Crack Initiation and Arrest in a SiC Whisker/A12O3 Matrix Composite

The fracture initiation and arrest stress intensity factors were determined for a SiC-whisker-reinforced AI₂O₃ matrix composite. A chevron-notched, three-point-bend specimen was used to genera e the load/displacement curve, which exhibited repeated crack initiation, followed by crack arrest behavior. Corresponding stress intensity factors were determined for both situations using the compliance technique. Calculated crack arrest positions were in agreement with fractographic observations. Both the crack arrest and the crack initiation stress intensity factors exhibited a rising R -curve with increasing crack length, suggesting the presence of wake toughening effects on the crack growth resistance.     

Effect of Slow Crack Growth on the Thermal-Stress Resistance of an Na2O-CaO-SiO2 Glass

The effect of slow crack growth on the thermal-shock resistance of an Na₂O-CaO-SiO₂ glass was studied. An analytic and numerical technique was developed to calculate the critical quenching temperature difference, Δ T_c , of circular rods quenched in water from known crack velocity data. For rods of a specific radius and crack depth, Δ T_c , was calculated to be 147°C, in favorable correspondence with experimentally observed values of 155° to 160°C. In the absence of crack growth, Δ T_c was estimated to be 238°C, well in excess of the observed value and indicative of the significant effect of slow crack growth on thermal-stress resistance. It is also shown that crack growth significantly extends the time-to-failure to a value much greater than the time of maximum thermal stress. A form of subcritical crack instability is predicted at stress intensity factors well below the critical stress intensity factor, at which catastrophic failure becomes inevitable over the duration of the transient thermal stress. It is suggested that, when all other factors are equal, the effect of slow crack growth on thermal-stress resistance can be minimized by maximizing thermal diffusivity. It is also argued that surface-compression strengthening will be more effective than reduction in flaw size in increasing thermal-stress resistance. Recommendations are made for the design and selection of brittle materials subjected to thermal stress in stress-corrosive environments.     

Crack Growth in Soda–Lime–Silicate Glass near the Static Fatigue Limit

The atomic force microscope (AFM) was used to explore the nature of features formed on the surfaces of cracks in soda–lime–silicate glass that were held at stress intensity factors below the crack growth threshold. All studies were conducted in water. Cracks were first propagated at a stress intensity factor above the crack growth threshold and then arrested for 16 h at a stress intensity factor below the threshold. The stress intensity factor was then raised to reinitiate crack growth. The cycle was repeated multiple times, varying the hold stress intensity factor, the hold time, and the propagation stress intensity factor. Examination of the fracture surface by optical microscopy showed surface features that marked the points of crack arrest during the hold time. These features were identical to those reported earlier by Michalske in a similar study of crack arrest. A study with the AFM showed these features to be a consequence of a bifurcation of the crack surface. During the hold period, waviness developed along the crack front so that parts of the front propagated out of the original fracture plane, while other parts propagated into the plane. Crack growth changed from the original flat plane to a bifurcated surface with directions of as much as 3° to 5° to the original plane. This modification of crack growth behavior cannot be explained by a variation in the far-field stresses applied to the crack. Nor can the crack growth features be explained by chemical fluctuations within the glass. We speculate that changes in crack growth direction are a consequence of an enhancement in the corrosion rate on the flank of the crack at stresses below the apparent crack growth threshold in a manner described recently by Chuang and Fuller.     

Cyclic Fatigue Crack Propagation in Alumina under Direct Tension—Compression Loading

Cyclically induced crack propagation occurs in alumina subjected to direct tension—compression loading. The crack increment per cycle (da/dN) has a power-law dependence on the peak stress intensity factor (K_max). Cyclic crack growth can occur at lower values of K_max than are required to produce static fatigue effects. Subcritical crack-growth behavior was found to be dependent on specimen geometry: it is suggested that direct compressive loads and crack length are both factors that affect cyclic fatigue behavior, and that the use of K alone to characterize fatigue crack growth in ceramics may be questionable.     

Cyclic Fatigue Crack Growth in PZT Under Mechanical Loading

Crack growth under static and cyclic mechanical loading in lead zirconate titanate was studied using four point bend specimens in poled and unpoled states. Fatigue crack growth occurred at lower stress intensity factors than crack growth observed under static loading. The relation between crack velocity and applied stress intensity factor under static loading was affected by poling and followed a power-law relationship. Crack velocity vs. stress intensity amplitude under cyclic loading followed a Paris power-law relationship and was found to be unaffected by poling. A controlled unloading experiment revealed that the apparent stress intensity factor for crack extension decreased with increased unloading time but was essentially unaffected when the unloading cycle was less than five seconds, hence indicating the absence of an extrinsic fatigue mechanism.     

Crack Shielding in Ce-TZP/Al2O3 Composites: Comparison of Fatigue and Sustained Load Crack Growth Specimens

Crack shielding stress intensities in in situ loaded compact tension specimens of two types of ceria-partially-stabilized zirconia/alumina (Ce-TZP/Al₂O₃) composites with prior histories of subcritical crack growth in sustained and tension-tension fatigue loading were directly assessed using laser Raman spectroscopy. Crack-tip stress fields within the transformation zones were measured by measuring a stress-induced frequency shift of a peak corresponding to the tetragonal phase. The peak shift as a function of the applied stress was separately calibrated using a ball-on-ring flexure test. Total crack shielding stress intensity was estimated from the far-field applied stress intensity and the local crack-tip stress intensity assessed from the measured near-crack-tip stresses. The shielding stress intensities were consistently lower in the fatigue specimens than in the sustained load crack growth specimens. The reduced crack shielding developed in the fatigue specimens was independently confirmed by measurements of larger crack-opening displacement under far-field applied load as compared to the sustained load crack growth specimens. Thus, diminished crack shielding was a major factor contributing to the higher subcritical crack growth rates exhibited by the Ce-TZP/Al₂O₃ composites in tension–tension cyclic fatigue. Calculations of zone shielding considering only the dilatational strains in the transformation zones accounted for 81% and 86% of the measured values in the sustained load crack growth specimens, but significantly overestimated the shielding in the fatigue specimens. Possible reasons for the diminished crack shielding in the fatigue specimens are discussed.     

Origin of the Static Fatigue Limit in Oxide Glasses

Oxide glasses exhibit slow crack growth under stress intensities below the fracture toughness in the presence of water vapor or liquid water. The log of crack velocity decreases linearly with decreasing stress intensity factor in Region I. For some glasses, at a lower stress intensity, K_o, log v asymptotically diminishes where there is no measurable crack growth. The same glasses exhibit static fatigue, or a decreasing strength for increasing static loading times, as cracks grow and stress intensity eventually reaches the fracture toughness. In this case, some glasses exhibit a low stress below which no fatigue/failure is observed. The absence of slow crack growth under a low stress intensity factor is called the fatigue limit. Currently, no satisfactory explanation exists for the origin of the fatigue limit. We show that the surface stress relaxation mechanism, which is promoted by molecular water diffusion near the glass surface, may be the origin of the fatigue limit. First, we hypothesize that the slowing down of slow crack growth takes place due to surface stress relaxation during slow crack growth near the static fatigue limit. The applied stress intensity becomes diminished by a shielding stress intensity due to relaxation of crack tip stresses, thus resulting in a reduced crack velocity. This diminishing stress intensity factor should result in a crack growth rate near the static fatigue limit that decreases in time. By performing Double Cantilever Beam crack growth measurements of a soda‐lime silicate glass, a decreasing crack growth rate was measured. These experimental observations indicate that surface stress relaxation is causing crack velocities to asymptotically become immeasurably small at the static fatigue limit. Since the surface stress relaxation was shown to take place for various oxide glasses, the mechanism for fatigue limit explained here should be applicable to various oxide glasses.     

Fatigue and Static Crack Propagation in Yttria-Stabilized Tetragonal Zirconia Polycrystals: Crack Growth Micromechanisms and Precracking Effects

The influence of precracking techniques in the crack growth behavior of yttria-stabilized tetragonal zirconia polycrystals (Y-TZP) is investigated. Load-bridge and cyclic-compression precracking enhance subsequent tensile crack growth rates, in comparison to results that are found with precracks that are extended under four-point bending prior to testing. The actual influence of these precracking techniques in the near-threshold crack growth regime is remarkably different. Although load-bridge precracking produces a pattern of crack growth fluctuations for stress intensity factors, K , lower than the effective crack-growth threshold of the material, compression-fatigue precracks start to propagate under far-field tensile loads at very fast growth rates and for K values that are slightly higher than the effective threshold. Crack-tip shielding by tetragonal-to-monoclinic transformation develops gradually, influencing the crack growth behavior in Y-TZP. Proposed fatigue crack growth micromechanisms involve damage accumulation at the crack-tip region. For K _max > 3 MPa·m^1/2, fatigue crack growth rates are strongly affected by environmental interactions at the crack tip, and postulated fatigue micromechanisms include the cyclic degradation of crack-tip shielding.     

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.     

Subcritical Crack Growth in Vitreous Carbon at Room Temperature

The velocity of crack propagation was measured as a function of stress intensity in vitreous carbon at room temperature. The double-torsion technique was used. In one vitreous carbon, the relation between crack velocity and stress intensity was In another vitreous carbon, repeated crack arrest prevented determination of the V-K₁ dependence. Vitreous carbon in air is virtually immune to static fatigue, compared with soda-lime glass in air. The ratio of times to failure when the materials are loaded to equal fractions of the critical stress intensity is log ( τ_vc/τ_sly )≃33. In addition to subcritical crack growth, other fracture mechanical properties, e.g. the modulus of rupture and critical stress intensity factor, were measured. These measurements confirmed the presence of a compressive surface layer on vitreous carbon.     

Prediction of crack propagation and fracture in residually stressed glass as a function of the stress profile and flaw size distribution

Engineered stress profile (ESP) glasses are noted for narrow strength distributions and the potential for stable growth of multiple surface cracks under applied tensile stress. This behavior depends on the interaction of the surface flaw size distribution with the residual stress profile in the material. In this work, several surface preparation methods were used to produce a range of flaw size distributions in soda lime silica glass specimens. Two ion exchange processes were then performed on these specimens to produce ESP glass. For each condition, crack growth behavior and fracture strength were experimentally observed. Residual stress profiles resulting from each ion exchange process were measured with an optical technique. These stress profiles were used to calculate stress intensity factors as a function of crack geometry, using a weight function method. Crack growth and fracture strength predictions based on these stress intensity factors were compared to experimental data, resulting in good agreement in most cases.     

Crack-Tip Structure in Soda–Lime–Silicate Glass

The topology of crack tips in soda–lime–silicate glass was investigated using atomic force microscopy (AFM). Studies were conducted on cracks that were first propagated in water and then subjected to stress intensity factors either at or below the crack growth threshold. Exposure to loads at the crack growth threshold resulted in long delays to restart crack growth after increasing the stress intensity factor to higher values. After breaking the fracture specimen in two, the "upper" and "lower" fracture surfaces were mapped and compared using AFM. Fracture surfaces matched to an accuracy of better than 0.5 nm normal to the fracture plane and 5 nm within the fracture plane. Displacements between the upper and lower fracture surfaces that developed after a critical holding time were independent of distance from the crack tip, and increased with holding time. Despite the surface displacement, crack tips appeared to be sharp. Results are discussed in terms of a hydronium ion–alkali ion exchange along the crack surfaces and corrosion of the glass surface near the crack tip by hydroxyl ions.     

Subcritical Crack Growth of Macrocracks in Alumina with R-Curve Behavior

Subcritical crack growth of macroscopic cracks in two Al₂O₃ ceramics is investigated with single-edge-notched bending specimens under constant load. The resulting v - K _I-curves are in complete contrast to the behavior of natural cracks. In spite of the monotonic increase of the externally applied stress intensity factor due to crack extension, the crack growth rates first decrease. This behavior is caused by crack shielding due to crack border interaction and can be described by a rising crack growth resistance. Two methods are applied to determine the R -curve under subcritical crack growth conditions.     

High-Temperature Failure of Polycrystalline Alumina: II, Creep Crack Growth and Blunting

Creep crack growth in fine-grain alumina is measured by using surface cracks. A narrow power-law crack growth regime occurs at both 1300° and 1400°C, wherein the power-law exponent and activation energy are comparable to steady-state creep values. Asymptotic crack velocity behavior is exhibited near both the critical stress intensity factor, K_C , and the crack growth threshold, K_th . The threshold occurs near 0.4 K_1C at both 1300° and 1400°C and is associated with a transition in the size and distribution of damage. Displacement measurements indicate that crack tip damage exerts a strong influence on the displacement field, as predicted by recent theories. Furthermore, use of the stress intensity factor as a loading parameter does not produce adequate correlation with displacement measurements and is, therefore, not strictly suitable for nonlinear creeping ceramic poly crystals.     

Fatigue Crack Growth from Small Surface Cracks in Transformation-Toughened Ceramics

A theoretical model based on the theory of complex potentials and dislocation formalism is used to simulate the fatigue crack growth of small cracks in a transformation-toughened ceramic. Assuming power-law crack growth in which the growth rate depends on the effective stress intensity at the crack tip instead of the applied stress intensity, it is shown that the crack growth rate decreases with the applied stress intensity in the initial stage of fatigue crack growth. This is in agreement with existing experimental evidence for the growth of small cracks in Mg-PSZ. New experimental results obtained by in situ observation in a scanning electron microscope of a similar material confirm this behavior. The numerical results also confirm the plausibility of using the steady-state toughness value obtained from quasi-static crack growth as a normalizing parameter in the power-law for fatigue 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.     

Time-dependent craze zone growth at a crack tip in polymer solids

By considering the polymer bulk as a linear viscoelastic body and the craze zone at crack tip as a nonlinear damage zone, the control equation for craze zone growth has been derived. It is shown that for a time-independent craze-zone stress, the craze zone would grow only if the crack-tip stress intensity factor is changed. If the crack-tip stress intensity factor remains constant during loading, the growth rate of the craze zone length will be interrelated to the crack-tip stress, the craze zone length and the rate of change of the craze-zone stress. If both the craze-zone stress and the crack-tip stress intensity factor are time-independent, the craze zone length will be constant during the crack growth, which is the case of self-similar crack growth. Moreover, a new stress distribution model in craze zone is presented based on the constructed damage evolution law, and the lengthening and thickening of the craze zone at the crack tip are also formulated. The numerical calculations from the proposed model agree well with the published experimental data.     

Crack Stability and T-Curves Due to Macroscopic Residual Compressive Stress Profiles

Stabilization of the fracture process and resistance to strength degradation have been observed for materials with increasing T -curves. In this study, the possibility of using residual compressive stresses to induce crack stabilization is examined theoretically. Nonmonotonic forms for the residual compressive stress profiles are assumed. The stress intensity factors for linear through-the-thickness cracks subjected to these profiles are derived. The stress intensity factors are then used to construct the T -curves for the stress profiles considered. It is demonstrated that the presence of these T -curves leads to crack stability under the action of applied tensile stresses, and to strength insensitivity to the initial flaw size. The effects of additional localized stress fields (similar to those produced by indentation) on crack growth in these materials are also considered. In this case, the strength is found to be relatively insensitive to the magnitude of the localized loading. It is therefore concluded that residual stresses can be used to improve mechanical reliability in ways which are usually associated with microstructural toughening mechanisms.     

The initiation and propagation of thermal shock cracks in graphite

Thermal shock resistance of a commercial grade of graphite was studied using an arc-discharge test. The thermal shock fracture initiation and crack propagation behaviour of the graphite disks at different input power levels were determined and analysed using fracture mechanics. The temperature gradient was measured experimentally and the profiles were force fitted with an even fourth-order polynomial. The thermal stresses were calculated from the force fits. A radial notch was introduced to the disk specimens to enable calculation of the thermal stress intensity factors. The crack mouth opening displacement was monitored using a special displacement transducer. The thermal stress and stress intensity factors were found to increase with increasing input current (and hence increasing thermal gradient). The thermal shock fracture toughness determined using the arc-discharge technique was found to increase from 0.8 to 1.4 MPa m^1/2 at temperatures from 220 to 420 °C. The longer the notch length, the shorter the time to crack, the smaller the crack mouth opening displacement jump and the shorter the unstable crack growth.     

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°.