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.     

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.     

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.     

Sigmoidal Indentation–Strength Characteristics of Polycrystalline Alumina

The fracture properties of a series of three polycrystailine aluminas are examined using indentationstrength and double cantilever beam techniques. The indentation-strength response is shown to be sigmoidal with concave-down behavior at small indentation loads and concave-up behavior at large indentation loads. A model is developed for the general response, combining increasing toughening by ligamentary bridging at small crack lengths and increasing residual-stress relief by lateral cracking at large indentation loads. The model is fit to the strength data and used to deconvolute the underlying toughness variation and predict the intrinsic strength of the materials. Direct measurements of toughness using the "long-crack" double cantilever beam geometry are shown to overestimate the toughness variations effective during "short-crack" strength tests.     

Crack-Growth Resistance of in Situ-Toughened Silicon Nitride

The fracture toughness of a commercial, hot-pressed, in situ -toughened silicon nitride with an elongated grain structure is determined by four different testing methods. The fracture toughness is found to be 5.76 ± 0.27, 8.48 ± 0.50, 10.16 ± 0.66, and 10.68 ± 0.39 Mpa.m^1/2, respectively, by indentation crack size measurement, indentation strength, single-edge-precracked-beam, and chevron-notched-beam methods. The discrepancy in fracture toughness between the testing methods is related to R -curve behavior, as measured using the indentation strength technique. These results indicate that there is no unique fracture toughness value and that a fracture toughness testing method with appropriate qualifiers is needed for rising R -curve materials. Therefore, care should be taken in interpreting and utilizing fracture toughness values evaluated from different testing methods if a material exhibits a rising R -curve. Complete characterization of the R -curve may be a prerequisite.     

Hardness and Fracture Toughness of SiC-Particle-Reinforced MoSi2 Composites

The indentation technique has been used to evaluate the hardness and fracture toughness of SiC-reinforced MoSi₂ composites made by hot-pressing. It is seen that the toughness increases with increasing indentation crack length (under increasing load) and a probable mechanism responsible for this behavior is described. It is also observed that there is an optimum volume fraction of SiC particles for which the maximum fracture toughness of the composite can be achieved.     

Measurement of Crack Tip Toughness in Alumina as a Function of Grain Size

Crack profile measurements near the crack tip in the SEM were used to measure crack tip toughness of alumina as a function of grain size (average grain size 0.9–16 μm). For comparative tests, two crack configurations were included in the present study: straight cracks (CT specimen) loaded with an in situ device; and radial indentation cracks. The measured crack tip toughness values were independent of crack geometry, and no grain size dependence could be discerned. A mean crack tip toughness of 2.3 MPam^1/2 was evaluated. The crack tip toughness determined from crack profile measurements is significantly lower than the toughness evaluated with conventional indentation techniques (e.g., indentation strength bending).     

Objective Evaluation of Short-Crack Toughness Curves Using Indentation Flaws: Case Study on Alumina-Based Ceramics

An objective methodology is developed for evaluating toughness curves ( T -curves) of ceramics using indentation flaws. Two experimental routes are considered: (i) conventional measurement of inert strength as a function of indentation load; (ii) in situ measurement of crack size as a function of applied stress. Central to the procedure is a proper calibration of the indentation coefficients that determine the K -field of indentation cracks in combined residual-contact and applied-stress loading, using data on an appropriate base material with single-valued toughness. Tests on a fine-grain alumina serve to demonstrate the approach. A key constraint in the coefficient evaluation is an observed satisfaction of the classical indentation strength–(load)^−1/3 relation for such materials, implying an essential geometrical similarity in the crack configurations at failure. T -curves for any alumina-based ceramic without single-valued toughness can then be generated objectively from inert-strength or in situ crack-size data. The methodology thereby circumvents the need for any preconceived model of toughening, or for any prescribed analytical representation of the T -curve function. Data on coarse-grained aluminas and alumina-matrix material with aluminum titanate second-phase particles are used in an illustrative case study.     

Fracture Toughness of Chemically Vapor-Deposited Diamond

The fracture toughness of chemically vapor-deposited diamond is estimated by a Vickers indentation method. Freestanding diamond films of 400-μm thickness are produced with plasma-enhanced chemical vapor deposition and highly polished for indentation testing. Indentation testing was performed with a microhardness tester using a load range of 5 to 8 N. The average fracture toughness is estimated as 5.3 ± 1.3 MPA · m^1/2.     

Transformation Driving Force for Indentation Cracking in Zirconia Ceramics

The transformation driving force for indentation cracking in phase-transformation-toughened ZrO₂ ceramics is confirmed with the direct crack measurement method. This driving force is produced by expansion of the plastic zone beneath the indenter due to stress-induced transformation, and it promotes the extension of the indentation cracks. The driving force cannot be neglected when evaluating the indentation fracture toughness of the materials.     

Hardness and Fracture Toughness of Pressureless-Sintered Boron Carbide (B4C)

This is a companion work to our previous study on the pressureless sintering of boron carbide (B₄C). The Vickers hardness and indentation fracture toughness of B₄C compacts were measured after various sintering heat treatments. Increases in hardness and decreases in indentation fracture toughness as the grain size decreased in sintered B₄C were attributed to the effects of more rapid strain hardening associated with dislocation pileups at grain boundaries.     

Estimation of Crack Closure Stresses for In Situ Toughened Silicon Nitride with 8 wt% Scandia

An 8-wt%-scandia silicon nitride with an elongated grain structure was fabricated. The material exhibited high fracture toughness (∼ 7 MPa · m^1/2) and a rising R -curve as measured by the indentation strength technique. The "toughening" exponent m was found to be m ∼ 0.1. The high fracture toughness and R -curve behavior was attributed mainly to bridging of the crack faces by the elongated grains. The crack closure (bridging) stress distribution in the wake region of the crack tip was estimated as afunction of crack size from the R -curve data, with an arbitrarily assumed distribution function.     

Determining indentation toughness by incorporating true hardness into fracture mechanics equations

The Lawn–Evans–Marshall (LEM) indentation fracture mechanics model for the well-developed half-penny crack is reexamined theoretically, with a particular emphasis on the physical meaning of the hardness parameter in this model. It is shown that there may be some confusion arising from the use of the hardness definition. A modified indentation toughness equation is then proposed, in which a true hardness number, rather than the apparent hardness, is incorporated. This modified equation predicts that it is the quantity a²/c^3/2, rather than P/c^3/2, that would keep constant in the half-penny crack regime. This prediction is verified by analyzing the previously published indentation data. It is also confirmed that a comparable value of indentation toughness can be deduced with this modified equation.     

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.     

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.     

Short-Crack Toughness and Abrasive Machining of Silicon Nitride

Hardness and toughness are often used to analyze the abrasive machining behavior of ceramic materials. However, toughness values of silicon nitride ceramics with microstructures containing elongated grains increase with crack extension. The present study investigates the effect of toughness on the process of abrasive machining to determine which value of toughness should be used in the analysis. The toughness curves (i.e., toughness as a function of crack length) of ten different silicon nitride materials are characterized by an indentation-strength technique and an indentation technique. The forces in surface grinding are measured as a function of the depth of cut. Examination of ground surfaces by scanning electron microscopy indicates that the material-removal processes in grinding follows the formation of short cracks (i.e., microcracks) and grain-scale material dislodgement. An indentation fracture model for material removal in abrasive machining is used to correlate the grinding forces with toughness and hardness of the materials. An agreement is obtained between the experimental results and the indentation model only when the toughness associated with short cracks is used. This study shows the importance of using appropriate toughness values corresponding to the microfracture processes in analyzing abrasive machining results for materials possessing rising toughness curves.     

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.     

Fracture Toughness Anisotropy and Toughening Mechanisms of a Hot-pressed Alumina Reinforced with Silicon Carbide Whiskers

The fracture toughness of a hot-pressed alumina and that of a hot-pressed alumina/SiC-whisker composite containing 33 vol% SiC whiskers were measured by four-point bending on single-edge precracked bend bars having sharp precracks created by "bridge indentation." Two batches of the composite were examined, one exhibiting a greater degree of whisker clustering than the other. The fracture toughness of the alumina was around 4 MN·m^-3/2 whereas that of the composite varied between 5 and 8 MN·m^-3/2 depending on microstructural uniformity and crack-propagation direction. Crack deflection in combination with a change in fracture from intergranular to transgranular fracture is proposed as an explanation of the superior fracture toughness of SiC-whisker-reinforced alumina as compared to unreinforced alumina. The composite exhibited a variation in fracture toughness with the crack-propagation direction in identical crack planes. This effect could with good accuracy be described in terms of crack deflection for the composite with uniform whisker distribution. However, in the material with whisker clustering the variation of the fracture toughness with crack-growth direction was greater and could not entirely be explained by crack deflection.     

A Crystalline Si3N4/Amorphous Si3N4 Composite

A composite consisting of elongated α-Si₃N₄ crystallites (5–50 (Am in diameter) embedded in an amorphous Si₃N₄ matrix was synthesized by chemical vapor deposition. The hardness and indentation fracture toughness of the amorphous matrix and of the composite have been evaluated at temperatures from ambient to 1200°C. It was found that the crystallites have relatively little influence on the hardness and indentation fracture toughness when the surrounding matrix is amorphous. However, a 1400°C heat treatment of the material results in a matrix consisting of small crystals (100 nm in diameter) surrounded by carbon-containing regions which appear to be amorphous in the TEM; TEM and EELS in nearby triple points revealed the presence of amorphous carbon. After heat treatment, the indentation fracture toughness at ambient and at 1200°C is increased due to extensive microcracking. The Vickers hardness at 1200°C also increased significantly as a result of the heat treatment. The relationship between the mechanical properties and the microstructure is discussed.     

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.