Crack-Shape Effects for Indentation Fracture Toughness Measurements

Various methods to measure fracture toughness using in-dentation precracks were compared using soda-lime glass as a test material. In situ measurements of crack size as a function of applied stress allow both the toughness K_c and the residual-stress factor χ to be independently determined. Analysis of the data showed that stress intensity factors based on classical half-penny crack shapes overestimate toughness values and produce an apparent R -curve effect. This is due to a constraint on crack shape imposed by primary lateral cracks in soda—lime glass. Models based on elliptical cracks were developed to account for the crack-shape effects.     

Fracture and Subcritical Crack Growth in Soda-Lime Glass under Combined Modes I and II Loading

Fracture and subcritical crack growth characteristics under combined modes I and II loading were studied using the compact tension shear specimens of soda–lime glass. The maximum normal stress criterion gives a good agreement with the experimental mode I–mode II fracture toughness envelope for initially straight cracks and kinked cracks. Subcritical crack growth characteristics were determined under sustained modes I and II loading in water. The values of K _I and K _II were calculated approximately by replacing the subcritical kinked crack with an assumed straight crack ā, and the K _Imax value based on the maximum normal stress criterion was used to describe this subcritical kinked crack growth. The experimental results show that subcritical crack growth under pure mode I, pure mode II, and various combined modes I and II loading can be well described by the K _Imax value based on the approximate maximum normal stress criterion.     

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.     

Morphology of Vickers Indent Flaws in Soda–Lime–Silica Glass

The subsurface structure of Vickers indents in soda–lime–silica glass was investigated using confocal microscopy and conventional microscopy. It was determined that the lateral cracks that form beneath the indentation site propagate away from the surface. The median/radial (MR) crack system was found to be semielliptical in shape. The growth of the lateral and MR cracks was found to be codependent such that the depth of the lateral crack limited the depth of the MR crack, and the presence of the MR crack caused deflections in the direction and increased the extent of lateral crack growth.     

Measurement of Very Slow Crack Growth in Glass

The rate of very slow crack growth in glass is measured by inducing small, controllable changes in the direction of propagation of Hertzian cone cracks at known times. After completion of a growth sequence, the sample is sectioned to reveal the fracture surface. The stress intensity factor at each stage of crack growth is calculated by using finite-element modeling of the stresses near the crack tip. Data are presented for crack growth velocities as low as 10⁻¹⁴ m/s in soda–lime glass. These data provide strong evidence for the existence of a subcritical limit for crack growth in this material.     

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.     

Scanning Acoustic Microscopy Observations of High-Temperature Crack-Bridging Mechanisms in Alumina

High-purity, fine-grained alumina showed a strong R -curve behavior for long cracks propagated at 1200°C. R -curve behavior was not observed at room temperature. A combined investigation using high-frequency scanning acoustic microscopy and scanning electron microscopy of crack profiles demonstrated asperity contact in the crack wake at 1200°C. A microcrack zone was not observed. Crack bridging, resulting from intergranular subcritical crack propagation was considered to be responsible for the toughness increase with increased crack length.     

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.     

Rising Crack-Growth-Resistance (R-Curve) Behavior of Toughened Alumina and Silicon Nitride

R -curves for a sinter/HIPed SiC(whisker)-reinforced alumina and a sintered silicon nitride were assessed by direct measurements of lengths of cracks associated with Vickers indentation flaws. The fracture toughness measurements based on (a) initial (as-indented) crack lengths, (b) equilibrium growth of cracks during increasing far-field loading, and (c) crack lengths corresponding to unstable fracture showed definitive trends of R -curves for both materials. The fracture mechanics analyses employed an indenter-material constant that was independently estimated using a physical model for the residual driving force and a free surface correction factor that accounted for the effects of size and shape of the cracks on stress intensity. It is shown that R -curve estimations based on crack length measurements have the intrinsic advantage that crack length dependence of fracture toughness is not assumed a priori as is done in conventional analysis based on strength. The measured fracture toughness of SiC(whisker)-reinforced alumina was in agreement with the prediction of a toughening model based on crack bridging by partially debonded whiskers.     

Extended Charles–Hillig Theory for Stress Corrosion Cracking of Glass

The work originally performed by Charles and Hillig (C&H) on the chemical stress corrosion cracking of glass is based on the chemical reaction rate theory and restricts the analysis to only the kinetic change at the exact location of the crack tip. As a result, crack sharpening/blunting is predicted when the applied stress lies above/below the static fatigue limit. The present paper extends the investigation within the same physical framework to the geometric change of the entire cavity surface, particularly in the vicinity of the cavity apex region. It has been found that a physical-property-dependent parameter ( m ) exists which exerts a strong influence on the crack-tip morphology. In the case of m = m _th, where m _th is a threshold m which assumes a value of ∼ 45 for an elliptical cavity having a minor to major axes ratio of 0.01, the current predictions reduce to the C&H results. In general, however, m ≠ m _th, and the single-valued fatigue limit degenerates into a range of applied stresses under which either enhanced blunting ( m > m _th) or necking ( m < m _th) is predicted to take place. Evaluation of m for soda–lime glass reveals that m > 45, suggesting that enhanced blunting takes place at the crack tip when external loads are applied at a moderate level for a typical crack having an initial major to minor axes ratio > 100 in a soda–lime glass specimen.     

Estimation of Crack Closure Stresses for In Situ Toughened Silicon Nitride with 8 wt% Scandia

An 8-wt%-scandia silicon nitride with an elongated grain structure was fabricated. The material exhibited high fracture toughness (∼ 7 MPa · m^1/2) and a rising R -curve as measured by the indentation strength technique. The "toughening" exponent m was found to be m ∼ 0.1. The high fracture toughness and R -curve behavior was attributed mainly to bridging of the crack faces by the elongated grains. The crack closure (bridging) stress distribution in the wake region of the crack tip was estimated as afunction of crack size from the R -curve data, with an arbitrarily assumed distribution function.     

Mechanism of Mechanical Strength Increase of Soda–Lime Glass by Aging

Two models have been proposed to explain the mechanical strength increase of abraded or indented soda–lime glasses upon aging, namely, crack tip blunting and the release of residual tensile stress near the crack tip. To clarify the mechanism, the time dependence of the strengthening of an abraded soda–lime glass was investigated. Effects of aging media, such as moist air, distilled water, 1 N HCI and 1 N NaOH solutions, as well as the abrasion flaw depth, were determined. The strength increase rate in water of abraded soda–lime glass was compared with those of borosilicate and high-silica glasses. The effect of stressing during aging was also investigated. It was found that the rate of strength increase was faster with decreasing abrasion flaw depth and with decreasing chemical durability. For a given flaw depth, an acidic solution produced the fastest strengthening. The strengthening rate was found to accelerate because of the "coaxing'effect of stressing during aging. From these observations, it was concluded that the strengthening rates relate to the diffusion process and chemical reactions, especially the alkali–hydrogen (or hydronium) ion-exchange reaction, near the crack tip. The role of the residual tensile stress appears to be similar to that of the applied tensile stress, helping the diffusion process near the crack tip. The observed strength increase of soda–lime glass by aging was thus attributed to the effective blunting of the crack tip geometry by the glass–water reaction.     

Determination of Fracture Toughness at High Temperatures after Subcritical Crack Extension

As a consequence of R -curve behavior, ceramic materials may exhibit increased fracture toughness ( K _Ic) following slow crack extention. In this investigation, the effect of crack propagation on fracture toughness is studied in static bending tests. For the calculation of stress intensity factors ( K _I) the stress distribution must be known at the moment of fracture. As a consequence of creep, this stress distribution must deviate from the linear distribution. The corresponding stress intensity factors are computed using the fracture mechanical weight function. Experimental results for fracture toughness are communicated for a 2.5%-MgO-doped hot-pressed Si₃N₄ at 1300°.     

Deformation and Fracture by Sharp Rolling Contacts

The contact mechanics of sharp "glass-cutting" rollers is analyzed. Assuming the contact to be plastic, expressions are developed for the width and length of a static contact and the width of a rolling track. The residual stress-intensity factor and stable length for median cracks generated beneath a roller track are derived, assuming the track to have been created by an equivalent wedge loading and modeling the plastic deformation zone as an expanding cylindrical cavity. The strengths of components containing dominant roller flaws are then derived by superposing an applied stress field onto the residual contact field and solving for instability. The contact dimensions, median crack lengths, and strengths are all expressed in terms of the roller radius and included angle, contact load, and indented material hardness, modulus, and toughness. Tests on soda–lime glass and aluminum confirm the predicted dependences.     

Measurement of Crack Tip Displacement Fields in Mixed Mode I–Mode III Fracture

A new method has been devised to propagate stable subcritical mixed mode I–mode III cracks in soda–lime–silicate and borosilicate glasses. The mode I content was measured using an original optical tunneling technique and mode III content via multiple-beam interferometry. Measurement of the mode III displacement field allows values of mode III fracture toughness, K_III, to be derived. K_III vs crack velocity (v) diagrams have been constructed for both glasses, and, in the case of the soda–lime–silicate glass, v vs K_III relationships have been determined for a variety of humidities. Comparison has been made with published K_I vs v data for this glass.     

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.     

In Situ Cube-Corner Indentation of Soda–Lime Glass and Fused Silica

Indentation fracture with a cube-corner diamond pyramid on soda–lime silicate glass and fused silica is investigated during the entire indentation cycle in both silicone oil and ambient-air environments. Radial cracks form immediately on loading in all cases. The two-component, elastic-contact + elastic-plastic mismatch (residual) stress field model that has been used successfully to describe radial crack evolution at Vickers indentations fails to describe the fracture response with the cube-corner. The amplitudes of both elastic-contact and residual stress-intensity factors as deduced from these cube-corner experiments are up to a factor of 10 greater than have been previously observed.     

Toughening Behavior of a Two-Dimensional SiC/SiC Woven Composite at Ambient Temperature: I, Damage Initiation and R-Curve Behavior

The damage initiation and R -curve behavior for a two-dimensional (2-D) SiC/SiC woven composite are characterized at ambient temperature and related to in situ microscopic observations of damage accumulation and crack advance. Matrix cracking and crack deflection/branching are observed and dominate fracture behavior in the early loading stage such that primary crack extension occurs at apparent stress intensity values as high as 12 MPam^1/2. Linear elastic fracture mechanics (LEFM), though questionable, was assumed to be valid in the early stages of damage initiation prior to primary crack advance, but was clearly invalid once primary crack extension had occurred. Such a high primary crack extension toughness value is confirmed by a renotch technique whereby the crack wake is removed and the fracture resistance drops close to the initial value. Based on microstructural observations, multiple matrix cracks are found to be arrested at fiber bundles. The key to toughening appears to be associated with the mechanics of crack arrest at fiber bundles in the woven architecture. Toughening mechanisms include multiple matrix cracking (similar to microcracking), crack branching, and crack deflection in the crack frontal zone. Application of models to evaluate toughening based on these mechanisms results in values comparable to experimental data. In the regime of primary crack extension, a J -integral technique was applied to investigate the R -curve behavior and results showed a rising J_R -curve which started at 1500 J/m² and reached 6150 J/m² after about 13 mm of primary crack extension. There was evidence of substantial crack bridging by fiber tows and fibrous pull-out in this regime of crack advance.     

Transformation Zone Shape, Size, and Crack-Growth-Resistance [R-Curve] Behavior of Ceria-Partially-Stabilized Zirconia Polycrystals

Transformation zone shape, size, and crack-growth-resistance ( R -curve) behavior were studied in precracked and annealed single-edge notch bend specimens of commercial-grade ceriapartially-stabilized zirconia polycrystals as a function of applied load. Well-defined transformation zones with a characteristic elongated shape in the plane of the crack were observed. It is shown that the observed zone shape is significantly different from the shape predicted by a combined shear/dilatation yield criterion and the stress field of the crack prior to the transformation. The length of the transformation zone directly ahead of the crack tip is in better agreement with the prediction of the Dugdale plastic strip zone model. The fracture toughness increment showed the characteristic square root dependence on the transformation zone width, but the magnitude of the toughness increment was not consistent with the predictions of the theoretical models of transformation toughening.