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.     

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.     

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.     

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.     

Analysis of Indentation Crack as a Wedge-Loaded Half-Penny Crack

Surface cracks produced by indentation with a Vickers indenter were modeled as half-penny cracks extended by symmetric disk-shaped wedges. The wedge diameter was assumed to be equal to the hemispherical plastic zone size, and the wedge thickness was calculated by equating the wedge volume to the hardness-impression volume. The resulting equilibrium relation between the indentation load and the radius of the half-penny crack is in good quantitative agreement with similar relations obtained from fracture toughness calibration.     

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-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.     

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.     

Experimental Measurement of Residual Stress Field around Sharp Indentation in Glass

A new technique is developed to measure the residual stress field around Vickers indentations in glass and ceramics. This technique uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. The approach is based on the observation that the crack lengths of the small indentation are changed under the influence of the residual stress field created by the large indentation. A simple fracture mechanics model is derived to calculate the residual stress from the measurement of the changes of the crack lengths of the small indentation. The results show that the residual stress around Vickers indentations is a nonequal biaxial field; both tensile and compressive stresses exist around a sharp indentation and decrease as the distance from the center of indentation increases. This technique can be easily extended to many other cases of residual stress in ceramics and composites.     

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.     

Fracture mechanics of sharp scratch strength of polycrystalline alumina

The strength of a polycrystalline alumina containing controlled scratches introduced by translated sharp contacts is investigated and described by a multiscale fracture mechanics model. Inert strength measurements of samples containing quasi‐static and translated Vickers indentation contacts showed that scratches degraded the strength at normal contact loads an order of magnitude less than those for quasi‐static indentation. The fracture mechanics model developed to describe strength degradation by scratches over the full range of contact loads included toughening effects by crack‐wake bridging at the microscale and lateral crack‐based residual stress relaxation effects at the mesoscale. A critical element of the model is the nonlinear scaling of the residual stress field of a scratch with the normal contact load acting during scratch formation. The similarities and differences in the scratch model in comparison with prior indentation‐strength fracture mechanics models are highlighted by parallel development of both. Central to the scratch model is the use of easily controlled normal contact load as the scratch‐strength measurement variable. Scratch length and orientation are shown to have significant effects on strength. The distributions of scratch widths controlling the intrinsic strengths of as‐received samples are determined and agreement with the observed scratch dimensions is demonstrated.     

Nonlinear Compliance Testing Applied to Indentation Cracking in Ceramics

Indentation cracking under sharp-pointed indenters is analyzed using compliance-based, nonlinear, fracture mechanics. The stress intensity factor, K , in linear elastic fracture mechanics is well known to be proportional to the load, P ; in this nonlinear analysis K is proportional to P ^3/4. The observed relation between indenter load-point displacement and crack length is based on similitude of crack lengths with load-point displacements as a strain-controlled fracture. The equations that relate load and a function of the crack length to the crack driving force, J , have been found for Vickers indentations. Analysis of the nonlinear load vs displacement assumes an equilibrium crack in the elastic material surrounding the indent. The hardness that describes the load vs load-point displacement during cracking is derived on a constant J line in load-displacement space. The crack length is shown experimentally to be proportional to the load-point displacement after crack initiation for several different indenters in ZnS. The measured loading curves are nonlinear and display crack initiation during loading. The K _Ic expressions found here are very similar to correlations that have been applied to indentation cracks.     

Indenter Flaw Geometry and Fracture Toughness Estimates for a Glass-Ceramic

Shapes of cracks associated with Vickers indenter flaws in a glass-ceramic were assessed by stepwise polishing and measuring surface traces as a function of depth. The cracks were of the Palmqvist type even at200-N indentation load. The toad dependence of crack lengths and fracture toughness estimates were examined in terms of relations proposed for Palmqvist and half-penny cracks. Estimates based on the half-penny crack analogy were in closer agreement with bulk fracture toughness measurements despite the Palmqvist nature of the cracks.     

Spherical and Vickers Indentation Damage in Yttria-Stabilized Tetragonal Zirconia Polycrystals

Damage induced in an yttria-stabilized tetragonal zirconia polycrystal by spherical and Vickers indentations was investigated. Scanning acoustic microscopy revealed that, as indentation stress increased, the spherical indentation gradually developed subsurface damage, until it experienced a transition to a fully plastic state, characterized by a highly anisotropic variation in the leaky Rayleigh wave velocity, v _R, and very similar to that for Vickers indentation. The transition was a result of the formation of a microcracked core beneath the contact. Indenter geometry had an appreciable effect only within the core; the distribution of microcracks differed depending on the indenter used, as confirmed by direct observations using a scanning electron microscope. In contrast, the residual stresses in the elastic-plastic zone were insensitive to indenter geometry. The resulting plastic zone was not hemispherical but rather cylindrical, irrespective of indenter geometry.     

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.     

Comparative Measurement of Indentation Fracture Toughness with Berkovich and Vickers Indenters

Measurements of the load dependence of the radial crack size with Vickers and Berkovich indenters are compared for a range of materials. It is found that the extent of radial cracks was slightly larger for the Berkovich than for the Vickers indenter. The observations reveal that cracks from a Berkovich indenter are best described by an expression developed by Laugier combined with a modification proposed by Ouchterlony to account for the number of radial cracks. It was also found that the Berkovich indenter, which offers advantages for ultramicroindentation, gave more consistent toughness values at lower loads than a Vickers indenter.     

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).     

Determination of Surface Residual Stresses in Brittle Materials by Hertzian Indentation: Theory and Experiment

Hertzian indentation has been used to determine the surface residual stress levels in brittle materials. In this method, a hard sphere is pressed into the surface of the material: at a critical load a preexisting surface-breaking crack in the neighborhood of the contact will propagate. There is a threshold load below which no such crack, of whatever size, can be propagated. The presence of a residual stress in the surface will lead to a shift in this threshold load. The effects of residual stresses on the minimum load to produce Hertzian fracture are predicted for alumina and glass, assuming that the variation of the residual stress over the length of the crack is small. Two methods of analysis (one approximate, one more general) are presented that enable the residual stress to be calculated from the shift in threshold load; the only further information required is a knowledge of the radius of the sphere, the elastic constants of the sphere and substrate, and also the fracture toughness of the substrate (or use of a stress-free specimen as a reference). No measurement of any crack length is necessary. Experimental results are presented for the residual stress levels determined in glass strengthened by ion exchange. Indenting balls of a variety of materials with a range of elastic mismatch to the glass substrate were used, so as to evaluate the effects of elastic mismatch and interfacial frictional tractions on the results obtained. The results obtained by Hertzian indentation are consistent with residual stress levels determined by differential surface refractometry. We also present results on alumina specimens with induced surface stresses.     

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.     

Lateral cracks during sliding indentation on various optical materials

A series of static and sliding indentation (ie, scratching) was performed and characterized on a wide range of optical workpiece materials [single crystals of Al₂O₃ (sapphire), SiC, Y₃Al₅O₁₂ (YAG), CaF₂, and LiB₃O₅ (LBO); a SiO₂–Al₂O₃–P₂O₅–Li₂O glass ceramic (Zerodur); and glasses of SiO₂:TiO₂ (ULE), SiO₂ (fused silica), and P₂O₅–Al₂O₃–K₂O–BaO (Phosphate)] at various applied loads using various indenters (Vickers, 10 µm conical, and 200 µm conical). Despite having different load dependencies, the lateral crack depth formed during sliding indentation quantitatively scales with that formed during static indentation, explaining why static indentation has been historically effective in describing various grinding parameters. Depending on the indenter geometry, the amount of residual trench damage (plastic deformation and local fracturing) during sliding indentation was often enhanced by more than an order of magnitude compared with static indentation. A simple ploughing scratch model, which considers both tangential and normal stresses (where the tangential stress is amplified by relatively small tangential contact area), explains this enhancement and other observed trends. Accounting for the high correlation between residual trench depth and volumetric fracturing, the model is extended to estimate the amount of fracture damage as a function of the material properties of the workpiece, indenter geometry, and applied load. Such a model has utility in the design of optimized grinding processes, particularly the abrasive geometry. Finally, at higher loads (>1 N), lateral cracks were often observed to preferentially propagate in the forward scratching direction, as opposed to perpendicular to the scratch as typically observed. High-speed imaging of the scratch process confirms that these cracks propagate ahead of the sliding indenter during the scratching event. Finite element stress analysis suggests the ploughing frictional forces increase the mode I tensile stresses at the leading edge of the sliding indenter explaining the direction of crack propagation of such cracks.