with (AD99) and one without (Lucalox) a grain boundary glassy phase, has been performed to determine the pertinent damage mechanisms during creep. Evidence is presented for a nucleation-controlled cavitation process where creep cavities nucleate primarily on two-grain facets, followed by cavity growth and coalescence to form grain-facet-sized cavities and microcracks. A variety of creep cavity morphologies were observed in Lucalox, including spheroidal and irregularly shaped cavities. The latter finding implies a strong influence of crystallographic orientation and the corresponding surface energy of the cavitated planes on the cavity shape. In contrast, classical spheroidal cavities were observed in AD99 due to the presence of a viscous phase along grain boundaries. Direct evidence for grain boundary sliding as the process driving force for cavitation in Lucalox is presented together with evidence for the nucleation of creep cavities at grain boundary ledges. These findings are compared to the grain boundary sliding (GBS) and small-angle neutron scattering (SANS) measurements performed previously on the same systems. Based on this study, the cavity nucleation process in the glassy-phase- and non-glassy-phase-containing aluminas is apparently similar as both involve the nucleation of rows of equally sized and equally spaced cavities.     

High-Temperature Creep and Cavitation of Polycrystalline Aluminum Nitride

Dense, polycrystalline AlN samples of grain size between 1.8 and 19 μm were fabricated by hot-pressing. Bar-shaped samples were subjected to creep in four-point bending under static loads in nitrogen atmosphere. The outer fiber stress was varied between 20 and 140 MPa and the temperature between 1650 and 1940 K. Steady-state creep rate, dɛ/d t was proportional to σ ⁿ d ^{− m} where the stress exponent, n , was between 1.27 and 1.43 and grain-size exponent, m , between ∼ 2.2 and ∼ 2.4. The activation energy for creep ranged between 529 and 625 kJ/mol. Both round (r type) and wedgeshaped (w type) cavities were observed in electron micrographs of the deformed samples. No noticeable change in the dislocation density was observed. Contribution of cavitation to the creep rate was estimated using an unconstrained cavity model. Based on this study it is concluded that the dominant mechanism of creep in polycrystalline AlN is diffusional.     

Ultra-high temperature deformation in TaC and HfC

TaC and HfC bars were thermo-mechanically tested up to 2900?°C using a non-contact loading method based on the Lorentz force. It was observed that HfC deflected more than TaC up to 2300?°C, which has been contributed to a difference in grain size facilitating diffusional creep, either Nabarro-Herring or Coble creep. Above 2500?°C, TaC continued to deflect more with temperature whereas HfC showed a reduced deflection. This reduced deflection was found to be an artifact of a preload plastic deformation response. Though both sets of samples were identified to have a prevalence of <110>{110} slip, at elevated temperatures, it appears that mass transport and diffusional creep mechanisms dominate evident by porosity in the grain boundaries. The activation energies of TaC were found to be 946?±?157?kJ/mol (between 2500–2700?°C) and HfC to be 685?±?54?kJ/mol (between 2100–2300?°C).     

A micromechanics study of competing mechanisms for creep fracture of zirconium diboride polycrystals

A micromechanics model was developed to simulate creep fracture of ceramics at high temperatures and material properties pertinent to zirconium diboride (ZrB₂) were adopted in the simulation. Creep fracture is a process of nucleation, growth, and coalescence of cavities along the grain boundaries in a localized and inhomogeneous manner. Based on the grain boundary cavitation process, creep fracture can be categorized into cavity nucleation-controlled and cavity growth-controlled processes. On the other hand, based on the deformation mechanism, the separation between two adjacent grain boundaries can be categorized into diffusion-controlled and creep-controlled mechanisms. In this study, a parametric study was performed to examine the effects of applied stress, cavity nucleation parameter, grain boundary diffusivity, and applied strain rate on cavity nucleation-controlled versus growth-controlled process as well as diffusion-controlled vs. creep-controlled mechanism during creep fracture of ZrB₂.     

Compressive Creep and Creep Failure of 8Y2O3/3Al2O3-Doped Hot-Pressed Silicon Nitride

The compressive creep properties of hot-pressed Si₃N₄8Y₂O₃—3Al₂O₃ (wt%) have been investigated in the temperature range of 1543–1603 K in air. The stress exponent, n , of the power creep law was determined to be 1.5, and the activation energy was determined to be 650 kJ/mol. Transmission electron microscopy observations showed that grain-boundary sliding occurred with cavitation formation in the grain-boundary glassy phase. The quasi-steady-state creep results were consistent with that of the diffusion-controlled solution—diffusion—precipitation creep mechanism, and the distinguished failure mechanism was cavitation creep damage controlled by the viscosity of the boundary glassy phase. The compressive creep failure time, obtained at 1573 K, in the stress range of 175–300 MPa, followed the MonkmanGrant relation, indicating that cavity growth was mainly controlled by the creep response of the material.     

Compressive Creep of Beryllium Oxide-Uranium Dioxide Mixtures

Beryllium oxide-uranium dioxide mixtures were deformed in compression in the region 1375° to 1540°C. The average apparent activation energy for creep of the oxide mixtures containing up to 10 wt% uranium dioxide is 95.1 kcal/mole. The activation energy is not sensitive to the applied stress and does not vary with urania additions. Creep rate is linearly dependent on the applied stress to 6000 psi. At constant stress and temperature, creep rate dependence on grain size for BeO-10 wt% UO₂ specimens can be described by the relation ɛ∼ 1/2². The creep rate dependence on the applied stress and grain size is consistent with the Nabarro-Herring mechanism. Creep behavior of the oxide mixtures is ascribed to the deformation of the beryllium oxide matrix.     

Compression Deformation Mechanism of Silicon Carbide: I, Fine-Grained Boron- and Carbon-Doped β-Silicon Carbide Fabricated by Hot Isostatic Pressing

The deformation behavior of boron- and carbon-doped β-silicon carbide (B,C-SiC) with an average grain size of 260 ± 18 nm containing 1 wt% boron was investigated by compression testing at elevated temperatures. Extensive grain growth during deformation was observed. The stress–strain curves were compensated for grain growth by assuming power-law type of dependence on grain size and strain rate. The stress exponent n was ∼1.3 and the grain size exponent p was ∼2.7 at temperatures ranging from 1593° to 1758°C. The apparent activation energy of deformation Q _d was ∼760 kJ/mol, which was lower than the activation energy for lattice diffusion of silicon and carbon in SiC and higher than that for grain-boundary diffusion of carbon in SiC. These results suggest that the deformation mechanism of the fine-grained B,C-SiC is grain-boundary sliding accommodated by the grain-boundary diffusion.     

A New Model for Tensile Creep of Silicon Nitride

The tensile creep rate of most commercial grades of Si₃N₄ increases strongly with stress. Although the usual power-law functions can represent the creep data, the data often show curvature and systematic variations of slope with temperature and stress. In this article, we present a new approach to understanding the creep of ceramics, such as Si₃N₄, where a deformable second phase bonds a deformation-resistant major phase. A review of experimental data suggests that the rate of formation and growth of cavities in the second phase controls creep in these materials. The critical step for deformation is the redistribution of the second phase away from the cavitation site to the surrounding volume. The effective viscosity of the second phase and the density of active cavities determine the creep rate. Assuming that the hydrostatic stresses in pockets of the second phase are normally distributed leads to a model that accurately describes the tensile creep rate of grades of Si₃N₄. In this model, the creep rate increases exponentially with the applied stress, is independent of Si₃N₄ grain size, is inversely proportional to the effective viscosity of the deformable phase, and is proportional to the cube of the volume fraction of the deformable phase.     

Experimental Assessment of Plasticity of Nanocrystalline 1.7 mol% Yttria Tetragonal Zirconia Polycrystals

High temperature mechanical behavior of nanocrystalline 1.7 mol% (3 wt%) yttria tetragonal zirconia polycrystals (nc-YTZP) was characterized by compression creep tests. The hot isostatically pressed nc-YTZP with mean grain size of 120 nm was subjected to grain growth to obtain grain sizes in the range of 120–310 nm. Direct measurements of the creep parameters were performed in the temperature range 1150°–1300°C and stress range 5–400 MPa. The strain rates at 1150°C ranged between 2 × 10⁻⁷ and 9 × 10⁻⁵ s⁻¹ when increasing the stress from 15 to 400 MPa. Values of the stress exponent, n =2.0±0.3, and the activation energy, Q =630±40 kJ/mol, were obtained for all test conditions. A value of the grain size exponent, p =1.5±0.3, was obtained at 1150°C in the stress range studied. Detailed microstructural observations revealed the absence of glassy phase at the grain boundaries. The creep parameters were compared with those from the literature, and the results were discussed in terms of the model recently developed by the authors, with a reasonable agreement.     

Diffusional Creep and Kinetic Demixing in Yttria-Stabilized Zirconia

The creep behavior of fine-grained yttria-stabilized zirconia with 25 mol% Y₂O₃ has been characterized as part of an investigation of kinetic demixing in solid-solution oxides which are subjected to a nonhydrostatic state of stress. At temperatures between 1400° and 1600°C, the steady-state strain rate of (Zr_0.6Y_0.4)O_1.8 samples with average grain sizes between 2.5 and 14.5 μm can be summarized by the flow law ɛ= 6.5 × 10⁻⁷σ^1.2 exp[−550 (kJ/mol)/ RT ] d ^−2.2 (s⁻¹) for stresses in the range 8 to 60 MPa, where σ is in pascals and d is in meters. This flow law indicates that deformation occurs by a Nabarro-Herring creep mechanism in which the creep rate is limited by cation lattice diffusion. Kinetic demixing was not observed in deformed polycrystalline samples even though diffusional creep was rate limited by cation lattice diffusion. This result can be explained if the cation diffusivities are approximately equal or if extensive grain rotation occurs during diffusional creep.     

High-Temperature Plastic Deformation of Polycrystalline Beryllium Oxide

High-density specimens were plastically deformed under four-point transverse bending. Tests were conducted in vacuum in the region 1400° to 1700°C under stresses of 1000 to 4500 psi. The activation energy for creep was 99.0 kcal/mole. Creep rate was directly proportional to the applied stress and inversely proportional to the square of the grain diameter. The deformation behavior is ascribed to a Nabarro-Herring type mechanism. Results show that creep was the same in tension and compression.     

The superplastic deep drawing of a fine-grained alumina–zirconia ceramic composite and its cavitation behavior

The synthesis, superplastic deep drawing and cavitation behavior of a fine-grained alumina–zirconia ceramic composite have been investigated. The results show that dense Al₂O₃/ZrO₂ samples with average grain diameter of 230 nm can be elongated to a dome height of at least 12 mm at the punch rate of 0.6 mm·min⁻¹ at 1400 °C. Deformed microstructure of the material indicates that not only the nucleation and growth of internal cavities are effectively suppressed but also the intragranular dislocation structures and sub-boundaries are observed around the nano-particles in alumina grains, which proves that intragranular dislocation creep is playing an important role in deformation. While the research on the deep drawing of the materials with the initial average grain size of 450 nm conforms that a plasticity controlled cavity growth process takes place during deformation.     

Cavity Development During Creep Deformation in Alumina with a Bimodal Grain Size Distribution

An alumina sample, codoped with equimolar proportions of magnesia and zirconia, exhibited a bimodal grain size distribution after hot-pressing. Flexural creep experiments were performed on this material at temperatures of 1673 and 1773 K in air. Inspection of the deformed specimens revealed extensive creep cavitation, with cavities developing preferentially in the coarse-grained regions. The nucleation, growth, and interlinkage of the cavities led to the formation of cracks. Crack growth occurred in the coarse-grained regions by the linkage of cavities with the crack tip. However, several cracks were observed to terminate after extending up to a fine-grained region of a specimen. A model has been developed to rationalize the observation that preferential cavitation occurs in the coarse-grained regions of a specimen undergoing creep deformation.     

Creep Cavitation in Liquid-Phase-Sintered Alumina

The early stages of cavitation during compressive creep of a liquid-phase-sintered alumina have been characterized using small-angle neutron scattering. Grain-boundary cavities were found to nucleate throughout creep, although at a steadily decreasing rate. The cavities were located on two-grain junctions as well as triple points and were spaced approximately 100 to 200 nm apart. The cavity spacing corresponded to the spacings observed for grain-boundary ledges, suggesting that the ledges were the cavity nucleation sites. Cavity nucleation was also found to be relatively independent of the applied stress. This behavior has been rationalized based on the decreasing ratio of ɛ_gbs/ɛ_t, where ɛ_gbs is the strain due to grain-boundary sliding and ɛ_t is the total strain, at increasing stresses. Cavity growth, on the other hand, was highly stress dependent. Above a certain "threshold" stress cavity growth was observed. In all cases, however, the observed growth was transient; i.e., the cavity growth rate decreased with time. Lowering the stress below the "threshold" resulted in a condition in which cavities nucleated but continued growth of the cavities did not occur. In all cases the cavities nucleated and grew, when growth did occur, with relatively equiaxed shapes.     

High-Temperature Deformation of Polycrystalline Fe2O3

The effects of stress, temperature, grain size, porosity, and O₂ partial pressure on the creep of polycrystalline Fe₂O₃ were studied in the range 770° to 1105°C by tests in 4-point bending and compression. Deformation rates are controlled by the stress-directed diffusion of either oxygen or iron. Diffusion coefficients computed from the Nabarro-Herring formula modified by including an empirical porosity-correction term are also consistent with the values reported for oxygen and iron.     

Damage-Enhanced Creep in a Siliconized Silicon Carbide: Mechanics of Deformation

Continuum mechanics methods were employed to analyze creep deformation of a grade of siliconized silicon carbide at elevated temperatures. Three loading modes (tension, compression, and bending) are considered in this analysis. In tension, deformation is accompanied by cavitation at stresses in excess of a temperature-dependent threshold level, resulting in bilinear power-law creep. In compression, greater applied stresses are required to achieve the same rate of strain, and although bilinear creep behavior is also observed, a single power-law creep equation was assumed to simplify the mathematical analysis of the flexure problem. Asymmetrical creep in siliconized silicon carbide leads to a number of unique features in flexural creep. At steady state, a threshold bending moment exists below which no damage occurs. The neutral axis shifts from the geometric center toward the compressive side of the specimen by an amount that depends on the level of applied stress. Cavitation zone shapes, which are predicted to develop in a four-point bend specimen as a function of load, are found to be in qualitative agreement with those obtained experimentally. For transient creep under bending, the time-dependent neutral axes for stress and strain do not coincide, although they do converge toward a single axis at steady state. Quantitative predictions are given for relaxation of tensile stresses at the outer fiber, reverse loading in the midplane region, and the growth of the damage zone toward the compressive side of the flexural specimen. This load redistribution leads to a prolonged transient stage as compared to its counterpart in uniaxial creep.     

Suitability of mullite for high temperature applications

High temperature mechanical behaviour of mullite has been studied. Our study include tensile, flexural and compressive creep behaviour and fracture up to 1400 °C. The results obtained in creep are analysed and compared with previous work in the literature. Two regions with different behaviour can be distinguished. The creep rates in bending, tension and compression are very similar in the first region at low stresses and temperatures. It is shown that in this region creep takes place by accommodated grain boundary sliding assisted by diffusion. At higher stresses slow crack growth from defects present in the sample occurs. The stress at which this transition in the deformation mechanism happens is dependent on several factors, the loading system during testing, the grain size, the amount and distribution of glassy phase and the environment. It is claimed the existence of a network of mullite–mullite grain boundaries free of glassy phase associated to the low surface energy of [001] planes. The diffusion rate through these boundaries controls the creep rate, and explains the high creep resistance of mullite. The results presented in this work lead to the conclusion that the mechanism controlling high temperature deformation resistance of mullite materials in a wide range of stress–temperature working conditions is independent of the glassy phase content. Slow crack growth limit the use of mullite at high stresses and temperatures.