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.     

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this first part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elastic/plastic indentation fracture mechanics. It is thereby asserted that the key to the radial crack response lies in the residual component of the contact field. This residual term has important implications concerning the crack evolution, including the possibility of post indentation slow growth under environment-sensitive conditions. Fractographic observations of cracks in selected "reference" materials are used to determine the magnitude of this effect and to investigate other potential complications associated with departures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the Indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely simple in procedure and economic in its use of material.     

Microstructure and mechanical properties of Al2O3–YSZ spherical polycrystalline composites

The mechanical behavior and microstructure of highly densified, spherically shaped, polycrystalline Al₂O₃–YSZ composites, processed from pseudoboehmite powders by sol–gel is reported here. Processing was carried out by combining nanometric sized α-Al₂O₃ (120 nm) seeds and YSZ particles of tetragonal structure. The YSZ particles were homogeneously distributed in a coarse-grained matrix of alumina, both inside grains and along grain boundaries. Fracture surfaces, achieved by impact tests showed toughening effects of the zirconia particles. The tetragonality of the YSZ phase stability even after fracture events and fracture toughness measurements by Vickers indentation, where the crack tip interacts with YSZ particles, are all provided and discussed. The local mechanical properties, such as elastic modulus, indentation hardness and the onset of plastic deformation or fracture contact pressure of both YSZ particles and the Al₂O₃ matrix were quantified by nanoindentation. Evidence of coercive contact pressure was observed in YSZ from indentation stress–strain curves.     

Mechanical evaluation of propylene polymers under static and dynamic loading conditions

The present investigation is concerned with the evaluation of the impact toughness of commercial‐grade Propylene polymers. Conventional impact static stress–strain and static fracture experiments were carried out. Static stress–strain experiments revealed different pattern behaviors among the materials that were reflected in the fracture behavior. Under static conditions, all materials exhibited ductile behavior and crack grew under J‐controlled conditions displaying stress whitening through the whole fracture surface with the sole exception of the homopolymer, which displayed a ductile instability after some stable crack growth. Under dynamic conditions the homopolymer exhibited brittle behavior, the block copolymer exhibited some plastic deformation at the crack tip, and the random copolymer samples exhibited a whitening effect due to voiding and craze formation through the whole fracture surface, indicating that stable crack propagation was occurring. Fracture mechanics tests were analyzed by following different methods, depending on the mode of fracture presented by the polymer. The Normalization J‐method was used under static conditions. The elastic method, the corrected elastic method, and the essential work of fracture methodology were used to characterize brittle, semibrittle, and ductile behavior, respectively. Fracture mechanics parameters arisen from both static and dynamic conditions are compared. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 2681–2693, 1999     

Mechanical and fracture behavior of an artificially ultraviolet‐irradiated poly(ethylene‐carbon monoxide) copolymer

In this work, 1 wt % carbon monoxide (CO) poly(ethylene‐carbon monoxide) (ECO) copolymer sheets were artificially exposed to ultraviolet (UV) light with a power density of 3 mW/cm² for up to 130 h. A thorough mechanical characterization of the irradiated material was conducted, in which both the stress–strain data and the values of the quasistatic crack initiation and growth toughness were measured and correlated with companion uniaxial tensile tests and single‐edge‐notched fracture tests. Average values of the elastic modulus, failure strain, and failure stress were determined from the tensile tests. The full‐field optical technique of digital image correlation was used to quantify in‐plane deformation (displacements and displacement gradients) during the fracture experiments and to extract values of the crack initiation and growth fracture toughness. The elastic modulus increased monotonically with UV irradiation for the exposure times used in this investigation. In addition, for low irradiation times of less than 5 h, both the failure strain and failure stress of ECO decreased, and this caused a corresponding decrease in the crack initiation and growth toughness. However, for longer irradiation times, the failure strain remained almost invariable, whereas the failure stress increased by about 25% over that of unirradiated ECO. As a result, for longer irradiation times (>5 h), 1 wt % CO ECO became not only stiffer but also stronger and tougher, as quantified by companion fracture experiments. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 139–148, 2004     

Flat R-Curve from Stable Propagation of Indentation Cracks in Coarse-Grained Alumina

The fracture toughness of coarse-grained A1₂O₃, known for pronounced "Iong"-crack R-curve behavior, was studied in the "short"-crack regime utilizing the stable propagation of indentation cracks in bending. A combination of in situ microscopic crack growth observations and mechanical testing enabled measurement of crack extension curves. They reflect the contributions of residual indentation stress intensity and applied bending stress intensity on the total crack driving stress intensity and allow determination of the residual stress factor χ and the toughness K_R. The results indicate that χ depends on indentation load and A_R is surprisingly constant rather than increasing. To resolve the latter contradiction with long-crack R-curve behavior, combined short/long-crack fracture tests were performed with the same specimens. Starting with stable indentation crack growth and continuing with stable long-crack extension, the previous toughness results were confirmed, i.e., constant toughness from indentation cracks and increasing toughness from long cracks. The influence of crack-opening behavior on bridging-controlled R-curve toughening can qualitatively explain the observed discrepancies.     

Analytical estimation of fracture toughness for circumferential cracks in thin hard films on ductile substrates

In this study, the fracture toughness of circumferential crack caused by indentation effect of a rigid indenter on a thin and elastic coating deposited on the elastic substrate was calculated. In the coating and substrate, the analytical solution of displacement and stress field was used. The complete adhesion was considered for the coating on the substrate. The location of maximum circumferential stress was investigated using the analytical calculation of the stress and it was found that this place was located at a distance away from the center of the indenter. Then, the stress intensity factor and energy release rate for plane strain state was determined, and consequently, the energy release rate for a channel crack was calculated. Finally, the fracture toughness was calculated with energy release rate curves for plane strain crack and crack channeling. This method was used to calculate the fracture toughness of TiN/TiCrN ceramic multilayer coating which was deposited on the GTD450 substrate using the Cathodic Arc PVD method. To validate the results, the analytically calculated crack radius was compared with the experimental crack radius in the fracture load and the difference between the radiuses was in the acceptable range.     

Prediction of ring crack initiation in ceramics and glasses using a stress–energy fracture criterion

Crack initiation in brittle materials upon spherical indentation is associated with the tensile radial stresses during loading. However, location of crack onset often differs (offset) from the site of maximal stress. In addition, experiments reveal a strong dependency of crack initiation forces on geometrical parameters as well as the surface condition of the sample. In this work, a coupled stress–energy fracture criterion is introduced to describe the initiation of ring cracks in brittle materials, which takes into account the geometry of the contact and the inherent strength and fracture toughness of the material. Several experiments reported in literature are evaluated and compared. The criterion can explain the location offset of the ring crack upon loading, as observed in various ceramics and glasses. It also predicts the ring crack initiation force upon contact loading, provided that surface compressive stresses, introduced during grinding or polishing processes, are taken into account. Furthermore, the stress–energy criterion may be employed to estimate the surface residual stress of ceramic parts, based on simple contact damage experiments.     

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.     

Effect of Crystallites on Surface Damage and Fracture Behavior of a Glass-Ceramic

A study was conducted of the effect of crystallization on the fracture toughness, strength, and resistance to surface damage of glass-ceramic materials with a range of microstructures obtained by different heat treatments. The hardness indentation method was used as a quantitative tool to simulate mechanical surface damage. In the uncrystallized glass and in the glass-ceramic heat-treated to result in a uniform fine-grained structure, crack size increased monotonically with indentation load. In contrast, in the glass-ceramics heat-treated to result in a microstructure consisting of larger crystallites (a few micrometers) contained within a fine-grained matrix, a discontinuity in the crack size vs load curve presented evidence for crack-pinning at crack sizes which were a small multiple of the intercrystallite spacing. At the position of crack-pinning, the fracture toughness showed a discontinuous increase with increasing crack size that was attributed to crack deflection. The strength of the glass and fine-grained glass-ceramic measured in biaxial flexure decreased monotonically with indentation load. The strength at low values of indenter load of the glass-ceramic heat-treated to yield the coarser crystallites within the fine-grained matrix was independent of indentation load, indicating stable crack propagation prior to fast fracture. At the higher values of indenter load, the coarse-grained glass-ceramics exhibited a monotonic decrease in strength with increasing indentation load. The results of this study indicate that the strengthening observed on crystallization of a glass can be attributed to a combination of a decrease in flaw size achieved at a given mechanical surface treatment, an increase in fracture toughness, and a modification in the mode of crack propagation.     

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.     

Mechanical properties of zirconia composite ceramics

Composite materials based on 8 wt% yttria partially stabilized zirconia, with additions of gadolinium zirconate, lanthanum lithium hexaaluminate, yttrium aluminum garnet and strontium zirconate were characterized. Samples were fabricated by hot-press sintering at 1550 °C. The effect of the secondary phase content on the mechanical properties of the composites was evaluated. Hardness, elastic modulus and fracture toughness of the fabricated composites were determined by means of depth-sensitive indentation testing. The fracture toughness of the samples as determined by the indentation method was found to increase with increasing YSZ content, reaching 3 MPa·m^0.5 for samples with 80 wt% YSZ. The fracture toughness appeared to be affected by thermal expansion coefficient mismatch, crack bridging and crack deflection.     

Fracture Toughness of Porous Material of LSCF in Bulk and Film Forms

Fracture toughness of La_0.6Sr_0.4Co_0.2Fe_0.8O_3‐δ (LSCF) in both bulk and film forms after sintering at 900°C to 1200°C was measured using both single‐edge V‐notched beam (SEVNB) 3‐point bending and Berkovich indentation. FIB/SEM slice‐and‐view observation after indentation revealed the presence of Palmqvist radial crack systems after indentation of the bulk materials. Based on crack length measurements, the fracture toughness of bulk LSCF specimens was determined to be in the range 0.54–0.99 MPa·m^1/2 (depending on sintering temperature), in good agreement with the SEVNB measurements (0.57–1.13 MPa·m^1/2). The fracture toughness was approximately linearly dependent on porosity over the range studied. However, experiments on films showed that the generation of observable indentation‐induced cracks was very difficult for films sintered at temperatures below 1200°C. This was interpreted as being the result of the substrate having much higher modulus than these films. Cracks were only detectable in the films sintered at 1200°C and gave an apparent toughness of 0.17 MPa·m^1/2 using the same analysis as for bulk specimens. This value is much smaller than that for bulk material with the same porosity. The residual thermal expansion mismatch stress measured using XRD was found to be responsible for such a low apparent toughness.     

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.     

A Fracture Toughness Test Using the Ball‐on‐Three‐Balls Test

A method for fracture toughness measurement of ceramics using small disks and plates is presented. Similar to the surface‐crack‐in‐flexure (SCF) method a semielliptical surface crack is introduced centrally into one plane side of the specimen which is fractured in a ball‐on‐three‐balls test. Finite element simulations are used to evaluate the stress intensity factor (SIF) for this loading geometry for a range of crack sizes and crack geometries. Empirical formulae for the geometric function are provided for evaluation of the test. The effect of position uncertainties is investigated using FEM and experiments. Other sources which may contribute to the measurement error are identified and quantified, resulting in recommendations for the practical realization of the test. A determination of the fracture toughness within ±10% measurement uncertainty is possible with specimens larger than 8 mm in diameter and thicker than 0.5 mm. With larger specimens an uncertainty comparable to other fracture toughness tests can be achieved. For precise measurements it is important to position the crack within ±120 μm of the stress maximum, to know Poisson's ratio exactly and to test cracks that have the maximum SIF at their deepest point. A method how this can be achieved is presented.     

钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析

针对钢化真空玻璃球形支撑物对玻璃压痕的应力场分布问题,采用接触力学,对Hertzian压痕方程进行了修正,推导了三维应力场方程,同时,对完全发展的锥形裂纹的应力强度因子进行了数值求解。结果表明,在球体与玻璃接触区域内,所有的主应力都是压应力,主应力σ₁导致了裂纹的萌生,而主应力σ₂形成了环形裂纹。与玻璃表面正交的最小主应力从接触边缘向外偏离,形成的近似平行的曲线即为锥形裂纹的形状,而最大拉应力总是垂直于这些曲线。因此,在最大主拉应力的作用下,球体加载后裂纹遵循最小主应力的轨迹。裂纹尖端的应力强度因子决定了断裂韧性,随着裂纹的扩展,应力强度因子减小,在离表面一定距离后,应力强度因子达到临界值,裂纹停止。不同压痕载荷下的归一化应力强度因子是一组具有相似形状的曲线。     

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.     

Effect of the t–m transformation morphology and stress distribution around the crack path on the measured toughness of zirconia ceramics: A case study on Ce-TZP/alumina nanocomposite

The t–m transformation zone and related residual stress fields around two types of crack used for toughness measurements, i.e. SEVNB (arrested crack induced by a V-notch) and IF methods (indentation crack induced by a Vickers impression), are reported for a Ce-TZP/Al₂O₃ nanocomposite, in comparison with 3Y-TZP. The fact that Ce-TZP/Al₂O₃ exhibits significant high toughness value on occasions when evaluated by the IF method was determined to be clearly linked to the presence of wide ranged three-dimensional transformation configuration and resulting substantial compressive residual stress fields. In contrast, for 3Y-TZP, transformation behaviors around the two types of crack were quite similar, which proves that 3Y-TZP shows near toughness values for both SEVNB and IF methods.