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.     

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.     

Comparison of conventional Knoop and Vickers hardness of ceramic materials

Ceramics generally have a lower Knoop than Vickers hardness. This difference is due to the elastic recovery occurring around a Knoop indentation and the difference in representative area considered to calculate the hardness value.Conventional hardness tests with Knoop and Vickers indenters were performed in order to show how Knoop hardness test can give the same hardness number obtained by Vickers hardness test. This is obtained when Knoop hardness number is calculated based on the residual plastically deformed area whether projected or true. Complementary hardness data obtained from the literature were used in this work in order to validate the method proposed in this work. A revision of the well-known relation of Marshall is proposed in order to determine the elastic modulus by means of one Knoop hardness test when the Vickers hardness is unknown.     

The indentation size effect and the hardness of single crystal diamond on the (001) 110

The hardness of single-crystal diamond is addressed through the analysis of independent Knoop and Vickers indentation microhardness data on the (001) 110. A proportional specimen resistance model is applied to separate the hardnesses into two components, one representative of the indentation size-load effect (ISE) and the other the load-independent hardness. The analysis yields a load-independent Knoop hardness of 4411 kg mm⁻² and a Vickers hardness of 9158 kg mm⁻². These values are compared with similar analyses for sapphire and silicon carbide and are related to the Plendl-Gielisse volumetric lattice energy concept of hardness. The extraordinarily high hardnesses which have been reported for diamond, values in excess of 10 000 kg mm⁻², are attributed to the elastic modulus and friction contributions to the ISE.     

Geometrical Effects in Elastic/Plastic Indentation

A general analysis of elastic/plastic indentation fracture for an arbitrary-shaped indenter is presented. The analysis is based on the observation that the residual indentation stress field provides the driving force for crack formation. After establishing that the influences of indenter geometry and load on the residual field are completely characterized by the volume of the indentation, a relation between the extent of radial cracking, the indentation volume, and the material properties is derived. Predictions of the analysis are examined by comparing calculated load/crack-length relations for two specific indenter geometries (Vickers pyramid and sphere) with experimental measurements in ZnS. For Vickers indentation the crack length is proportional to (load)^2/3, whereas for spherical indenters the variation of crack length with load is nearly linear.     

Preparation and mechanical characterization of dense and porous zirconia produced by gel casting with gelatin as a gelling agent

A modified gel casting procedure based on a natural gelatin for food industry and commercial polyethylene spheres as pore formers was successfully exploited to produce dense and porous ceramic bodies made of yttria stabilized tetragonal zirconia polycrystal (Y-TZP). Vickers and Knoop microhardness, elastic modulus and fracture toughness measurements on dense samples obtained by experimental investigation closely matched results found in the literature for similar materials. However, after a careful analysis of obtained results, no indentation size effect and a lower scattering of experimental data from low load indentations were observed, in comparison with literature.     

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.     

Microhardness and Fracture Toughness Anisotropy in Cubic Zirconium Oxide Single Crystals

Vickers and Knoop indentation tests have been used to study the fracture and deformation characteristics of 9.4-mol%-Y₂O₃-stabilized ZrO₂ single crystals. K_c is anisotropic, with values of 1.9 and 1.1 MPa·m^1/2 for radial cracks propagating along (100) and (110), respectively. The toughness for these two orientations was also determined using the single-edge notched-beam geometry, and yielded values of 1.9 and 1.5 MPa·m^1/2.     

Recommendations for Determining the Hardness of Armor Ceramics

It is empirically known that an armor ceramic should be as hard or harder than the projectile it intends to defeat. Quasi-static indentation testing is one of the most widely utilized techniques for determining the hardness of armor ceramics. Hardness measurements can also be used to generate other property values that may be relevant to ballistic performance (fracture toughness, elastic properties, and even the yield strength). While the indentation methodologies are simple and straight forward, the resultant hardness values for ceramic materials can be influenced by the indenter geometry, indentation load, loading rate, specimen surface finish, and microstructure. This presentation will summarize the results of a study to determine the hardness of a variety of armor-grade ceramics with different indenter geometries (Vickers and Knoop) over a range of indentation loads (0.98-98 N) and discuss the implications for armor ceramics. The resulting data strongly indicate that the best means of determining the hardness of armor ceramics is the use of 19.6-N Knoop indentations.     

Microhardness and Indentation Fracture of Potassium Dihydrogen Phosphate (KDP)

Potassium dihydrogen phosphate (KDP) is an important electrooptic tetragonal crystal, often used in third harmonic generation in laser systems. We have used microindentation to measure the Vickers and Knoop hardness of KDP and the resulting cracking on (100) and (001) faces. Hardness anisotropy on the (001) face, or among the (100) and (001) faces, was small (∼20%). We observed an indentation size effect for both Vickers and Knoop hardness, for indenting loads in the range 0.24–1.96 N. The large-load Vickers hardness was estimated as 1.4 ± 0.1 GPa. We observed anisotropy in the crack sizes on (100) and (001) faces. Cracks were longer on (100) faces than on (001) faces. Assuming elastic and plastic isotropy, crack sizes were analyzed, and fracture toughness, K_c , was extracted. We present here an approximate model for analyzing crack-load microindentation data in tetragonal crystals. The model uses the minimum elastic modulus of the material. The effect of the isotropic assumption on the extracted fracture toughness is estimated at ∼33%, with a 23% contribution resulting from elastic anisotropy and 10% from the slip-system plastic anisotropy.     

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.     

Mechanical Properties of Polycrystalline Translucent Cubic Boron Nitride as Characterized by the Vickers Indentation Method

Mechanical properties of polycrystalline translucent cubic boron nitride (cBN) were characterized by Vickers indentation measurement. The calculated hardness decreased from 54 to 49 GPa as the load increased to 39 N, and then remained constant for values above this load. According to the relationship between crack length and applied indentation load, the formation of the median/radial type of cracks seems to take place at an applied load above 29 N. Assuming that the ratio of hardness and Young's modulus is constant in the polycrystalline cBN, the fracture toughness, K_IC , of cBN was estimated to be 5.0 ± 0.5 MPa·m^1/2.     

Cracking analysis of HVOF coatings under Vickers indentation

The fracture strength of five HVOF coatings, which are made of hard metals, Tribaloy alloy, and superalloys, respectively, coated on 1018 low carbon steel substrate, is studied under Vickers indentation, associated with FEA stress computation. The cross sections of the coating specimens are examined on a Hitachi Model S-570 scanning electron microscope (SEM), which investigates the quality and measures the geometry of the coatings. The mechanical properties of the coatings and the substrate are determined in the cross sections using the nano-indentation technique. The cracking behavior of the coatings under different indentation loads is investigated using a Vickers hardness tester. Three-dimensional finite element analysis (FEA) simulation of the Vickers indentation test is conducted to determine the stress fields in the coating/substrate systems in order to understand the fracture mechanisms of the coatings under the indentation loads using the ABAQUS software package. The FEA stress results are in good agreement with the experimental observation of Vickers indentation.     

Real indentation hardness of nano-polycrystalline cBN synthesized by direct conversion sintering under HPHT

The hardness characteristic of nano-polycrystalline cBN synthesized by direct conversion sintering was thoroughly investigated using Vickers and Knoop indenters. It was found that nano-polycrystals consisting of smaller cBN grains increase the elastic recovery of indentations during unloading of the indenters and the diagonal of Vickers indentations and the minor diagonal of Knoop indentations significantly decrease in length. Thus, if a Vickers indenter is used, the apparent hardness value increases, making it impossible to perform an accurate evaluation, e.g. incorrect Vickers hardness values in excess of 80 GPa were obtained from nano-polycrystalline cBN with a grain size of 50 nm or less. On the other hand, it was verified that a Knoop indenter ensures an accurate hardness evaluation even if the constituent grains are fine because its major diagonal length which is used for measurement is less susceptible to elastic recovery. In an accurate evaluation of the hardness of different types of nano-polycrystalline cBN using a Knoop indenter, the hardness of each type of cBN was around 45 GPa, and there was no clear Hall–Petch relationship between hardness and grain size without a slight bell-like correlation. These results suggest that reported hardness values higher than 80 GPa of similar nano-polycrystalline cBN evaluated using a Vickers indenter are incorrect values caused by elastic recovery occurring at the indentation.     

Measurement of Residual Stresses in Coatings on Brittle Substrati by Indentation Fracture

A method for evaluating stresses in coatings on brittle substrates by indentation is described. The basis for evaluations is fracture mechanics model of the radial crack system in the Vickers geometary, incorpeorating the effects of a thin surface demonstrate the methodology. The crack size on these coated specimens are found to be considerebly small than those on uncoated controls, indicating substantial (∼50 MPa) in-plane expansions observed after applying the coatings to already indented sufaces, are found to make an unexpectedly large contribution to the fracture susceptibility. The procedure offers a simple means for quantifying the mechanical integrity of coating configuration for ceramic components.     

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.     

Thermal Shock Resistance of Silicon Nitrides Using an Indentation–Quench Test

Thermal shock resistance of silicon nitrides is investigated using an indentation–quench method. Four commercially available silicon nitrides with different microstructures are investigated. The extension of Vickers radial cracks is measured as a function of quenching temperature for each material, up to the critical temperature for failure. An indentation fracture mechanics analysis is used to account for the crack responses, with due allowance for R -curve behavior. The analysis confirms the important role of microstructure in thermal shock resistance.     

Mechanical properties of thermally sprayed porous alumina coating by Vickers and Knoop indentation

Depending on the thermal spraying conditions, coatings obtained can present different defects, like pores, cracks and/or unmelted particles, and different surface roughnesses, that can affect the determination of the hardness and elastic modulus. The present work investigates the mechanical properties, determined by means of Knoop and Vickers indentations, of a plasma as-sprayed alumina coating, obtained with a nano-agglomerated powder sprayed using a PTF4 torch, in order to highlight how the surface defects interfere into the indentation process. As a main result, Knoop indentation compared to Vickers one gives less dispersive results (15% and 33%, respectively), that are, in addition, more representative of the coating properties. The mean values obtained are 110 ± 40 GPa for the elastic modulus and 1.75 ± 0.42 GPa for the hardness. In addition, and for the two indenter types used, multicyclic indentation has been performed because it allows a more appropriate characterization of such heterogeneous coatings due to the representation of the mechanical properties as a function of the indentation load and/or the penetration depth, leading to more reliable results according to the depth-variability of the coating microstructure.     

Effect of Lateral Cracks on Fracture Toughness Determined by the Surface-Crack-in-Flexure Method

The surface-crack-in-flexure (SCF) method uses a Knoop indenter to create small, semielliptical surface precracks in beam specimens. Lateral cracks may interfere with the primary median crack and cause errors of up to 10% in determination of fracture toughness, particularly for materials for which the fracture toughness is ∼3 MPa·m^1/2 or less. Although the residual-stress-damage zone is ground or polished away by hand by removing 4.5–5 times the indentation depth, this amount may not be sufficient to completely remove the lateral cracks in low-fracture-toughness materials. A series of tests were conducted on sintered alpha silicon carbide with different amounts of material removed after indentation. Once the lateral cracks were fully removed, the SCF results concurred with single-edged-precracked-beam and chevron-notched-beam data collected in accordance with ASTM Designation C1421. A simple remedy for the SCF method is to examine the outer ground surface for remnants of lateral cracks before fracture and to remove more material if necessary.     

Comparison of instrumented Knoop and Vickers hardness measurements on various soft materials and hard ceramics

Vickers and Knoop hardness measurements performed on various ceramics (hard metals) and light alloy materials (soft metals) are compared. The results show that the Knoop hardness number is, in general, lower than the Vickers hardness number for the highest values of hardness, and this behaviour is reversed when the hardness values are low. This change in values, which occur at 8 GPa, has no real physical meaning and, therefore, it is difficult to interpret such behaviour in terms of the elasto-plastic deformation around the indent such as sinking-in, piling-up, and bulging of the indent faces, phenomena which take place during indentation or after the withdrawal of the indenter.Prior to interpreting the hardness difference, it is very important to consider the same area in the hardness calculations. That is why we have compared the available hardness data obtained from the literature and recalculated them by considering the projected and true areas of the contact. If the objective is to compare the two hardness numbers, it seems more suitable to consider the true area of contact, procedure which will provide a Vickers hardness number higher than the Knoop hardness number all over the range of the hardness values.