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.     

Comparison of Slow Crack Growth Behavior in Alumina and SiC-Whisker-Reinforced Alumina

Results of dynamic fatigue experiments in water at room temperature on an indented Al₂O₃/25 wt% SiC whisker composite material have shown that this composite has a high resistance to slow crack growth. Aging tests in water revealed that the residual stress due to the indentation does not play an important role, and interrupted fatigue tests showed that the crack starts to grow at very low stress intensities, but the velocity is very low. Detailed fractography indicated that the slow crack growth path is intergranular in the whisker composite. The slow crack growth behavior in the whisker composite is discussed in association with the indentation residual stress, the change of the crack shape during the bending test. These results are compared with a bio-grade Al₂O₃ with lower resistance to slow crack growth, and important differences are pointed out.     

Post-Indentation Slow Growth of Radial Cracks in Glasses

An expression is developed for the slow growth of radial cracks after indentation using established notions of slow crack growth and residual stresses at the tip of radial cracks. This expression is substantiated by data gathered on indentation of microscope slides tested in air and water environments. The agreement is reasonable with the published values of the glass stress-corrosion susceptibility coefficients. It is suggested that the present approach represents a simple and straightforward method of measuring the stress-corrosion susceptibility of glasses.     

Crack Initiation by Indentation Fatigue in Lead Alkali and Soda–Lime Glass

An indentation technique using a conventional Vickers microhardness tester was used to evaluate fatigue properties of lead-alkali and soda-lime silica glasses. The specimens were indented repeatedly at the same point with subcritical loads until radial cracks were initiated. The number of cycles to initiate the cracks at different subcritical loads demonstrated typical fatigue curves for both glasses. The uniqueness of the experiment was that the diagonal lengths of the deformed cavity were observed to increase with the number of cycles. This increase of the deformed cavity for a certain number of cycles prior to the visibility of crack initiation was analyzed, correlating the elastic-plastic phenomenon and the accumulation of the residual stress in each cycle.     

Determination of Subcritical Crack Growth Parameters by In Situ Observation of Indentation Cracks

A technique to determine stress intensity factor—crack velocity (K— v ) relationships for subcritical crack growth from in situ observation of indentation cracks is described. To minimize the effect of residual contact stresses and lateral crack interaction, measurements were made only on cracks that had undergone significant subcritical crack growth. Crack shapes were determined fractographically from crack-arrest markings, produced by temporary unloading during the crack extension process. The subcritical crack growth parameters obtained by this technique were in excellent agreement with those determined from dynamic fatigue and previous studies.     

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this first part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elastic/plastic indentation fracture mechanics. It is thereby asserted that the key to the radial crack response lies in the residual component of the contact field. This residual term has important implications concerning the crack evolution, including the possibility of post indentation slow growth under environment-sensitive conditions. Fractographic observations of cracks in selected "reference" materials are used to determine the magnitude of this effect and to investigate other potential complications associated with departures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the Indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely simple in procedure and economic in its use of material.     

A technique for measuring stresses in small spatial regions using cube-corner indentation: Application to tempered glass plates

Vickers indentation cracks have been used to estimate residual stress in materials; however, a high threshold load for cracking limits the smallest spatial region for stress measurement. Cube-corner indenters have a lower included angle, and their sharpness leads to lowered cracking thresholds enabling stress measurement in small spatial regions. Cube-corner indentations on tempered glass plate and on annealed soda-lime-silica glass revealed that crack surface traces on the tempered material were significantly smaller. Cracks were found to be quarter-penny shaped as opposed to half-penny/radial for Vickers indentation. Using an appropriate stress-intensity factor and a stress-intensity factor superposition approach, surface stresses in the tempered plate were calculated. The stresses were in good agreement with those determined using well-established Vickers indentation approach; however, the spatial region sampled is 6–10 times smaller. An estimate of the smallest spatial region at which a particular stress may be measured using this technique is presented.     

Influence of Composition on Fatigue Behavior and Threshold Stress Intensity Factor of Borosilicate Glasses

Fatigue behavior of borosilicate glasses was studied using the analysis of subcritical propagation of Vickers indentation cracks. Glasses containing various amounts of glass-network modifiers, mainly soda, were considered. Cone and median/radial crack systems were observed, depending on glass composition, indenter geometry, and test environment. Indentation tests were performed in water, holding the maximum load for durations ranging from 15 s to 6 d. The analysis of the crack length as a function of dwell time allowed evaluation of the subcritical growth parameters and fatigue limit at crack arrest. The influence of composition on fatigue parameters and fatigue limit was discussed in terms of fourfold-coordinated boron atoms fraction compared with the content of glass-network modifier ions.     

Strength Variability of Indented Soda-Lime Glass

Studies of annealed indentation flaws show that specimen strength is inversely proportional to the square root of the surface trace dimension of the strength-controlling radial crack over a range of indentation loads. Using the surface trace as the characteristic dimension in the appropriate fracture mechanics equations, however, underestimates the measured strengths by about 30%. There is also a lack of correlation between the individual strengths and the surface traces at a given indentation load. Despite the complex nature of indentation flaws, strength predictions of individual indentation cracks based on the radial crack depth (not the surface trace) are in agreement with measured strengths. Strength variability of indented glass specimens at a given indentation load is due mainly to the spectrum of crack depths.     

Failure of Glass with Subthreshold Flaws

Conventional postthreshold crack analysis cannot be used to predict the strength and fatigue behavior of glass with subthreshold flaws. Therefore, a fracture mechanics model for failure of glass with subthreshold indentation flaws was developed. This model accounts for both the near- and farfield residual stresses associated with the indentation impression. It is shown that these stresses play a major role in the initiation and subsequent propagation of cracks that eventually cause failure. The model predicts "pop-in" of a well-developed crack and failure under continuous and discontinuous crack growth in both inert and fatigue conditions. The results of experiments with bare fused silica fibers with indentation subthreshold flaws in inert and fatigue (water) environments were in good agreement with the predictions by the model.     

Controlled Crack Shapes for Indentation Fracture of Soda–Lime Glass

Radial cracks for indented soda–lime glass aged in distilled water were highly elliptical because of truncation by lateral cracks. Indentation in silicone oil minimized radial/lateral crack interaction but still produced cracks having nominally constant ellipticity during bend testing. Analysis of applied stress/indentation crack length data using stress intensity factors based on half-penny crack shape resulted in apparent R -curve behavior and/or overestimation of the fracture toughness. Incorporation of elliptical shape factors eliminated the R -curve behavior and reduced measured toughness to near the accepted value for soda–lime glass.     

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.     

New insights into nanoindentation crack initiation in ion‐exchanged sodium aluminosilicate glass

The effect of ion‐exchange on the fracture behavior and the threshold load is investigated for radial crack initiation resulting from cube‐corner indentation. Both tin and air sides of the sodium aluminosilicate float glass are considered. The threshold load and mechanical properties are experimentally measured by nanoindentation. A qualitative explanation of crack initiation is developed by analyzing the stresses at the indentation site. The ion‐exchanged glasses show a lower threshold load for radial crack initiation with a cube‐corner indenter than the raw glass, and this is due to a higher crack driving stress for ion‐exchanged glasses. However, the compressive stress on the surface of the ion‐exchanged glasses can inhibit the expanding of the radial cracks. The air side always shows higher values for the threshold load than the tin side before and after ion‐exchange, which is in accordance with the calculated crack driving stress results.     

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.     

Repeated Indentation Method for Studying Cyclic Fatigue in Ceramics

A new method for studying cyclic fatigue in ceramics in proposed. It is based on the repeated indentation of the ceramic surface with a sharp indenter and on the relation between the indentation load and the number of indentation cycles needed to produce chipping. The technique is analyzed on the basis of observations on the development of the lateral cracks produced below the identation cavity in a high-grade alumina and on the model of elastic/plastic indentation damage. It is shown that cyclic compressive forces across the lateral crack faces are needed to produce chipping and that a fatigue limit exists in terms of these forces. The scope and limitations of the technique are discussed.     

Cyclic Fatigue Behavior of an Alumina Ceramic with Crack-Resistance Characteristics

The behavior under cyclic tension—tension loading of an alumina ceramic with pronounced crack-bridging (R-curve) characteristics is studied. Tests on disk specimens with indentation cracks reveal no failures below the static fatigue limit. Theoretical predictions of the stress-lifetime response, based on the premise that environmentally assisted slow crack growth is the sole factor determining lifetime, are consistent (within experimental scatter) with the data. The results indicate that there is no significant cyclic degradation from potential damage to the bridges, at least in the short-crack region pertinent to strength properties.     

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.     

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.     

Prediction of ring crack initiation in ceramics and glasses using a stress–energy fracture criterion

Crack initiation in brittle materials upon spherical indentation is associated with the tensile radial stresses during loading. However, location of crack onset often differs (offset) from the site of maximal stress. In addition, experiments reveal a strong dependency of crack initiation forces on geometrical parameters as well as the surface condition of the sample. In this work, a coupled stress–energy fracture criterion is introduced to describe the initiation of ring cracks in brittle materials, which takes into account the geometry of the contact and the inherent strength and fracture toughness of the material. Several experiments reported in literature are evaluated and compared. The criterion can explain the location offset of the ring crack upon loading, as observed in various ceramics and glasses. It also predicts the ring crack initiation force upon contact loading, provided that surface compressive stresses, introduced during grinding or polishing processes, are taken into account. Furthermore, the stress–energy criterion may be employed to estimate the surface residual stress of ceramic parts, based on simple contact damage experiments.     

Effects of residual stress and orientation on the fatigue of injection molded polysulfone

The tensile fatigue behavior of unnotched injection molded polysulfone specimens has been investigated. The effects of orientation and residual stress were studied by comparing asmolded specimens with annealed or annealed and quenched specimens with a known residual stress pattern. The treatments are shown to have differing effects at high stresses, where failure is by shear yielding and necking, and at intermediate stresses, where failure is by fatigue crack propagation. The geometries of fatigue cracks are described for each case. An attempt is made to separate the effects of crack and craze initiation from crack propagation, and cyclic loading from cumulative time under load.