Dynamic Fatigue Analysis of Indentation Flaws Using an Exponential-Law Crack Velocity Function

The effect of residual contact stresses on the dynamic fatigue behavior of indentation flaws was analyzed using an exponential-law crack velocity function based on stress corrosion theory. Analysis of strength data from Vickers-indented soda-lime glass specimens in water showed that the contact residual stress can be properly accounted for and that the exponential-law fatigue parameters can be straightforwardly obtained.     

Indentation Crack-Shape Evolution during Subcritical Crack Growth

Indentation crack-shape evolution during subcritical crack growth was examined in soda-lime glass. Crack-arrest markings were generated on the fracture surfaces by temporary unloading during subcritical crack growth. Crack shapes were determined from these crack-arrest markings by optical microscopy. The shapes were found to be semielliptical, but the ellipticity changed significantly with crack extension under an applied bending stress. Crack-shape evolution was predicted by using the stress intensity factor equation for a semielliptical crack for the applied stress distribution and the subcritical crack growth parameters for the material/environment system. Experimental results were found to be in excellent agreement with the predictions. The influence of the initial crack size and shape, the loading configuration, and the subcritical crack growth exponent n on crack-shape evolution was also investigated in the simulations. It was found that, for the particular loading configuration and material, there is an equilibrium shape associated with the subcritically growing crack. The variation in crack shape with its extension during subcritical crack growth was found to be an important factor in lifetime prediction.     

Indentation Crack Initiation and Propagation in Tempered Glass

Indentation crack initiation and propagation in tempered glass surfaces are examined and the results compared to those in annealed and in ion-exchange-strengthened glasses. The presence of surface compression due to tempering inhibits median crack initiation during the loading cycle of the indentation and depresses the radial crack initiation load during unloading. However, the extent of lateral cracking is enhanced in tempered glass surfaces. In situ crack propagation experiments reveal that the compressive stress tends to weakly stabilize crack extension prior to failure. The degree of crack stabilization is considerably lower than expected from a theoretical analysis.     

Indentation Determination of Crack Growth Parameters in Gallium Arsenide

Indentation measurements of the environmentally enhanced crack growth parameter, n , in GaAs have been made in water, acetonitrile, and methanol. Reasonable agreement with n values obtained from double-cantilever-beam tests was obtained. It is concluded that the range of n values which can be measured by the indentation technique is much wider than previously observed, and is strongly dependent upon the experimental configuration employed.     

Quantitative Characterization of Indentation Crack Path in a Cubic Zirconia-10 vol% Alumina Composite

Stereological measurements were performed to characterize the indentation crack path in a cubic zirconia-10 vol% alumina (c-ZrO₂-10 vol% Al₂O₃) composite. Cracks were generated using Vickers indentation, and the crack propagation behavior was characterized as a function of the indentation loading/unloading rates. Cracks that were produced by Vickers indentation formed at higher crack velocities as the loading/unloading rates increased. The amount of contact between the crack and the Al₂O₃ particles increased as the indentation rate decreased. The total number of crack-particle interactions per unit crack length also increased as the indentation rate decreased, because of an increase in the number of particles that were fractured per unit crack length, whereas the number of particles that were debonded remained relatively constant as the indentation rate changed. These results suggest that residual thermal mismatch stresses have predominant control of the crack path at lower crack velocities (low indentation loading/unloading rate), whereas elastic mismatch stresses predominate at higher crack velocities (high indentation loading/unloading rate).     

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.     

Critical Load for Median Crack Initiation in Vickers Indentation of Glasses

Critical load characteristics for the indentation-induced median crack in ternary lead-zinc-borate and commercial silicate glasses were investigated. The critical load is directly proportional to the fracture toughness/Vickers microhardness term, supporting the Lawn-Evans model; however, the magnitude of the load is considerably greater than that estiated from the model. The relation of critical load to deformation/fracture properties is discussed in terms of the stress field around the indent area and fractography.     

Indentation Crack Length Anisotropy in Silicon Nitride with Aligned Reinforcing Grains

Vickers indentation was performed on surfaces of silicon nitride with an aligned microstructure in order to study the interaction between cracks and the microstructure. Although there was not much evidence of crack bridging, the transverse radial cracks were very short, resulting in high fracture toughness values. The longitudinal radial cracks tended to propagate along the grain boundary of the reinforcements and were much longer than the transverse cracks. As the sintering temperature increased, the lateral cracks on the casting surface led to spalling and consumed more energy for the crack formation, making the longitudinal cracks shorter. On the surface normal to the alignment direction, there was no spalling and the indentation cracks became longer as the sintering temperature increased.     

Cracking of Surface Mount Capacitors: Crack Susceptibility by Vickers Indentation Techniques

Crack susceptibility of surface mount capacitors fabricated using NPO, Z5U, and X7R materials have been evaluated using Vickers indentation techniques. Capacitors from two sources using X7R have been compared. A relative quality scale between the four surface mount capacitors has been made using the calculated critical stress factor necessary to initiate a crack. It is shown the Vickers indentation technique can be used to determine positional dependence of crack susceptibility. Z5U and NPO materials are used as examples. The Vickers indentation technique has potential of being used to distinguish between acceptable and rejectable lots. It appears from this study that the technique can be an aid to incoming inspection of devices that use ceramic material in their construction, such as surface mount capacitors, electronic packaging devices, and superconductor devices.     

Measurement of Indentation Residual Stresses in Materials Susceptible to Slow Crack Growth

Knowledge of the size and distribution of the indentation residual stress field is important when interpreting slow crack growth data for indented ceramic materials. A technique based on compressively loading indentation cracks has been used to measure the wedging residual stresses at radial indentation cracks. The method also gives information on the fatigue limit and can be applied on any ceramic material susceptible to slow crack growth. Soda–lime glass specimens were indented and the resulting residual stresses, wedging the radial cracks, were measured as a function of indentation load. Calculations of K ₀, the fatigue limit, were made for both virgin indentation cracks and cracks aged until saturation. The magnitude of closing stress needed to prevent slow crack growth was found to depend linearly on the indentation load. For example, for indentation loads of 20 and 60 N, the corresponding closing stresses were 14 and 26 MPa, respectively.     

Indentation Fracture Toughness of Sintered Silicon Carbide in the Palmqvist Crack Regime

The fracture toughness of a sintered dense α-SiC was estimated by the Vickers indentation microfracture method in the low-load Palmqvist crack regime. It was observed that the use of simultaneously obtained Vickers hardnesses does not yield reliable fracture toughness values, nor does application of the median-crack-derived equations. It is necessary to utilize a load-independent, crack-free hardness value with this toughness estimation method. Although several of the curvefitting equations yield similar toughnesses, it is concluded for the Palmqvist crack system in this α-SiC that the Niihara-Morena-Hasselman equation is the only one which yields fracture toughness values in agreement with conventional measurement techniques.     

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.     

Elastic/Plastic Indentation Damage in Ceramics: The Lateral Crack System

The mechanics of lateral crack propagation in a sharp-indenter contact field are described. The driving force for fracture has its origin in the residual component of the elastic/plastic field, which becomes dominant as the indenter is unloaded. Expressions for equilibrium crack evolution are derived, with due allowance for the close proximity of crack plane and specimen free surface. As with the median/radial crack system considered in an earlier paper, the ratio hardness-to-modulus complements toughness in the fracture relations. The basic predictions of the theory are examined in terms of experimental measurements of lateral crack dimensions in materials with a wide range of mechanical properties. The prospects of predicting the extent of lateral fracture in other ceramics, and thence of establishing a base for analyzing such important practical properties as surface erosion, are discussed.     

Relation Between Multiregion Crack Growth and Dynamic Fatigue of Glass Using Indentation Flaws

The influence of transport-limited kinetic crack growth on the fatigue properties of soda-lime glass was examined. Dynamic fatigue data were taken on specimens with controlled indentation flaws and were compared with the predicted response from measured crack velocity characteristics. Heptane was used as the operational test environment because of its pronounced crack velocity plateau; control tests in water served to establish a baseline reference for comparing the results. Frac-tographic observations using a stress wave marker technique showed a complex growth history for flaws broken in heptane compared to that for flaws broken in water. The magnitude of the predicted region II influence is too small to be detected in the dynamic fatigue results, even allowing for the relatively high degree of data reproducibility. The implications of this conclusion for lifetime predictions are discussed.     

Atomic Force Microscopy as a Characterization Tool for Contact Lenses: Indentation Tests and Grain Analysis

Nondestructive methods for testing mechanical properties of soft contact lenses allow quality control and testing to be performed on same sample by considering various parameters. A novel alternative to conventional mechanical test technique for contact lenses is presented implementing atomic force microscopy (AFM) and force spectroscopy (FS) technique as pico-indentation and mechanical characterization tool. This technique gives nN force resolution with producing nm range elastic deformation. FS and AFM topography results are evaluated simultaneously to compare mechanical and topographical properties of contact lenses such as Young's modulus, grain size evaluation, surface roughness, and adhesion force. Mechanical properties of soft contact lenses were reported by considering equilibrium water content of contact lens.     

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.     

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.     

Elastic/Plastic Indentation Damage in Ceramics: The Median/Radial Crack System

A theory for describing the evolution of the median/radial crack system in the far field of sharp-indenter contacts is developed. Analysis is based on a model in which the complex elastic/plastic field beneath the indenter is resolved into elastic and residual components. The elastic component, being reversible, assumes a secondary role in the fracture process: although it does enhance downward (median) extension during the loading half-cycle, it suppresses surface (radial) extension to the extent that significant growth continues during unloading. The residual component accordingly provides the primary driving force for the crack configuration in the final stages of evolution, where the crack tends to near-half-penny geometry. On the hypothesis that the origin of the irreversible field lies in the accommodation of an expanding plastic hardness impression by the surrounding elastic matrix, the ensuing fracture mechanics relations for equilibrium crack growth are found to involve the ratio hardness-to-modulus as well as toughness. Observations of crack evolution in soda-lime glass provide a suitable calibration of indentation coefficients in these relations. The calibrated equations are then demonstrated to be capable of predicting the widely variable median and radial growth characteristics observed in other ceramic materials. The theory is shown to have a vital bearing on important practical areas of ceramics evaluation, including toughness and strength.     

Strength vs Stressing Rate and Indentation Crack Growth Behavior of Indium(III) Phosphide

Susceptibility of InP to environmentally enhanced crack growth behavior was investigated in water and in 50% relative humidity by strength vs stressing rate and indentation crack length measurements. Statistical analysis indicated that, at the 95% confidence level, no environmentally enhanced fracture was detected for InP in liquid or gaseous water.     

The Compelling Case for Indentation as a Functional Exploratory and Characterization Tool

The utility of indentation testing for characterizing a wide range of mechanical properties of brittle materials is highlighted in light of recent articles questioning its validity, specifically in relation to the measurement of toughness. Contrary to assertion by some critics, indentation fracture theory is fundamentally founded in Griffith–Irwin fracture mechanics, based on model crack systems evolving within inhomogeneous but well‐documented elastic and elastic–plastic contact stress fields. Notwithstanding some numerical uncertainty in associated stress intensity factor relations, the technique remains an unrivalled quick, convenient and economical means for comparative, site‐specific toughness evaluation. Most importantly, indentation patterns are unique fingerprints of mechanical behavior and thereby afford a powerful functional tool for exploring the richness of material diversity. At the same time, it is cautioned that unconditional usage without due attention to the conformation of the indentation patterns can lead to overstated toughness values. Limitations of an alternative, more engineering approach to fracture evaluation, that of propagating a precrack through a “standard” machined specimen, are also outlined. Misconceptions in the critical literature concerning the fundamental nature of crack equilibrium and stability within contact and other inhomogeneous stress fields are discussed.