Effect of Surface Flaw Size on Fracture Strength of Alumina Ceramics

Semielliptical surface flaws of different sizes were introduced into Al₂O₃ by Knoop microhardness indentation. The specimens were fractured by four-point bending and the profiles of the indentation flaws were determined by observing the fracture surfaces with a scanning electron microscope. The relation between the indentation flaw size and the fracture strength could be well explained by applying the fracture-mechanics analysis for semielliptical surface flaw in bending. The calculated values of the as-indented critical stress intensity factor, K_IC, were lower than previously reported presumably because of the influence of the residual stresses produced by the indenter.     

Controlled Surface Flaws in Hot-Pressed Si3N4

Surface flaws of controlled size and shape were produced in high-strength hot-pressed Si₃N₄ with a Knoop microhardness indenter. Fracture was initiated at a single suitably oriented flaw on the tensile surface of a 4-point-bend specimen, with attendant reduction in the measured magnitude and scatter of the fracture strength. The stress required to propagate the controlled flaw was used to calculate the critical stress-intensity factor, K _IC, from standard fracture-mechanics formulas for semielliptical surface flaws in bending. After the bend specimen had been annealed, the room-temperature K _IC values for HS-130 Si₃N₄ increased to a level consistent with values obtained from conventional fracture-mechanics tests. It was postulated that annealing reduces the residual stresses produced by the microhardness indentation. The presence of residual stresses may account for the low K _IC, values. Elevated-temperature K_IC values for HS-130 Si₃N₄ were consistent with double-torsion data. Controlled flaws in HS-130 Si₃N₄ exhibited slow crack growth at high temperatures.     

Microhardness and Fracture Toughness Anisotropy in Cubic Zirconium Oxide Single Crystals

Vickers and Knoop indentation tests have been used to study the fracture and deformation characteristics of 9.4-mol%-Y₂O₃-stabilized ZrO₂ single crystals. K_c is anisotropic, with values of 1.9 and 1.1 MPa·m^1/2 for radial cracks propagating along (100) and (110), respectively. The toughness for these two orientations was also determined using the single-edge notched-beam geometry, and yielded values of 1.9 and 1.5 MPa·m^1/2.     

Controlled Surface Flaws in Hot-Pressed SiC

Controlled semi-elliptical surface flaws were produced in hot-pressed SiC by Knoop microhardness indentation. Flawed specimens were placed in 4-point bending in order to determine their critical stress intensity factor, K_IC, at both room and high temperatures. Room-temperature fracture and K_IC values after annealing were sensitive to the annealing environment; this behavior correlated with the active/passive nature of the oxidation process. Flaw healing was observed for annealing exposures in air. Room-temperature K_IC values increased with increasing annealing temperature. High-temperature K_ICvalues decreased with increasing temperature as a result of a decrease in the fracture surface energy.     

Controlled Surface Flaw-Initiated Fracture in Reaction-Densified Silicon Carbide

Controlled surface flaws were produced in commercial reaction-densified SiC by Knoop microhardness indentation. The flaws themselves could not be observed easily, thus an etching technique was used to delineate their semielliptical shape, thereby enabling calculation of the critical stress- intensity factor K _IC at room temperature. Room-temperature fracture was insensitive to annealing environment (air or vacuum), flaw "healing" being observed at ≫1000°C. The variation in fracture stress of indented specimens with temperature showed 3 distinct regions of behavior which were interpreted in terms of residual stress relief, flaw healing, and Si-SiC bond weakening.     

Influence of Surface Stress on indentation Cracking

A simple, two-dimensional fracture mechanics analysis was used to determine the influence of nonuniform residual surface stresses on the formation of radial indentation cracks. The indentation behavior depends on the depth of the compressive stresses, such that the apparent fracture toughness passes through a maximum with increasing indentation load. The analysis was used to estimate the surface stress from indentation data for a zirconia-toughened ceramic and was compared to previous X-ray diffraction measurements of this stress. The comparison gives only fair agreement; the sources of possible error are discussed. Such surface stresses also influence the accuracy of K _{I C} measurements when an indentation crack length technique is used; surface preparation is a critical factor in the measurement. Finally, the K _{I C} values obtained from indentation crack sizes were compared with those obtained by the double-cantilever-beam technique.     

Controlled Flaws in Ceramics: A Comparison of Knoop and Vickers Indentation

Application of indentation fracture analysis to Knoop and Vickers indentation is examined, with particular emphasis on determining the limitations of the point force representation for the residual stress field. Deviation from the point force approximation is insignificant for crack-size/plastic-zone-size ratios 1.3. The Vickers deformation/fracture configuration in brittle materials invariably conforms to this requirement, whereas the Knoop configuration does not (except at very high indentation loads). However, stable crack growth during a failure test extends the crack sufficiently that the strength degradation for both types of indentation is well described by the point force approximation.     

Microhardness and Indentation Fracture of Potassium Dihydrogen Phosphate (KDP)

Potassium dihydrogen phosphate (KDP) is an important electrooptic tetragonal crystal, often used in third harmonic generation in laser systems. We have used microindentation to measure the Vickers and Knoop hardness of KDP and the resulting cracking on (100) and (001) faces. Hardness anisotropy on the (001) face, or among the (100) and (001) faces, was small (∼20%). We observed an indentation size effect for both Vickers and Knoop hardness, for indenting loads in the range 0.24–1.96 N. The large-load Vickers hardness was estimated as 1.4 ± 0.1 GPa. We observed anisotropy in the crack sizes on (100) and (001) faces. Cracks were longer on (100) faces than on (001) faces. Assuming elastic and plastic isotropy, crack sizes were analyzed, and fracture toughness, K_c , was extracted. We present here an approximate model for analyzing crack-load microindentation data in tetragonal crystals. The model uses the minimum elastic modulus of the material. The effect of the isotropic assumption on the extracted fracture toughness is estimated at ∼33%, with a 23% contribution resulting from elastic anisotropy and 10% from the slip-system plastic anisotropy.     

Indentation Fracture Response and Damage Resistance of Al2O3-ZrO2 Composites Strengthened by Transformation-Induced Residual Stresses

Indentation fracture behavior of three-layer Al₂O₃-ZrO₂ composites with substantial compressive residual stresses was compared with the behaviors of monolithic Al₂O₃ and Al₂O₃-ZrO₂ ceramics without intentionally introduced residual stresses. The indentation cracks were smaller in the three-layer specimens relative to the monolithic specimens in agreement with the predictions of indentation fracture mechanics theory. Indentation and strength testing were used to show that a residual compressive stress of approximately 500 MPa exists in the outer layers of the three-layer composites. The three-layer specimens showed excellent damage resistance in that the strength differential between the three-layer and monolithic indented specimens was maintained at indentation loads up to 1000 N, the maximum indentation load used in the experiments.     

Knoop and Vickers Indentation in Ceramics Analyzed as a Three-Dimensional Fracture

A three-dimensional fracture analysis is applied to the Knoop and Vickers indentation fracture of ceramics. A brief discussion of the accuracy of the analysis applied to model the step load on the crack face caused by the residual stresses is given. A study is made of the effect of the elongated plastic zone in Knoop indentation on the unloaded radial fracture. It is shown that for small indentation loads the published experimental data can be verified by varying the depth reached by the semielliptical plastic zone with given surface length. An analysis and interpretation of the interaction between the two halfpenny-shaped radial cracks induced by Vickers indentation is also given.     

Rising Fracture Toughness from the Bending Strength of Indented Alumina Beams

The analytical function of crack extension to a fractional power is used to represent the fracture resistance of a vitreous-bonded 96% alumina ceramic. A varying flaw size, controlled by Vickers indentation loading between 3 and 300 N, was placed on the prospective tensile surfaces of four-point bend specimens, previously polished and annealed. The lengths of surface cracks were measured by optical microscopy. Straight lines were fitted to the logarithmic functions of observed bending strength versus indentation load in two series of experiments: (I) including the residual stress due to indentation and (II) having the residual stress annealed out at an elevated temperature. Within the precision of measurement these lines have the same slope, being about 32% less than the -1/3 slope which a fracture toughness independent of crack extension would indicate. Considering the criteria for crack extension and specimen failure, the fracture mechanics equations were solved for the conditions of the two series of experiments. Approximately the same values of fracture toughness, rising as a function of indentation flaw size, were obtained from both series of experiments.     

Mixed-Mode Fracture of Hot-Pressed Si3N4

The mixed-mode fracture of hot-pressed Si₃N₄ was investigated using inclined indentation surface flaws in bending and large crack geometries in combined tension/torsion. Non-coplanar fracture was observed in all cases. Values of K_Ic, K_IIc, and K_IIIc stress intensity factors were obtained, with ratios K_IIc/K_Ic= 0.79 and K_IIIc/K_Ic= 1.55 observed. For large cracks, mode II conditions had more of an effect on mode I fracture than mode III conditions. The mixed-mode I-II fracture of surface flaws was significantly different from that for large cracks, suggesting surface flaw shear resistance effects. A model describing these effects was derived, based on the ratio of the crack-opening displacement to the crack surface asperity height.     

Geometrical Effects in Elastic/Plastic Indentation

A general analysis of elastic/plastic indentation fracture for an arbitrary-shaped indenter is presented. The analysis is based on the observation that the residual indentation stress field provides the driving force for crack formation. After establishing that the influences of indenter geometry and load on the residual field are completely characterized by the volume of the indentation, a relation between the extent of radial cracking, the indentation volume, and the material properties is derived. Predictions of the analysis are examined by comparing calculated load/crack-length relations for two specific indenter geometries (Vickers pyramid and sphere) with experimental measurements in ZnS. For Vickers indentation the crack length is proportional to (load)^2/3, whereas for spherical indenters the variation of crack length with load is nearly linear.     

Fracture mechanics of sharp scratch strength of polycrystalline alumina

The strength of a polycrystalline alumina containing controlled scratches introduced by translated sharp contacts is investigated and described by a multiscale fracture mechanics model. Inert strength measurements of samples containing quasi‐static and translated Vickers indentation contacts showed that scratches degraded the strength at normal contact loads an order of magnitude less than those for quasi‐static indentation. The fracture mechanics model developed to describe strength degradation by scratches over the full range of contact loads included toughening effects by crack‐wake bridging at the microscale and lateral crack‐based residual stress relaxation effects at the mesoscale. A critical element of the model is the nonlinear scaling of the residual stress field of a scratch with the normal contact load acting during scratch formation. The similarities and differences in the scratch model in comparison with prior indentation‐strength fracture mechanics models are highlighted by parallel development of both. Central to the scratch model is the use of easily controlled normal contact load as the scratch‐strength measurement variable. Scratch length and orientation are shown to have significant effects on strength. The distributions of scratch widths controlling the intrinsic strengths of as‐received samples are determined and agreement with the observed scratch dimensions is demonstrated.     

Mixed-Mode Fracture of Ceramics in Diametral Compression

Mixed-mode fracture of a glass-ceramic and an alumina ceramic from inclined Knoop indenter flaws was studied in diametral compression and four-point-bend tests. In annealed specimens the directions of extension of the cracks and mode I and mode II stress-intensity factors at fracture were analyzed and compared to the predictions of a maximum crack-tip hoop stress theory. Knoop flaws in all cases extended in directions normal to the principal maximum tension rather than in the direction of maximum hoop stress near the crack tip. Mixed-mode fracture envelopes assessed in experiments, particularly with the diametral-compression test, showed significant deviation to higher K_II values relative to the fracture-mechanics predictions. As a consequence, an apparent K _IIc value assessed in the diametral-compression test was approximately twice the value of K _Ic.     

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.     

Hardness, Toughness, and Brittleness: An Indentation Analysis

The ratio H/K_c, wjere His hardness (resistance to deformation) and K_c. is toughness (resistance to fracture), is proposed as an index of brittleness. Indentation mechanics provides the scientific basis for this proposal. The analysis, developed in terms of a model contact system, indicates that all materials are more susceptible to deformation in small-scale loading events and to fracture in large-scale events. By normalizing the characteristic dimensions of the two competing processes and the contact load in terms of appropriate functions of H and K_c a universal deformation/fracture diagram can be constructed. From this diagram the mechanical response of any material of known hardness and toughness may be predicted for any prospective in-service contact loading conditions. The concept offers a simple approach to materials classification for design purposes.     

Mechanical Behavior of a Borosilicate Glass Under Aqueous Corrosion

In France, fission products are being vitrified for a possible final geological disposal. Under disposal conditions, corrosion of the glass by groundwater as well as stress corrosion because of stresses occurring at surface flaws cannot be excluded. Within this framework, the mechanical behavior of the French simulated nuclear waste glass SON68 was studied by Vickers indentation and fracture experiments in air and in a corrosive solution. The glass was corroded at 90°C in a solution enriched with Si, B, and Na. The results showed that the glass corrosion enhances the cracks propagation relative to experiments in air. The indentation fracture toughness ( K _{I C} ) obtained using a four-point bending test showed that the K _{I C} of the glass decreased with increasing corrosion time.     

Mixed-Mode Fracture in Soda-Lime Glass

Soda-lime-silica glass was fractured under combined mode I and mode II loading from flaws produced by hardness indentations. Critical stress intensities calculated from K₁ and K₁₁ combined using four analyses, are compared to K_IC measured by a fracture mechanics technique and to values of K_IC determined by measuring fracture-mirror size. The comparison showed that K_IC calculated using a noncoplanar strain-energy release-rate analysis gave the best agreement with values obtained by fracture mechanics techniques over the widest range of crack orientations. K_ICcalculated from mirror sizes was constant regardless of the orientation of the original flaw.