A quantitative analysis of the indentation fracture of fused silica

It is unclear how the densification of fused silica influences the damage of its precision optics subjected to machining. This paper presents a quantitative analysis of the indentation fracture of fused silica involving densification with the embedded center of dilation (ECD) model. The Hertzian stress field and the ECD-induced stress field were superposed to provide the overall stress distribution in the loading stage. A new method was established to accurately determine the strength of the ECD-induced stress field with densification effects. With the aid of the ECD model, the starting locations, initiation stages and initiation sequence of crack morphologies were predicted by analyzing the stress fields. To quantitatively study the initiation of conical cracks in fused silica, the strain energy release rate was calculated by linear elastic fracture mechanics (LEFM). The predicted minimum threshold load leading to conical cracking was consistent with the measured values.     

Methodology for measuring fracture toughness of ceramic materials by instrumented indentation test with vickers indenter

Virtual crack closure technique and elastoplastic finite element method were employed to calculate the stress intensity factors (SIF) of ceramic materials on the tip of both half‐penny crack (HPC) and radial crack (RC) induced by Vickers indenter and the value of fracture toughness (K_IC) was extracted by the design of equi‐SIF contour of HPC and RC crack front. Through dimensional theorem and regressive analysis, a functional relationship between instrumented indentation parameters, crack length of Vickers impression and fracture toughness of ceramic materials was established, thus a novel methodology has been presented for measuring fracture toughness of ceramic materials by instrumented Vickers indentation. Both numerical analysis and experiments have indicated that this methodology enjoys higher measurement precision compared with other available indentation methods. The methodology is universally suitable for HPC, RC as well as transition cracks and capable of determining fracture toughness and elastic modulus in a single indentation test. In addition, it saves the effort of measuring the diagonal length of Vickers impression in case that the impression remains unclear.     

Indentation-Induced Contact Deformation and Damage of Glasslike Carbon

Fracture mechanics are examined for the Vickers-indentation-induced contact deformation and damage of glassy carbons produced by different densification processes. The indentation load versus indentation depth relationship during the loading-unloading cycle reveals that the contact deformation is purely elastic even under such a sharp indentation, which subsequently leads to an indentation-induced ring/cone crack system instead of the median/radial crack system. The processes and mechanisms of such an anomalous surface crack system are related to the very open microstructure of glassy carbons. The ring/cone cracks induced by Vickers indentation are, however, significantly different in nature from the well-known Hertzian cone crack which is induced by pressing a spherical indenter on a brittle surface. Demonstrated is the superiority of glassy carbons to ordinary brittle ceramic materials in resistance to strength degradation by contact with hard particles such as in ballistic situations.     

Cone Crack Nucleation at Sharp Contacts

The distribution of initiation loads for cone cracking during Vickers indentation is studied by direct experimental observation of the indentation process and by simulation. Observations on three different glasses show that cone cracks initiate at the edge of the contact impression and yield distributions of initiation loads with nonzero minima. The simulations, based on a model of an expanding indentation impression in a random array of active crack nuclei, yield distributions of initiation loads with minima of zero. Cone cracks at sharp contacts are concluded to be initiated from nuclei generated by the contact process itself, rather than by nuclei preexisting on the contact surface.     

The Mechanics of Indentation Induced Lateral Cracking

The mechanics governing the lateral cracks that form when a hard object plastically penetrates a ceramic is presented. The roles of indentation load, penetration depth, and work of indentation are all highlighted, as are the influences of the mechanical properties of the material. A closed form solution for cracking induced by expansion of a two-dimensional cavity is used to bring out essential features related to parametric dependence and scaling. The three-dimensional axisymmetric problem for an annular crack driven by a rigid spherical or conical indenter is solved using numerical methods. The region of highest tensile stress is identified corresponding to the location where a crack is most likely to nucleate. This location coincides with the depth below the surface where the crack will expand parallel to the surface under mode I conditions. The solutions have been substantiated by comparison with measurements of the cracks that form upon Vickers indentation. The basic formula for the crack radius has been used to predict trends in cracking upon static penetration and impact by a projectile. In both cases, the extent of the cracking is substantially diminished by increasing the toughness of the material. The yield strength has a much smaller effect. The cracks caused by penetration and the volume removed per impact both decrease marginally at higher yield strength.     

A finite element study on the effects of densification on fused silica under indentation

The pressure-induced densification significantly affects the deformation and damage behavior of fused silica. This paper presents a finite element analysis (FEA) of the densification and its effects on the deformation in fused silica under indentation. An elliptical constitutive model was refined to consider the influence of densification on elastic properties and its saturation with hydrostatic pressure. By matching the simulated indentation hardness to experiments, the plastic properties of fused silica were more accurately identified. FEA shows that the modified elliptical model can improve the prediction accuracy of the load-displacement curve of Berkovich indentation. As a widely-used reference material, the heavy densification in fused silica dose not influence the calibration accuracy of the tip area function in the Oliver-Pharr method, which provides a theoretical foundation for the use of fused silica as a reference material. With the modified elliptical model, the FEA successfully predicted the geometry of plastic zone, and the extent of elastic recovery and densification, which provided input parameters for the analytical embedded center of dilation (ECD) model of indentation stress field. Results show that the stress fields under a conical indenter predicted by the FEA agreed well with the ECD model.     

Effect of Indenter Geometry on Controlled-Surface-Flaw Fracture Toughness

Fracture toughness values obtained using both Knoop and Vickers-indentation-produced controlled surface flaws were compared as a function of indentation load for a well-characterized glass-ceramic material. At the same indentation load, Knoop cracks were larger than Vickers. As-indented K_c values calculated from fracture mechanics expressions for surface flaws were higher for Knoop flaws than Vickers, but both types gave low K_c values due to indentation residual stress effects. Analysis suggested that theoretical formalisms for indentation residual stress effects based on fracture mechanics solutions for a center-loaded penny crack in an infinite medium should apply to both indentation types. K_c values calculated using the residual stress approach were identical for Knoop and Vickers controlled surface flaws when a "calibration" value for a constant term in the expression for K_c was used for both indentation types.     

Subsurface Indentation Damage and Mechanical Characterization of α-Sialon Ceramics

Two hot-pressed sintered α-sialon samples of differing microstructures, but identical chemical composition, were evaluated first, in terms of indentation hardness and modulus, by depth-sensing indentation (DSI) tests on planes parallel and normal to the hot-pressed surface. The surface and subsurface cracks created under the DSI tests have also been investigated in relation to the effect of microstructure. Subsequently, Vickers indentation tests were conducted to explore the deformation and fracture characteristics in the two samples. The effect of microstructure and grain orientation on the development of different types of cracks, in particular subsurface cracks, was revealed and analyzed. Additionally, it suggested that the focused ion beam (FIB) miller is a preferred tool, in comparison to the conventional cross-sectioning techniques, for examining subsurface crack formation and structural characteristics.     

Crack propagation during Vickers indentation of zirconia ceramics

A quarter finite element model of 3 mol% yttria stabilized tetragonal zirconia polycrystal (3Y-TZP) ceramics undergoing Vickers indentation was established to simulate the evolution of stress and the propagation of cracks inside a sample. The indentation experiment was carried out on the Micro Vickers Hardness Tester. The results of the geometric characteristic parameters, such as the indentation diagonal half-length a, the crack length c and the maximum indent depth h_m, from the indentation simulation and experiment were similar. The types of indentation cracks under various loads were determined according to the Lawn-Evan model, which exactly correspond to the simulation results. In addition, the propagation of indentation cracks was discussed based on the maximum principal stress contour plots at various stages, and the conclusions were verified by the indentation analysis model proposed by Yoffe. As a result, the model developed in this paper can be used in indentation studies to solve the related problem.     

The impact of densification on indentation fracture toughness measurements

The fracture toughness was measured by the Vickers indentation method and by chevron notch for a series of xCaO-xAl₂O₃-(100 − 2x)SiO₂ glasses. As the silica content was increased, the fixed ξ value Vickers indentation fracture toughness (IFT) values increased, while the chevron notch values decreased. Glasses with higher silica contents deform with more densification and less shear when indented with a Vickers tip, thus resulting in reduced residual stress in the region surrounding the indent. The reduction in residual stress for high silica glasses results in less median/radial crack extension and unreasonably high Vickers IFT values. This indicates that a fixed ξ value of 0.016 is not appropriate for the glasses in this series. By repeating the IFT method with a sharper 110° four-sided pyramidal diamond indenter, it is demonstrated that indentation toughness and chevron notch toughness values now trend in the same direction and are in good agreement with a fixed ξ value of 0.0297. With the sharper indenter tip, the densification component to the deformation is substantially reduced for all glass types such that it no longer has such a prominent influence on the residual stress field. This result suggests that a fixed ξ value IFT method may be appropriate for all glass types if a sharper indenter tip is substituted in the place of the Vickers tip.     

Revealing crack profiles in polycrystalline tetragonal zirconia by ageing

Exposure to hot water vapour is shown to be useful for staining indentation crack profiles in doped zirconia polycrystals. This is illustrated here in 3Y-TZP with two different grain sizes, for which Vickers indentation cracks are of Palmqvist type, as well as in 3Y-TZP with 2.5 wt.% cerium oxide, for which indentation cracks are half-penny. The crack profile is clearly revealed on the fracture surface after biaxial flexural testing in all the specimens previously exposed to hot water vapour. The contrast in 3Y-TZP is induced by t–m transformation caused by hydrothermal degradation, which induces an intergranular fracture zone in front of the initial position of the indentation crack tip. The biaxial strength and apparent fracture toughness of 3Y-TZP increase substantially with the time of exposure at a rate that depends on the grain size. On the contrary, in 3Y-TZP doped with ceria no signal of t–m transformation is found and the flexure biaxial stress remains practically constant, but the initial position of the indentation crack is also clearly revealed by an intergranular fracture zone in front of the initial position of the crack tip. In this case, this is associated to environmentally assisted slow crack growth under the indentation residual stress during exposure to hot water vapour in autoclave.     

Nanoindentation Method for Measuring Residual Stress in Brittle Materials

The lowered threshold load for cracking with the cube-corner indenter has been used in developing a method that can be used to measure residual stresses in small volume brittle materials. By studying a series of orthogonal cracks generated at loads not exceeding 10 mN with the cube-corner indenter, a variation of crack length with position around a large Vickers impression in soda–lime glass was observed. Using an indentation fracture mechanics approach residual stresses were evaluated at the positions where the cube-corner indents had been made. The stress values thus evaluated were generally higher than those reported in the literature where micro-Vickers indents had been used to measure the stresses. Possible reasons for the disparity are discussed.     

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.     

Indentation responses of a graded zirconium phosphate–filled epoxy resin

The effects of load and time on the Vickers indentation responses of a graded zirconium phosphate (ZP)–filled epoxy resin are described. The hardness of this material is dependent on the concentration of ZP dispersed within the epoxy matrix. In the region poor in ZP, the hardness response is independent of load. In contrast, the hardness response in the region rich in ZP is profoundly load‐dependent as a combined result of particle agglomeration and an indentation‐size effect. When compared with the ZP‐rich‐epoxy, the ZP‐poor epoxy exhibits a larger creep and a more pronounced elastic recovery in the Vickers impression. The nature and degree of deformation in the vicinity of Vickers contacts are also studied. During indentation the ZP‐rich epoxy exhibits no contact‐induced cracks but displays microscale plasticity, which can be associated with intergrain sliding, debonding, and grain push‐out. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 931–935, 2001     

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.     

High-Temperature Behavior of Indent and Creep-Nucleated Cracks in Vitreous-Bonded Alumina

Crack behavior was studied at elevated temperatures in a commercial vitreous-bonded alumina for two types of cracks: one introduced by indentation at room temperature and the other by the creep process. Indentation cracks with relatively small initial size grew progressively longer during creep before they became blunt and arrested; however, they continued to widen throughout the creep process. Larger indentation cracks under high stress condition continued to grow until failure. The evolution of creep-nucleated cracks was so fast that they were observed only in their arrested state. Once observed, their length remained essentially constant, but they did grow in width. The crack-opening displacement rates of both types of cracks were linearly related to the creep rate as predicted by fracture mechanics for stationary cracks. All but the specimens with the largest indentation crack exhibited flaw tolerance in that they failed by the coalescence of creep-nucleated cracks instead of the growth of a single crack. The results illustrate the crack behavior in the brittle-to-ductile transition regime for ceramics that deform by grain boundary sliding.     

Anisotropy of Mechanical Properties of Zirconia-Based Ceramics Tested for Bending

The effect of bending stress s of different magnitudes and signs on the fracture toughness K _1c of polycrystalline specimens of partially stabilized zirconia (PSZ) is considered. A method for testing pre-stressed PSZ specimens by Vickers indentation using a four-point bending scheme is proposed. The dimensions of the impression from a diamond pyramid and the length of the radial cracks generated thereby are determined. An anisotropy of strength properties is revealed in the specimens tested, which is explained by the involvement of two mechanisms: forcing action of an external stress on the crack opening and activation of the tetragonal- monoclinic phase transition in the tensile stress field.     

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.     

Effect of Flaw State on the Strength of Brittle Coatings on Soft Substrates

A study is made of the role of flaw state on the strength properties of brittle ceramic coating layers bonded to soft polycarbonate substrates. We introduce Vickers radial cracks at prescribed loads into the coating undersurfaces prior to bonding to control the sizes and locations of the starting flaws. A spherical indenter is then loaded on the top bilayer surfaces, directly above the Vickers indentation sites, subjecting the radial cracks to flexural tensile stress. Radial crack responses are monitored in situ , using a camera located below the transparent substrate. Critical loads to cause radial crack instability, and ensuing growth of the arrested cracks, are recorded. Conventional biaxial flexure tests on corresponding monolith coating materials provide a baseline for data comparison. Relative to the monolith flexure specimens, the bilayers show higher strengths, the more so the larger the flaw, indicating enhanced flaw tolerance. A simple fracture mechanics analysis of the radial crack evolution in the concentrated-load field, with due account for distribution of flexural tensile stresses at the coating undersurface, is unable to account completely for the enhanced bilayer strengths for the larger Vickers flaws. It is hypothesized that the epoxy used to bond the bilayer components enters the cracks, causing crack-wall adherence and providing an increased resistance to radial crack instability. The fracture mechanics are nevertheless able to account for the arrest and subsequent stable extension of the radial cracks beyond the critical loads once this extraneous adherence has been overcome.     

Effect of Growth and Coalescence of Multisurface Cracks on Static Fatigue Behavior of Glass Ceramics

In order to study the effect of the interaction and coalescence of multisurface cracks on the static fatigue behavior of brittle materials such as glass and ceramics, a single crack and three collinear cracks were introduced on the surfaces of plate specimens of glass ceramics by Vickers microhardness indentation and were subjected to a constant four-point bending load. It was found that time-to-failure for a certain applied stress significantly decreased with the decrease in the crack center distance of indentation cracks, and the effect of interaction and coalescence of multicracks was shown to be significant. On the basis of the crack growth parameters for a single crack, time-to-failure for multicracks was predicted by taking the interaction and coalescence into consideration. It was demonstrated that the proposed multicrack coalescence model gives better predictions.