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.     

Instrumented indentation study of materials edge chipping

The resistance to local fracture of brittle materials is currently characterized by the value of edge toughness. An “instrumented micro-edge chipping” (IMEC) is proposed and tested. This test was carried out on various brittle materials: light krone glass LK-5, polycrystalline silicon Si, partially stabilized dioxide zirconium ceramic TS and tetragonal dioxide zirconium ceramic Y-TZP. IMEC test provides a closer correlation between the edge toughness Fr values at different values of the distance L between the test specimen edge and the indentation point than with the macro-EF test. Comparison of the macro-EF and IMEC tests for studied materials showed the almost identical trend in the ratio of the edge toughness values for all the studied materials. It was found that there is a significant time from the moment of crack formation to the full realization of the edge chip. The duration of the chip process is different for the studied materials.     

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.     

A critical evaluation of indentation crack lengths in air

An extensive overview is presented of Vickers indentation crack lengths in ceramics in air. Measurement of such crack lengths is one of the most common and powerful assessments of the fracture properties of ceramics and the overview provides a critical evaluation of observed behavior as functions of material type and indentation load, and an extensive basis for comparison of results from new materials and analyses. The overview considers single crystals, polycrystals, transforming materials, glasses, and multiphase materials, including cermets, glass-ceramics, and tooth enamel. The coverage extends over structural and electronic ceramics, including oxides, carbides, nitrides, and titanates. The data are presented in a single format for ease of interpretation in terms of idealized indentation fracture and for inter-material comparisons; most data are unique to this work, but the results of selected studies from the published literature are included. The overview considers the precision and accuracy of crack length measurements and demonstrates a simple quantitative evaluation and ranking scheme for ceramic fracture based on load-adjusted crack length and cracking susceptibility. Indentation hardness and cracking threshold are also determined and related to the susceptibility. Material toughness is related to cracking susceptibility by fracture mechanics analyses: typical crack length measurements in air are shown to provide estimates of inert toughness with a relative uncertainty of ±50%.     

Measurement of the Fracture Toughness of Ceramic Materials Using a Miniaturized Disk-Bend Test

The fracture toughness of several ceramic materials has been measured using a miniaturized disk-bend test apparatus and methodology based on small disk-shaped samples 3 mm in diameter. The method involves the Vickers indentation of specimens ranging in thickness from 300 to 700 μm, and testing them in a ring-on-ring bending mode. New experiments on a glass-ceramic (GC) and Si₃N₄ have been performed to demonstrate the validity of the technique, supplementing the original work on ZnS. The fracture resistances of these materials increase with increasing crack length ( R -curve behavior). The data are analyzed using a specific model for the relationship between fracture resistance and crack length; this model enables the R -curve behavior to be treated analytically, and the fracture resistance at "infinite" crack length to be evaluated using a straightforward graphical procedure. The resulting values of the fracture toughness for ZnS, GC, and Si₃N₄ are 0.74 ± 0.02, 2.18 ± 0.09, and 4.97 ± 0.07 MPa-m^1/2, respectively, which are all in very good agreement with values obtained from conventional fracture toughness tests on large specimens. The results verify the utility of the miniaturized diskbend method for measuring the fracture toughness of brittle materials.     

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.     

Rising Crack-Growth-Resistance (R-Curve) Behavior of Toughened Alumina and Silicon Nitride

R -curves for a sinter/HIPed SiC(whisker)-reinforced alumina and a sintered silicon nitride were assessed by direct measurements of lengths of cracks associated with Vickers indentation flaws. The fracture toughness measurements based on (a) initial (as-indented) crack lengths, (b) equilibrium growth of cracks during increasing far-field loading, and (c) crack lengths corresponding to unstable fracture showed definitive trends of R -curves for both materials. The fracture mechanics analyses employed an indenter-material constant that was independently estimated using a physical model for the residual driving force and a free surface correction factor that accounted for the effects of size and shape of the cracks on stress intensity. It is shown that R -curve estimations based on crack length measurements have the intrinsic advantage that crack length dependence of fracture toughness is not assumed a priori as is done in conventional analysis based on strength. The measured fracture toughness of SiC(whisker)-reinforced alumina was in agreement with the prediction of a toughening model based on crack bridging by partially debonded whiskers.     

Contact-Induced Failure of Prestressed Glass Plates

An indentation fracture technique was used to determine critical contact conditions under which prestressed brittle surfaces are subject to catastrophic failure. A theoretical model based on the growth of a well-developed, contact-induced half-penny crack leads to a simple inverse-cube power relation between indentation load and tensile prestress. The analysis is developed in terms of fracture parameters which are readily calibrated in routine indentation/strength tests. Experiments on glass disks loaded simultaneously in biaxial flexure and Vickers indentation confirm the essential failure predictions of the theory; toughness is the key material parameter controlling resistance to failure. The results emphasize the danger of spurious tensile stresses in ceramic systems exposed to severe contact events.     

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.     

New method for extracting fracture toughness of ceramic materials by instrumented indentation test with Berkovich indenter

Applying finite element analysis, a method is proposed for evaluating fracture toughness of ceramic materials by instrumented indentation with Berkovich indenter. The crack-tip K_I (Stress intensity factor) of Berkovich-produced crack is numerically calculated by using virtual crack closure technique, in particular, three kinds of crack pattern, i.e., radial crack, transition crack and half-penny crack are identified and their crack fronts meet the equi-K_I requirement. The validity of the proposed method is verified by instrumented indentation tests on standard SRM2100 (Si₃N₄) and CRM156 (Fused Silica) samples. Comparison with six representative conventional indentation methods indicates that the proposed method has advantages including wide application range, high accuracy and applicability to different crack patterns. Additionally, it’s revealed that the conventional indentation fracture toughness formulae derived from Lawn-Evans-Marshall formula tend to exhibit larger test error when applied to materials of relatively high indentation work ratio W_e/W_t.     

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.     

Fracture Modes in MoSi2

The room-temperature fracture behavior of polycrystalline MoSi₂ was characterized using Vickers indentation fracture. Fracture analysis was aided by the optically active grain structure of MoSi₂ revealed under polarized light. Radial crack propagation from indentations was found to be predominantly transgranular. The approximate indentation fracture toughness of MoSi₂ was 3 MPa.m^1/2, while the measured hardness was 8.7 GPa. Fracture behavior is believed to be controlled by anisotropy and cleavage energy of the tetragonal MoSi₂ crystal structure.     

Predicting subsurface damage in silicon nitride ceramics subjected to rotary ultrasonic assisted face grinding

Silicon nitride is an advanced ceramic used in high performance applications. One of the main problems in machining of brittle materials such as silicon nitride is subsurface damage (SSD). On the other hand, rotary ultrasonic assisted face grinding (RUAFG) is considered as state of the art machining process for brittle and hard to machining materials such as ceramics and optical glasses. In this research, a new study on SSD generation in RUAFG by establishing both ductile deformation and brittle fracture conducted. To achieve this goal, initially single diamond grit cutting force based on Vickers hardness correlation and indentation fracture mechanics established and placed in crack propagation formulas to anticipate SSD. Verification tests performed and average 8% error detected. Moreover, RUAFG depicted up to 30% SSD reduction in comparing to conventional face grinding (CFG). Besides, scanning electron microscope utilized to investigate cracks morphology.     

Nanoindentation pop-in in oxides at room temperature: Dislocation activation or crack formation?

Most oxide ceramics are known to be brittle macroscopically at room temperature with little or no dislocation-based plasticity prior to crack propagation. Here, we demonstrate the size-dependent brittle to ductile transition in SrTiO₃ at room temperature using nanoindentation pop-in events visible as a sudden increase in displacement at nominally constant load. We identify that the indentation pop-in event in SrTiO₃ at room temperature, below a critical indenter tip radius, is dominated by dislocation-mediated plasticity. When the tip radius increases to a critical size, concurrent dislocation activation and crack formation, with the latter being the dominating process, occur during the pop-in event. Beyond the experimental examination and theoretical justification presented on SrTiO₃ as a model system, further validation on α-Al₂O₃, BaTiO₃, and TiO₂ are briefly presented and discussed. A new indentation size effect, mainly for brittle ceramics, is suggested by the competition between the dislocation-based plasticity and crack formation at small scale. Our finding complements the deformation mechanism in the nano-/microscale deformation regime involving plasticity and cracking in ceramics at room temperature to pave the road for dislocation-based mechanics and functionalities study in these materials.     

Fracture behavior of solid electrolyte LATP material based on micro-pillar splitting method

The NASICON type solid electrolyte LATP is a promising candidate for all-solid-state Li-ion batteries considering energy density and safety aspects. To ensure the performance and reliability of batteries, crack initiation and propagation within the electrolyte need to be suppressed, which requires knowledge of the fracture characteristics. In the current work, micro-pillar splitting was applied to determine the fracture toughness of LATP material for different grain orientations. The results are compared with data obtained using a conventional Vickers indentation fracture (VIF) approach. The fracture toughness obtained via micro-pillar splitting test is 0.89 ± 0.13 MPa?m^1/2, which is comparable to the VIF result, and grain orientation has no significant effect on the intrinsic fracture toughness. Being a brittle ceramic material, the effect of pre-existing defects on the toughness needs to be considered.     

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.     

On the Vickers Indentation Fracture Toughness Test

The Vickers indentation fracture toughness test, or VIF, is addressed by considering its origins and the numerous equations that have been applied along with the technique to estimate the fracture resistance, or the K _{I c} of ceramics. Initiation and propagation of cracks during the VIF test are described and contrasted with the pre-cracking and crack growth for internationally standardized fracture toughness tests. It is concluded that the VIF test technique is fundamentally different than standard fracture toughness tests. The VIF test has a complex three-dimensional crack system with substantial deformation residual stresses and damage around the cracks. The VIF test relates to an ill-defined crack arrest condition as opposed to the rapid crack propagation of the standardized fracture toughness tests.
Previously published fracture toughness results employing the VIF technique are reviewed. These reveal serious discrepancies in reported VIF fracture toughness values. Finally, recent fracture resistance measurements by the VIF technique for the Standard Reference Material SRM 2100 are presented. These are compared with standardized test results for the same material. It is concluded that the VIF technique is not reliable as a fracture toughness test for ceramics or for other brittle materials. What the VIF actually measures in terms of fracture resistance cannot be readily defined. It is recommended that the VIF technique no longer be acceptable for the fracture toughness testing of ceramic materials.     

Comparison of the sandwiched beam (SB) and opposite roller loading (ORL) techniques for the pre-cracking of brittle materials

The “sandwiched beam” (SB) and “opposite roller loading” (ORL) methodologies suitable to introduce sharp through-thickness cracks in brittle materials are critically reviewed and compared in this work. In both cases a sharp crack is obtained in a notched specimen by means of a suitable loading. In the SB technique the specimen is placed between two support bars and bent in a 3- or 4-point configuration. The ORL procedure is based on the symmetrical loading by four rollers which induces a local tensile stress. Results show that both techniques are successfully usable on brittle materials: in both cases suitable specimens are obtained for fracture toughness measurements. The crack length can be reasonably controlled and varies in a wide range. The SB procedure typically provides cracks with α≌0.5, while shorter cracks are obtained by the ORL technique. Fracture toughness is measured on specimens prepared using the two techniques. The obtained values result in good agreement with literature data.     

Short-Crack Fracture Toughness of Silicon Carbide

The fracture toughness of four different silicon carbides was measured using single-edge precracked beam (SEPB) and indentation/strength techniques. Two were development grades with similar microstructures and chemistries, and yet exhibited different fracture modes. The grade that exhibited a predominantly intergranular fracture had an SEPB fracture toughness (6.4 MPa√m) 88% higher than the one that showed primarily a transgranular fracture (3.4 MPa√m). The higher fracture toughness was associated with a modest increase in average strength (25%), although there was a significant increase in the Weibull modulus (11–32). Fracture toughness at short crack lengths was assessed by an indentation method that used fracture strengths, crack lengths at fracture, and a new method of estimating the constant δ that characterizes the residual driving force of the plastic zones based on the stable growth of the indentation cracks from the initial ( c ₀) to the instability ( c ^*) lengths. The results showed a rising crack-growth-resistance behavior for the grade exhibiting intergranular fracture, while the grade showing transgranular fracture had a flat crack-growth resistance. Tests on two commercial grades of silicon carbide showed similar behaviors associated with the respective fracture modes.     

The fracture toughness of inorganic glasses

Measuring the fracture toughness (K_Ic) of glasses still remains a difficult task, raising experimental and theoretical problems as well. The available methods to estimate K_Ic are reviewed, with emphasis on their respective advantages and drawbacks. In view of our current understanding, this analysis gives precedence to the SEPB method. The ultimate glass strength, the critical flaw size, and the indentation load for the onset of crack initiation are discussed, in the light of the fundamentals of fracture mechanics and classical background regarding the mechanics of brittle materials. Analytical expressions were further proposed to predict the fracture energy and fracture toughness of glasses from different chemical systems from their nominal compositions. The theoretical values were compared with the experimental ones, as obtained by self‐consistent methods when available. The agreement observed in most cases suggests that measured K_Ic values correspond to the crack propagation regime (as opposed to the crack initiation threshold), and supports previous investigations in glasses and ceramics, which showed that a crack tip is nearly atomically sharp in these materials (but for metallic glasses). Some ideas to design tougher glasses are finally presented.