Indentation Studies on Y2O3-Stabilized ZrO2: II, Toughness Determination from Stable Growth of Indentation-Induced Cracks

Stable indentation cracks were grown in four-point bend tests to study the fracture toughness of two Y₂O₃-stabilized ZrO₂ ceramics containing 3 and 4 mol% Y₂O₃. By combining microscopic in situ stable crack growth observations at discrete stresses with crack profile measurements, the dependence of toughness on crack extension was determined from crack extension plots, which graphically separate the crack driving residual stress intensity and applied stress intensity factors. Both materials exhibit steeply rising R -curves, with a plateau toughness of 4.5 and 3.1 Mpa·m^1/2 for the 3- and 4-mol% materials, respectively. The magnitude of the plateau toughness reflects the fraction of tetragonal grains contributing to transformation toughening.     

Slow Crack Growth Behavior in Transformation-Toughened Al2O3-ZrO2(Y2O3) Ceramics

Significant increases in the critical fracture toughness (K _IC ) over that of alumina are obtained by the stress-induced phase transformation in partially stabilized ZrO₂ particles which are dispersed in alumina. More importantly, improved slow crack growth resistance is observed in the alumina ceramics containing partially stabilized ZrO₂ particles when the stress-induced phase transformation occurs. Thus, increasing the contribution of the ZrO₂ phase transformation by tailoring the Y₂O₃ stabilizer content not only increases the critical fracture toughness (K_IC) but also the K _Ia to initiate slow crack growth. For example, crack velocities ( v )≥10^–9 m/s are obtained only at K _Ia≥5 MPa.m^1/2 in transformation-toughened ( K _IC=8.5 MPa.m^1/2) composites vs K _Ia≥2.7 MPa.m^1/2 for comparable velocities in composites where the transformation does not occur ( K _IC=4.5 MPa.m^1/2). This behavior is a result of crack-tip shielding by the dissipation of strain energy in the transformation zone surrounding the crack. The stress corrosion parameter n is lower and A greater in these fine-grained composite materials than in fine-grained aluminas. This is a result of the residual tensile stresses associated with larger (≥1 μm) monoclinic ZrO₂ particles which reside along the intergranular crack path.     

Effect of Subcritical Crack Growth on Fracture Toughness and Work-of-Fracture Tests Using Chevron-Notched Specimens

A correlation between the plane strain stress intensity factor K_I , load, and crack extension has been analyzed for constant displacement and constant loading rate experiments, using chevron-notched, four-point-bend specimens. It is assumed that at the beginning of the experiment the chevron triangle tip is not ideally sharp. As loading continues, the crack initially moves with velocity v_t at K_I equal to a threshold value K_t . Maximum crack velocity is reached at K_I= K_IC , the fracture toughness. Depending on the type of material tested, a specific displacement or loading rate must be used to correlate the maximum load with K_Ic . An error in K_IC calculation is estimated if different displacement rates are applied. Repeated loading-unloading work-of-fracture (WOF) experiments generate values related to the resistance of the material to fracture initiation, K_t , only when the crack length approaches 100% of the specimen width. Values related to material's fracture toughness, K_IC are not generated in WOF tests.     

Fractographic Criteria for Subcritical Crack Growth Boundaries in 96% Al2O3

The percent intergranular fracture (PIF) was measured along radii extending from fracture origins in 96% A1₂O₃ specimens, fractured at various loading rates and temperatures, and plotted vs estimates of stress intensity factors ( K ₁) at the corresponding crack lengths. Two types of curves were observed. The first was similar to curves previously observed for hot-pressed alumina. In this case the subcritical crack-growth boundary was located approximately where the minimum in the PIF occurred near K ₁=4MPa·m^½, as was also the case for hotpressed alumina. Therefore, the location of this minimum or the projecting grams formed by intergranular fracture as the crack velocity increased can be used as criteria for locating the subcritical crack-growth boundary. The second type of curve lacks the minima in PIF characteristic of the first type and is characterized by a gradual trend toward higher PIF beginning at K ₁=3MPa·m^½. This type of curve may be caused by acceleration of the crack to high crack velocities at values of K ₁ approximately equal to or slightly greater than those necessary to cause critical crack growth on the lower fracture-energy planes in sapphire. Assuming that this is the case, the K ₁ at which the trend toward higher PIF begins can be used to calculate the radius to the critical flaw boundary for this type of fracture.     

Mixed-Mode Fracture Toughness of Ceramic Materials

An experimental technique whereby pure mode I, mode II, and combined mode I-mode II fracture toughness values of ceramic materials can be determined using four-point bend specimens containing sharp, through-thickness precracks is discussed. In this method, notched and fatigue-precracked specimens of brittle solids are subjected to combined mode I-mode II and pure mode II fracture under asymmetric four-point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I-mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al₂O₃. Multiaxial fracture mechanics of the Al₂O₃ ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness K _Ic, the mode III fracture initiation toughness is 2.3 times higher than K _Ic. The predictions of fracture toughness and crack path based on various mixed-mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed-mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.     

Silicon Carbide Monofilament-Reinforced Silicon Nitride or Silicon Carbide Matrix Composites

SiC-monofilament-reinforced SiC or Si₃N₄ matrix composites were fabricated by hot-pressing, and their mechanical properties and effects of filaments and filament coating layers were studied. Relationships between frictional stress of filament/matrix interface and fracture toughness of SiC monofilament/Si₃N₄ matrix composites were also investigated. As a result, it was confirmed experimentally that in the case of composites fractured with filament pullout, the fracture toughness increased as the frictional stress increased. On the other hand, when frictional stress was too large (>about 80 MPa) for the filament to be pulled out, fracture toughnesses of the composites were almost the same and not so much improved over that of Si₃N₄ monolithic ceramics. The filament coating layers were found to have a significant effect on the frictional stress of the SiC monofilament/Si₃N₄ matrix interface and consequently the fracture toughness of the composites. Also the crack propagation behavior in the SiC monofilament/Si₃N₄ matrix composites was observed during flexural loading and cyclic loading tests by an in situ observation apparatus consisting of an SEM and a bending machine. The filament effect which obstructed crack propagation was clearly observed. Fatigue crack growth was not detected after 300 cyclic load applications.     

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.     

Flat R-Curve from Stable Propagation of Indentation Cracks in Coarse-Grained Alumina

The fracture toughness of coarse-grained A1₂O₃, known for pronounced "Iong"-crack R-curve behavior, was studied in the "short"-crack regime utilizing the stable propagation of indentation cracks in bending. A combination of in situ microscopic crack growth observations and mechanical testing enabled measurement of crack extension curves. They reflect the contributions of residual indentation stress intensity and applied bending stress intensity on the total crack driving stress intensity and allow determination of the residual stress factor χ and the toughness K_R. The results indicate that χ depends on indentation load and A_R is surprisingly constant rather than increasing. To resolve the latter contradiction with long-crack R-curve behavior, combined short/long-crack fracture tests were performed with the same specimens. Starting with stable indentation crack growth and continuing with stable long-crack extension, the previous toughness results were confirmed, i.e., constant toughness from indentation cracks and increasing toughness from long cracks. The influence of crack-opening behavior on bridging-controlled R-curve toughening can qualitatively explain the observed discrepancies.     

K R -Curve Behavior of Duplex Ceramics

The fracture toughness behavior during crack growth ( K ^R -curve behavior) of duplex ceramics is investigated. Different types of K ^R -curves can be distinguished depending on the microstructural designs of these materials which are characterized by the volume fraction and size of the dispersed pressure zones, and by their effective volume expansion. According to their K ^R -curve behavior, duplex ceramics can be subdivided into two groups consisting of "short-range" and "long-range" toughened materials. The experimental results are discussed regarding the appearance of different toughening mechanisms which are documented by crack path micrographs. An unusual toughening effect, a "crackbranching chain reaction," is documented by in situ observations. The critical stress to nucleate the observed process zone development is calculated and compared with the internal stress intensity factor K _i which has been previously proposed for these materials and with the material strength.     

Effect of Precrack "Halos" on Fracture Toughness Determined by the Surface Crack in Flexure Method

The surface crack in flexure method, which is used to determine the fracture toughness of dense ceramics, necessitates the measurement of precrack sizes by fractographic examination. Stable crack extension may occur from flaws under ambient, room-temperature conditions, even in the relatively short time under load during fast fracture strength or fracture toughness testing. In this article, fractographic techniques are used to characterize evidence of stable crack extension, a "halo," around Knoop indentation surface cracks. Optical examination of the fracture surfaces of a high-purity Al₂O₃, an AlN, a glass-ceramic, and a MgF₂ reveal the presence of a halo around the periphery of each precrack. The halo in the AlN is merely an optical effect due to crack reorientation, whereas the halo in the MgF₂ is due to indentation-induced residual stresses initiating crack growth. However, for the Al₂O₃ and the glass-ceramic, environmentally assisted slow crack growth is the cause of the halo. In the latter two materials, this stable crack extension must be included as part of the critical crack size to determine the appropriate fracture toughness.     

Dynamic Fracture Toughnesses of Reaction-Bonded Silicon Nitride

Dynamic fracture toughness specimens consisting of 5.1-mm thick, modified wedge-loaded, tapered double-cantilever-beam (WL-MTDCB) specimens, which are side-grooved on one side, were used to establish the room-temperature dynamic fracture toughness, K _ID vs crack velocity, a , relations of two reaction-bonded silicon nitrides. The measured dynamic crack extension histories were then used to drive a dynamic finite-element code in its generation mode which computes the dynamic stress intensity factors for a given crack extension. Results indicate that the K _ID vs a relations of reaction-bonded silicon nitrides do not follow the general trend in those relations of brittle polymer and steel. The slow initial crack velocity which was reported for glass was observed again in silicon nitride and resulted in a nonunique K _ID vs a relation, in contrast to the unique K _ID vs a material properties reported for brittle polymers and metals.     

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.     

Fracture of an Aluminosilicate Fiberboard

Mode-I fracture of aluminosilicate fiberboard that is used in large mirror casting molds was studied. The material was idealized as a transversely isotropic, layered composite that was composed of planar sheets of crosslinked fibers. Elastic constants, the toughness ( K_R ) curve, and the fracture work were measured at room temperature. The observed rising K_R behavior was attributed to crack bridging. Experimental measurements of the bridging stress were made using a specimen-renotching technique. Relationships between the bridging stress, K _R , and fracture work were explored and shown to be consistent.     

Dynamic Fracture Characterization of Al2O3 and SiCw/Al2O3

The dynamic stress intensity factors, which were determined with newly developed bar impact facilities and a new data reduction procedure, for an Al₂O₃ ceramic and 29 vol% SiC_w/Al₂O₃ composite were virtually identical, thus indicating that the short SiC whiskers were ineffective under dynamic fracture. SEM studies revealed five distinct fracture morphologies with increased percentage area of transgranular fracture in both materials with rapid crack propagation. Also, the high dynamic stress intensity factor caused multiple microscopic crack planes to form and then join as the crack advanced.     

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.     

Crack–Tip Toughness of a Soft Lead Zirconate Titanate

Crack–opening displacement (COD) measurements were performed on a commercial lead zirconate titanate (PZT). The intrinsic fracture toughness (or crack–tip toughness) of this material was determined using a new evaluation procedure, which takes into account the near–tip CODs and complete crack profile CODs. The crack–tip toughness K _I0 was determined from an extrapolation of COD data obtained at various loading stages, thus avoiding the complications caused by subcritical crack growth in PZT. Results for plane strain and plane stress condition are presented.     

Cyclic Fatigue-Crack Propagation in Magnesia-Partially-Stabilized Zirconia Ceramics

The subcritical growth of fatigue cracks under (tension-tension) cyclic loading is demonstrated for ceramic materials, based on experiments using compact C(T) specimens of a MgO-partially-stabilized zirconia (PSZ), heat-treated to vary the fracture toughness K _c from ∼3 to 16 MPa·m^1/2 and tested in inert and moist environments. Analogous to behavior in metals, cyclic fatigue-crack rates (over the range 10⁻¹¹ to 10⁻⁵ m/cycle) are found to be a function of the stress-intensity range, environment, fracture toughness, and load ratio, and to show evidence of fatigue crack closure. Unlike toughness behavior, growth rates are not dependent on through0-thickness constraint. Under variable-amplitude cyclic loading, crack-growth rates show transient accelerations following low-high block overloads and transient retardations following high-low block overloads or single tensile overloads, again analogous to behavior commonly observed in ductile metals. Cyclic crack-growth rates are observed at stress intensities as low as 50% of K _c , and are typically some 7 orders of magnitude faster than corresponding stress-corrosion crack-growth rates under sustained-loading conditions. Possible mechanisms for cyclic crack advance in ceramic materials are examined, and the practical implications of such "ceramic fatigue" are briefly discussed.     

Hardness, Toughness, and Scratchability of Germanium–Selenium Chalcogenide Glasses

Ge–Se chalcogenide glasses are characterized by relatively low hardness (0.39–2.35 GPa) and low fracture toughness (0.1–0.28 MPa·m^1/2). Actually, the hardness of chalcogen-rich glasses is low enough so that the brittleness parameter, B = H / K _c , is lower than that of silicate glasses. Whereas hardness and Young's modulus increase with increasing germanium contents, fracture toughness follows a trend similar to that of the density and exhibits a maximum for the Ge₂₀Se₈₀ composition, which corresponds to the rigidity percolation threshold. Optical microscopy and atomic force microscopy observations suggest that the indentation deformation proceeds by a localized shear deformation phenomenon. Glasses in the chalcogen-rich region behave viscoelastically at room temperature. As a consequence, an increase of the loading time results in a decrease of hardness and toughness.     

Cyclic Fatigue-Crack Growth and Fracture Properties in Ti3SiC2 Ceramics at Elevated Temperatures

The cyclic fatigue and fracture toughness behavior of reactive hot-pressed Ti₃SiC₂ ceramics was examined at temperatures from ambient to 1200°C with the objective of characterizing the high-temperature mechanisms controlling crack growth. Comparisons were made of two monolithic Ti₃SiC₂ materials with fine- (3–10 μm) and coarse-grained (70–300 μm) microstructures. Results indicate that fracture toughness values, derived from rising resistance-curve behavior, were significantly higher in the coarser-grained microstructure at both low and high temperatures; comparative behavior was seen under cyclic fatigue loading. In each microstructure, Δ K _th fatigue thresholds were found to be essentially unchanged between 25° and 1100°C; however, there was a sharp decrease in Δ K _th at 1200°C (above the plastic-to-brittle transition temperature), where significant high-temperature deformation and damage are first apparent. The substantially higher cyclic-crack growth resistance of the coarse-grained Ti₃SiC₂ microstructure was associated with extensive crack bridging behind the crack tip and a consequent tortuous crack path. The crack-tip shielding was found to result from both the bridging of entire grains and from deformation kinking and bridging of microlamellae within grains, the latter forming by delamination along the basal planes.     

Transformation Toughening in ZrO2-Containing Ceramics

Transformation toughening in ZrO₂-containing ceramics is discussed. Specifically, microstuctures of the three distinct types of ZrO₂-toughened ceramics are presented, after which microstructural evolution in MgO-partially-stabilized ZrO₂ Mg-PSZ) is reviewed. The mechanical properties of such transformation-toughened ceramics are dominated by "resistance-curve" ( R -curve) behavior, wherein the crack resistance increases during the course of crack propagation. Ceramics subject to R -curve behavior require a more detailed failure criterion than those subject to the usual linear elastic fracture mechanics criterion involving a critical stress intensity factor, K_IC.R -curve-controlled fracture in ceramics provides a degree of very desirable flaw insensitivity, but can lead to counterintuitive relationships concerning strength, toughness, and initial flaw size. Examples of R curves of Mg-PSZ with different thermal histories are given.