Weight Function Analysis on the R-Curve Behavior of Multilayered Alumina–Zirconia Composites

The single-edge V-notched-beam (SEVNB) testing geometry was used to measure the crack growth resistance ( R -curve) behavior of multilayered alumina–zirconia composites. Fracture mechanics weight function analysis was applied to predict the R -curve behavior of multilayered composites having a stepwise change in composition. These results were then used to differentiate the influence of residual stresses from crack-bridging stresses on the measured R -curve behavior.     

Crack-Bridging Analysis for Alumina Ceramics under Monotonic and Cyclic Loading

Frictional degradation of grain-localized bridges behind a crack tip has been recognized as the major cyclic fatigue mechanism in alumina ceramics. Such a fatigue mechanism implies that the crack growth resistance ( R ) curve behavior during cyclic fatigue is different from that of monotonic loading due to the reduction in crack-tip shielding. A recent crack-bridging theory based on crack compliances is used to study the bridging stresses under monotonic loading and during cyclic fatigue. The bridging-stress distributions of two coarse-grained aluminas under monotonic loading are determined using compliance measurements. Because the interlocking grain bridges at the crack wake are subject to frictional damage from cyclic loading, the bridging-stress distribution evaluated during cyclic fatigue is distinct from that for monotonic loading. These results indicate that it is incorrect to incorporate the R -curve behavior from monotonic loading to the analysis of cyclic fatigue of alumina ceramics.     

Fracture Resistance of SiC-Fiber-Reinforced Si3N4 Composites at Ambient and Elevated Temperatures

The crack growth behavior in unidirectional SiC-fiber-rein-forced Si₃N₄-matrix composites fabricated in our laboratories was investigated as a function of fiber volume fraction and temperature. Both the stress-intensity factor and an energy approach were adopted in the characterization of the crack growth behavior. Crack resistance increased with crack extension ( R -curve or T -curve) as a result of bridging effects associated with the intact fibers. Large-scale bridging was observed, and was considered in the determination of the R -curves. Temperature and fiber volume fraction affected the crack propagation behavior. At room temperature a single crack was initiated at the notch tip; it then branched and delaminated upon further loading. In contrast, at 1200°C, little crack branching was observed. Increasing fiber volume fraction increased the degree of crack branching. Temperature and fiber volume fraction also affected the R -curve behavior. Raising the temperature to 1200°C did not significantly degrade the room-temperature R -curve effect. Increasing the fiber volume fraction from 14% to 29% substantially enhanced the toughening effect and the R -curve behavior.     

Analytical Modeling for Bridging Stress Function Involving Grain Size Distribution in a Polycrystalline Alumina

In order to investigate the microstructural effect on the R -curve behavior in a polycrystalline alumina, an analytical model has been proposed based on the relationship between bridging stress and crack opening displacement. The crack opening displacement was measured using an in situ SEM fracture method, and then used for a fitting procedure to obtain the bridging stress distribution. The results indicated that the bridging stress function and the R -curve computed by the current model were consistent with those computed by the power-law relation, and that the grain size distribution was closely related to the bridging stress. Thus, the current model explained well the correlation between the bridging stress distribution and the local-fracture-controlling microstructural parameter to interpret the microfracture mechanism, including the R -curve behavior.     

Influence of the Metal Particle Size on the Crack Growth Resistance in Mullite–Molybdenum Composites

The R -curve for mullite–molybdenum (32 vol%) composites, which were obtained at 1650°C under reducing conditions with three different Mo average grain sizes (1.5, 3, and 9 μm), was estimated by the indentation-strength method and compared with that monolithic mullite obtained under similar conditions. The composites material exhibited rising R -curve behavior. The composite with larger grain size, however, displayed better damage tolerance and higher resistance to crack growth. Microscopic observation of the crack path revealed, in the composites, the systematic presence of dispersoids acting as bridging sites in the crack wake. Therefore, the increased fracture toughness of these ceramic-matrix composites with adherent ductile phase can be attributed to clamping forces applied by metal ligaments that bridge the crack faces behind the crack front. These clamping forces retard the crack from opening as an external stress is applied. It was inferred that this superior performance of the larger Mo particle size composite can be attributed mainly to more effective bridging of the metal grains. Because of this, a higher applied stress intensity will be required to propagate the crack tip. These results suggest that the rising R -curve should be proportional to the metal grain size, since the grain bridging area is proportional to the metal grain size.     

Improved Resistance to Damage of Silicon Carbide-Whisker-Reinforced Silicon Nitride-Matrix Composites by Whisker-Oriented Alignment

The effects of whisker-oriented alignment on resistance to damage of SiC( w )/Si₃N₄ composites have been investigated by the Vickers indentation method and R -curve behavior. It is shown that increasing the degree of whisker-oriented alignment decreases the lengths of Vickers impressions and indentation cracks. The results exhibit rising R -curve behaviors for the SiC( w )/Si₃N₄ composites with different degree of whisker-oriented alignment. Moreover, the initial crack length c _i, the threshold of crack growth resistance K _i, and the upper bound of crack growth resistance K _∞ change regularly with increasing degree of whisker-oriented alignment. All results suggest that the whisker-oriented alignment improves the resistance to damage of the composites, resulting in a more reliable and usable composite.     

Determination of the R-Curve from the Strength—Indentation Load Relation

Strength as a function of indentation load has been measured to evaluate toughness versus crack size curves (i.e., R -curves) of ceramics. In the past, this evaluation is achieved by generating a family of global stress intensity versus crack size curves (i.e., K -curves) at each indentation load and its corresponding strength, and then fitting an envelope of tangency points to these curves. This envelope yields the R -curve. A methodology is proposed in the present study to define the point in the K -curve at which the R -curve intersects. This methodology complements the conventional "tangency condition" approach in determining the R -curve from the experimental strength-indentation load relation.     

R-Curve Behavior of Si3N4–BN Composites

R -curve behavior of Si₃N₄–BN composites and monolithic Si₃N₄ for comparison was investigated. Si₃N₄–BN composites showed a slowly rising R -curve behavior in contrast with a steep R -curve of monolithic Si₃N₄. BN platelets in the composites seem to decrease the crack bridging effects of rod-shaped Si₃N₄ grains for small cracks, but enhanced the toughness for long cracks as they increased the crack bridging scale. Therefore, fracture toughness of the composites was relatively low for the small cracks, but it increased significantly to ∼8 MPa·m^1/2 when the crack grew longer than 700 μm, becoming even higher than that of the monolithic Si₃N₄.     

Fracture Toughness and Thermal Shock Behavior of Silicon Nitride–Boron Nitride Ceramics

Fracture toughness behavior, stress–strain behavior, and flaw resistance of pressureless-sintered Si₃N₄-BN ceramics are investigated. The results are discussed with respect to the reported thermal shock behavior of these composites. Although the materials behave linear-elastic and exhibit no R -curve behavior, their flaw resistance is different from that of other linear-elastic materials. Whereas the critical thermal shock temperature difference (Δ T _c) is enhanced by adding BN, the content of BN has no influence on the strength loss during severe thermal shocks.     

Strength and Toughness of Slip-Cast Fused-Silica Composites

The effects of fiber composition, size, and surface treatment on the mechanical behavior of slip-cast fused-silica composites were investigated. The ambient and 1000°C stiffness and strength, fracture toughness, G _R -curve behavior, and fiber-matrix interface bond strength were determined. Quantitative fractography and scanning electron microscopy were used to ascertain the mechanisms of toughening and strengthening. Composites with weak interface bonding exhibited good strength retention and rising G _R -curve behavior. The fracture resistance was improved primarily through crack deflection.     

Role of Grain Size in the Strength and R-Curve Properties of Alumina

An investigation of the interrelationships between strength, crack-resistance ( R -curve) characteristics, and grain size for alumina ceramics has been carried out. Results of identation-strength measurements on high-density aluminas with uniform grain structures in the size range 2 to 80 μm are presented. A theoretical fit to the data, obtained by adjusting parameters of a constitutive frictional-pullout relation in a grain-bridging model, allows determination of the critical microstructural parameters controlling the R -curve behavior of these aluminas. The primary role of grain size in the toughness characteristic is to determine the scale of grain pullout at the bridged interface. It is shown that the strength properties are a complex function of the bridged microstructure, governed at all but the finest grain sizes by the stabilizing effect of the R -curve. The analysis confirms the usual negative dependence of strength on grain size for natural flaws that are small relative to the grain size, but the dependence does not conform exactly to the −1/2 power predicted on the basis of classical "Griffith-Orowan" flaws. The analysis provides a self-consistent account of the well-documented transition from "Orowan" to "Petch" behavior.     

R-Curve Behavior in a Silicon Carbide Whisker/Alumina Matrix Composite

R -curve measurements were performed on a SiC whisker/Al₂O₃ matrix composite. A controlled flaw/strength technique was utilized to determine fracture resistance as a function of crack extension. Rising R -curve behavior with increasing crack extension was observed, confirming the operation of wake toughening effects on the crack growth resistance. Observations of crack/microstructure interactions revealed that bridging by intact whiskers in the crack wake was the mechanism responsible for the rising R -curve behavior.     

Mechanical Behavior of Alumina Reinforced with Carbon-Coated Silicon Carbide Whiskers

SiC whiskers with 0, 20, and 50 Å carbon coatings were incorporated into an alumina matrix to modify residual thermal stress and interfacial bonding. Composites were characterized using triaxial X-ray diffraction for residual stress determination and electron microscopy to explore interfacial chemistry. Fracture toughness and R -curve behavior were examined for short and long crack lengths. Uncoated SiC whiskers optimized strength, fracture toughness, and R -curve behavior of these composites. A graphite interphase at the whisker/matrix interface decreased contributions to crack bridging without promoting additional toughening by whisker pullout.     

R-Curve Behavior of Long Cracks in Alumina

Coarse-grained alumina is among those monolithic ceramics which can exhibit an increase in crack resistance with crack extension. This R -curve behavior is most pronounced for intergranular fracture and does not depend exclusively on material properties. Crack and specimen geometries also influence the shape of the R -curves. The magnitude of the effect increases with increasing crack surface roughness, which is microstructure-dependent, and with crack-opening displacement, which is geometry-dependent. Based on experimental observations, a "dynamic" R -curve model is presented which relates the increasing resistance to an increasing crack tip shielding caused by crack surface bridging. Applying a J -integral approach, R -curves are calculated for two specimen geometries (short double cantilever beam and single-edged notched beam) and different grain sizes. The good agreement between calculation and experiment indicates that the R -curve behavior of long cracks in alumina can be predicted by a simple wake model.     

Stress–Strain Behavior of Alumina, Magnesia-Partially-Stabilized Zirconia, and Duplex Ceramics and Its Relevance for Flaw Resistance, KR-Curve Behavior, and Thermal Shock Behavior

The stress–strain behavior for Al₂O₃ of different grain size, for three different Mg-PSZ grades, and for various differently composed duplex structures is investigated and compared with their flaw resistance, K^R -curve behavior, and thermal shock behavior measured in previous works. The experimental results seem to reveal that, for most materials, quasi ductility increases with increasing flaw resistance, increasingly pronounced K^R -curve behavior, and increasing thermal shock retained strength. However, brittle ceramics can exhibit rising K^R -curves, whereas pronounced quasiductile materials can exhibit flat K^R -curves. An explanation for the apparent pseudo relationship between quasi ductility and K^R -curve behavior may be that, apart from genuine transformation ductility, most quasi-ductile effects such as microcracking have only a minor contribution to rising R -curve behavior, but require the existence of strong residual stresses, which are, on the other hand, responsible for the occurrence of most toughening mechanisms. Also discussed is the influence of microcracking on flaw resistance and thermal shock strength degradation.     

Short Crack R-Curves in Ferroelectric and Electrostrictive PLZT

This work describes the measurement of R -curve behavior in ferroelectric ceramics using four-point bend specimens with controlled semielliptical surface cracks. The results are compared for two compositions of lead lanthanum zirconate titanate. One exhibits ferroelastic behavior, the other electrostrictive linear elastic behavior. R -curves are measured in the crack length regime of 0.1 to 0.8 mm. The ferroelastic composition displays a toughness increase from 0.5 to 1.2 MPa·m^1/2. The linear elastic composition displays a flat R -curve. The R -curve behavior is attributed to ferroelastic toughening.     

Alumina Agglomerate Effects on Toughness-Curve Behavior of Alumina–Mullite Composites

Toughness-curve ( T -curve) behavior of composites of spherical, polycrystalline, coarse-grained, alumina agglomerates dispersed throughout a constant-toughness, fine-grained, 50–50 vol% alumina–mullite matrix has been evaluated as a function of agglomerate content for the range 15 to 45 vol%. T -curve behavior was evaluated using the indentation-strength method. Increasing alumina agglomerate content resulted in a progressive increase of large indentation load strengths with negligible change of plateau strength levels at small indentation loads. This behavior is consistent with underlying T -curves that rise to greater values and are shifted toward longer crack lengths with increasing agglomerate content, suggesting that both bridge spacing and bridge potency increase with increasing agglomerate content over the range tested. The proposed relationships between bridge spacing and agglomerate content, and bridge potency and agglomerate content, are rationalized in terms of residual stress considerations. The indentation-strength data also demonstrated that the composite containing the greatest alumina agglomerate content, 45 vol%, exhibited the greatest flaw tolerance.     

Effect of Shear Damage on the Fracture Behavior of Carbon–Carbon Composites

The notch insensitivity of carbon–carbon composites (C/Cs) has been believed to result primarily from shear damage near sources of stress concentration. To evaluate this hypothesis, notch sensitivity has been examined for C/Cs with crossply laminates (CP-C/Cs) and quasi-isotropic (QI-C/Cs) laminates. The main difference in both laminates involves their shear behavior: the QI-C/Cs have an almost-linear stress–strain curve and high strength, whereas the CP-C/Cs exhibit strong nonlinearity and low strength. Thus, the effect of shear damage can be extracted by comparison of both materials. Experimental results from the present study have shown that the fracture behaviors of both C/Cs are quite similar. Finite-element analyses also have revealed that the stress redistribution caused by shear nonlinear deformation is too small to explain its toughening behavior, even in the CP-C/C. From these results, it is concluded that the notch-insensitive behavior of the C/Cs cannot be explained by the already-proposed shear-damage mechanism. To this end, a discussion has been conducted on a new possible toughening mechanism that is capable of generating the R -curve and notch insensitivity.