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.     

Fracture Resistance Behavior of Highly Anisotropic Silicon Nitride

The R -curve behavior was characterized by the Vickers indentation flaw technique, for highly anisotropic silicon nitride, a silicon nitride whose fibrous grains are highly aligned. The measured crack lengths ranged from 30 to 500 μm. The fracture resistance of a conventional self-reinforced silicon nitride was determined for comparison using the same procedures. While in the self-reinforced material several hundred micrometers of crack extension were required to obtain a high fracture toughness, the highly anisotropic material exhibited a high toughness from the beginning of the measured crack length range with little increase in the following range. It is suggested that the toughness of the highly anisotropic material steeply rises in a very short crack extension, which is advantageous in avoiding catastropic fractures.     

Indentation Studies on Y2O3-Stabilized ZrO2: II, Toughness Determination from Stable Growth of Indentation-Induced Cracks

Stable indentation cracks were grown in four-point bend tests to study the fracture toughness of two Y₂O₃-stabilized ZrO₂ ceramics containing 3 and 4 mol% Y₂O₃. By combining microscopic in situ stable crack growth observations at discrete stresses with crack profile measurements, the dependence of toughness on crack extension was determined from crack extension plots, which graphically separate the crack driving residual stress intensity and applied stress intensity factors. Both materials exhibit steeply rising R -curves, with a plateau toughness of 4.5 and 3.1 Mpa·m^1/2 for the 3- and 4-mol% materials, respectively. The magnitude of the plateau toughness reflects the fraction of tetragonal grains contributing to transformation toughening.     

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.     

The effect of local residual stress on the fractal dimension of silicate glasses

Local residual stress caused by impacts, machining and indentation results in a decrease in strength in most materials that fail in a brittle manner. The ratio of the critical crack size, c, and the fracture mirror size, r, also is affected by the existence of local residual stress. The global fracture toughness of non-R curve materials is not affected by the local residual stress. The fractal dimension of the fracture surface as characterized by the fractal dimensional increment, D*, is directly related to the square of the fracture toughness. This paper addresses the question of the effect of the local residual stress on the fractal dimension of the fracture surface. We derive a relationship between the fractal dimensional increment and the c/r ratio for materials fractured with and without local residual stress. We then compare the prediction with two cases of experimental results. We show the fractal dimension remains constant with the change in the c/r ratio for local residual stress conditions.     

Mechanisms of Failure from Surface Flaws in Mixed-Mode Loading

Mechanisms of failure from surface cracks in combined tension and shear are identified by directly observing the cracks during failure testing. Under the combined influences of residual contact stresses and applied loading, indentation cracks propagate stably and realign normal to the principal applied tension prior to failure. Annealing of indentation flaws causes relaxation of the residual stresses and thereby leads to a change in the mechanics of fracture; unstable propagation occurs from the initial crack at a critical applied loading, with an abrupt change in fracture plane. Strengths of indentation flaws and machining damage in both the as-formed and annealed states are measured as a function of flaw orientation relative to an applied uniaxial tension. Strength variations of indentations and machining flaws are similar. The results are assessed in terms of various proposed mixed-mode fracture criteria, and the implications of the results for nondestructive testing using scattering of surface acoustic waves are discussed.     

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.     

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.     

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.     

Statistical investigation of the influence of maximum shear stresses induced by thermal treatments on fracture toughness of soda-lime silica glasses: Comparison between Hertzian and Vickers indentations

Hertzian and Vickers indentation tests have been performed to estimate the hardness and the fracture toughness of a soda-lime silica glass fabricated by the float process. A comparison between as-prepared glass, annealed glass (90 min at 680°C), and tempered glass (quenched from 660°C to 25°C) has been conducted to investigate the influence of thermal treatments on fracture toughness. In this study, a new method based on acoustic emission, recorded during Hertzian indentation tests, has been used in order to determine precisely the minimum load for fracture of these glasses having various thermal histories. Experimental results have shown the existence of a threshold load below which no crack can be propagated in glass. These critical loads have been used to determine Weibull’s fracture laws as a function of surface quality and maximum shear stresses. It has been also shown that the presence of residual stresses induced by quenching leads to a shift of this threshold load and modifies Weibull’s laws. Therefore, this method, which requires no measurement of any crack length, can be used to accurately estimate residual stresses induced by quenching in soda-lime silicate glasses.     

Theory of Fatigue for Brittle Flaws Originating from Residual Stress Concentrations

A theory is formulated for the general fatigue response of brittle flaws which experience residual stress concentrations. The indentation crack is taken as a model flaw system for the purpose of setting up the basic fracture mechanics equations, but the essential results are expected to have a wider range of applicability in the strength characterization of ceramics. A starting fatigue differential equation is first set up by combining an appropriate stress intensity factor for point- or line-contact flaws with a power-law crack velocity function. Analytical solutions are then obtained for the case of static fatigue. The resulting relation between lifetime and failure stress is shown to have exactly the same power-law form as the conventional solution for Griffith (residual-stress-free) flaws. This "equivalence" is used as a basis for extending the results to dynamic fatigue. A comparison of these analytical solutions with numerical counterparts defines the limits of accuracy of the theoretical procedure. However, while the form of the lifetime relation remains invariant, the values of the exponent and coefficient differ significantly for flaws with and without residual stress. Accordingly, the application of conventional fatigue theory to evaluate crack velocity parameters, without due regard for the nature of the critical flaw, can lead to serious errors. Explicit conversion formulas are given for transforming "apparent" velocity parameters for indentation flaws directly into "true" parameters. The implications of these results concerning the use of the indentation method for materials evaluation 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.     

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.     

Strengthening Mechanisms in MLCCs: Residual Stress Versus Crack Tip Shielding

Failure by fracture is a serious problem with multilayer ceramic capacitors (MLCCs), and the interior electrodes are known to strengthen MLCCs. Historically, it has been assumed that the dominant strengthening mechanism is crack tip shielding via direct crack tip‐electrode interactions. However, we have found that residual stresses arising from differential thermal contraction after device sintering are actually responsible for the observed increase in strength. In addition, the fracture initiation sites in MLCCs are located outside of the electrode array, so the established idea that the electrical and mechanical failure controlling flaw populations are one and the same cannot be true. Weibull distributions were compared from the bending fracture of two populations of MLCCs with barium titanate (X7R) dielectric, nickel electrodes, and the same exterior geometries (but different electrode array configurations). MLCCs had characteristic strengths of 236 MPa versus a strength of 190 MPa for 19‐ and 3‐electrode MLCCs, respectively. Fractography, a critical flaw size computation, an analytical residual stress approximation, and in situ electrical measurements taken during bending were also used to examine the fracture process and demonstrate that residual stress and not crack tip shielding is an important strengthening mechanism in MLCCs.     

High temperature fracture toughness and residual stress in thermal barrier coatings evaluated by an in-situ indentation method

High temperature fracture toughness and residual stress are important for the evaluation of TBCs. In this paper, an in-situ high temperature indentation method was originally developed to investigate the high temperature fracture toughness and residual stress in a typical TBC, nanostructured 8?wt% yttria partially stabilized zirconia (YSZ) coating. The cracks caused by in-situ high temperature indentation tests were observed, and high temperature fracture toughness and residual stress were experimentally measured. The fracture toughness was measured to be 1.25, 0.91 and 0.75?MPa*m^1/2 at 25, 800 and 1000?°C, respectively. The residual stress was measured to be ? 131.3, ? 55.5 and ? 45.5?MPa, correspondingly. Moreover, the residual stress and fracture toughness both decrease with increasing environmental temperature. It is also found that the fracture toughness without consideration of residual stress is significantly larger than the intrinsic fracture toughness, which may result from the compressive stress state.     

Effect of Surface Flaw Size on Fracture Strength of Alumina Ceramics

Semielliptical surface flaws of different sizes were introduced into Al₂O₃ by Knoop microhardness indentation. The specimens were fractured by four-point bending and the profiles of the indentation flaws were determined by observing the fracture surfaces with a scanning electron microscope. The relation between the indentation flaw size and the fracture strength could be well explained by applying the fracture-mechanics analysis for semielliptical surface flaw in bending. The calculated values of the as-indented critical stress intensity factor, K_IC, were lower than previously reported presumably because of the influence of the residual stresses produced by the indenter.     

Multi‐Scale Effects in the Strength of Ceramics

Multiple length‐scale effects are demonstrated in indentation‐strength measurements of a range of ceramic materials under inert and reactive conditions. Meso‐scale effects associated with flaw disruption by lateral cracking at large indentation loads are shown to increase strengths above the ideal indentation response. Micro‐scale effects associated with toughening by microstructural restraints at small indentation loads are shown to decrease strengths below the ideal response. A combined meso‐micro‐scale analysis is developed that describes ceramic inert strength behaviors over the complete indentation flaw size range. Nano‐scale effects associated with chemical equilibria and crack velocity thresholds are shown to lead to invariant minimum strengths at slow applied stressing rates under reactive conditions. A combined meso‐micro‐nano‐scale analysis is developed that describes the full range of reactive and inert strength behaviors as a function of indentation load and applied stressing rate. Applications of the multi‐scale analysis are demonstrated for materials design, materials selection, toughness determination, crack velocity determination, bond rupture parameter determination, and prediction of reactive strengths. The measurements and analysis provide strong support for the existence of sharp crack tips in ceramics such that the nano‐scale mechanisms of discrete bond rupture are separate from the larger scale crack driving force mechanics characterized by continuum‐based stress‐intensity factors.     

Influence of Surface Stress on indentation Cracking

A simple, two-dimensional fracture mechanics analysis was used to determine the influence of nonuniform residual surface stresses on the formation of radial indentation cracks. The indentation behavior depends on the depth of the compressive stresses, such that the apparent fracture toughness passes through a maximum with increasing indentation load. The analysis was used to estimate the surface stress from indentation data for a zirconia-toughened ceramic and was compared to previous X-ray diffraction measurements of this stress. The comparison gives only fair agreement; the sources of possible error are discussed. Such surface stresses also influence the accuracy of K _{I C} measurements when an indentation crack length technique is used; surface preparation is a critical factor in the measurement. Finally, the K _{I C} values obtained from indentation crack sizes were compared with those obtained by the double-cantilever-beam technique.