Comparison of fracture resistance as measured by the indentation fracture method and fracture toughness determined by the single-edge-precracked beam technique using silicon nitrides with different microstructures

Because of the industrial need for an assessment of fracture resistance, K_R from small ceramic parts, K_R of Si₃N₄ ceramics has been measured by the indentation fracture (IF) method using representative formulae to evaluate the compatibility with the fracture toughness, K_Ic determined from the single-edge-precracked beam (SEPB) technique. K_R of the fine Si₃N₄ showed little dependence on the crack length, whereas the samples with coarse microstructures exhibited a rising R-curve behavior. The IF equation which gave the nearest value to K_Ic from SEPB was different depending on the microstructures. The assessment of fracture resistance with Miyoshi's equation was considered to be preferable for the flat R-curve behavior. By contrast, in the case of the rising R-curve behavior, it was revealed that the relationship between the IF and SEPB values was difficult to explain unless the effective crack extension against K_Ic for SEPB was clarified.     

Three-parameter (3P) weibull distribution for characterization of strength of ceramics showing R-Curve behavior

Strength distribution of advanced ceramics is commonly characterized by two-Parameter (2P) Weibull distribution. However, deviation of strength distribution from 2P-Weibull distribution may occur in ceramics due to various mechanisms. R-curve behavior is one of these mechanisms where increase of fracture resistance with the extension of crack occurs. In such cases, 2P-Weibull distribution may not be the best fitting distribution function based on the goodness-of-fitness tests. This article examines the effectiveness of three-parameter (3P) Weibull distribution function for fitting the strength variation due to R-curve effect by using experimental and virtual strength data. The effect of Weibull parameters, degree of increase in crack resistance and number of samples on effectiveness of fitting via 3P-Weibull distribution is investigated. It is reported that 3P-Weibull distribution function fits the strength distribution better than 2P-Weibull distribution function for materials showing R-curve behavior when the crack resistance curve is steep and Weibull modulus is high. Furthermore, it is shown that at least 100 samples should be used for a reliable estimate when the material exhibits R-curve behavior.     

Analysis of Near-Tip Crack Bridging in WC/Co Cermet

The remarkable toughening effect usually found in WC/Co cermets has been analyzed by means of a fracture mechanics approach based on R-curve characterization and in situ measurements of crack opening displacement (COD). The use of a crack stabilizer specially designed for the bending geometry enabled to detect the rising R-curve behavior of the material starting from the very neighborhood behind the crack tip (i.e.<100 μm). In situ COD measurements were related to the rising R-curve behavior through theoretical equations for bridged cracks. As a result, the toughening effect in the cermet was explained using a constant (average) distribution of bridging stress which shields the crack in the very neighborhood behind its tip. The magnitude of the bridging stress was found to be close to the ultimate strength of the Co metal phase. Only a very minor effect on toughening was found to be operated by metal ligaments in regions far away from the crack tip.     

Extension of Hasselman's thermal shock theory for crack/microstructure interactions in refractories

Thermal shock damage resistance in advanced refractories depends on the crack interactions with the microstructure. These energy dissipation mechanisms during crack propagation are not directly considered in the original classical thermal shock model of Hasselman. They are imbedded within the N and γ terms of his derivations. In this extension of Hasselman's work, an expression is presented, which estimates the final crack size (?_f) as the fracture surface energy ratio between γ_NBT and γ_WOF. That expression directly considers the crack interaction mechanisms with the refractory microstructure as it includes the R-curve behavior effects. In addition, the equation presented allows a quantitative evaluation of the volumetric density of cracks in refractories.     

R-Curve Behavior of Long Cracks in Alumina

Coarse-grained alumina is among those monolithic ceramics which can exhibit an increase in crack resistance with crack extension. This R -curve behavior is most pronounced for intergranular fracture and does not depend exclusively on material properties. Crack and specimen geometries also influence the shape of the R -curves. The magnitude of the effect increases with increasing crack surface roughness, which is microstructure-dependent, and with crack-opening displacement, which is geometry-dependent. Based on experimental observations, a "dynamic" R -curve model is presented which relates the increasing resistance to an increasing crack tip shielding caused by crack surface bridging. Applying a J -integral approach, R -curves are calculated for two specimen geometries (short double cantilever beam and single-edged notched beam) and different grain sizes. The good agreement between calculation and experiment indicates that the R -curve behavior of long cracks in alumina can be predicted by a simple wake model.     

R-curves of lead zirconate titanate (PZT)

R-curves were measured for ferroelectric ceramic lead zirconate titanate (PZT) using surface cracks in flexure (SCF) in a single composition of unpoled, ferroelastic PZT. The effects of several parameters on the R-curves were experimentally determined. These included grain size, indentation load, polishing away the residual stress zone associated with the Knoop indentation, and thermal depolarization after indentation. The larger grain size resulted in a higher plateau value of the R-curve, a result consistent with the larger amount of ferroelastic switching observed in the stress/strain curve. Increasing the indentation load from 10 to 50 N resulted in larger initial crack sizes. This had some effect on the early part of the R-curve, but did not much affect the plateau value. Polishing away the residual stress zone eliminated the residual stress contribution of the Knoop indentation to the stress intensity factor. This resulted in the most accurate measurement of the intrinsic toughness (0.4 MPa m^1/2). Thermal depolarization to remove any potential ferroelastic crack tip switching zone associated with the indentation had little or no effect on the measured R-curves.     

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.     

Ferroelastic domain switching and R-curve behavior in lead zirconate titanate (Zr/Ti = 52/48)-based ferroelectric ceramics

In this work, ferroelastic domain switching and R-curve behavior in lead zirconate titanate (Nb/Ce co-doped Pb(Zr_0.52Ti_0.48)O₃, ab. PZT-NC)-based ferroelectric ceramics were investigated, using the indentation-strength-in-bending (ISB) method. Firstly, Vickers indentation test examined the notable fracture anisotropy of PZT-NC ceramics between the poling direction and its perpendicular direction, and the crack open displacement (COD) profiles in the two directions were also theoretically calculated from the indentation fracture mechanics. And then two kinds of ferroelastic domain switching modes (in-plane and out-of-plane) were used for explaining such anisotropic propagation behavior of indentation cracks. The subsequent three-point bending test illustrated the dependence of fracture strength on indentation load and the rising crack growth resistance curves (R-curves) in two directions. The resulted R-curves were fitted by the Hill's type Growth Function successfully, giving the reasonable values of crack extension exponential (n), plateau fracture toughness (K_max), and initial fracture toughness (K_ini). The in-plane ferroelastic domain switching was identified as a more significant toughening mechanism for PZT-NC ceramics than the out-of-plane switching due to more switchable domains.     

R-curve analysis of solid-phase-sintered and liquid-phase-sintered silicon carbide ceramics by indentation fracture and indentation-strength-in-bending methods

The R-curve behavior of SiC ceramics was investigated from aspects of microstructure and test methods. Two groups of silicon carbide ceramics were prepared by solid-phase-sintering and liquid-phase-sintering methods. One from each, determined by systematic evaluation on microstructure and mechanical properties, was selected for. R-curve behavior study by two methods of IF and ISB. It is found that for both SSiC and LSiC, IF fracture toughness decreases while the ISB one increases with the increasing indentation load – inconsistent R-curve behaviors observed with different method. IF and ISB methods were examined on its own theoretical basis and ISB method was determined the correct method for R-curve evaluation of SSiC and LSiC. That LSiC ceramic possesses better mechanical properties than SSiC material, indicated by ISB R-curve, well matches the mechanical evaluations.     

Influence of the Metal Particle Size on the Crack Growth Resistance in Mullite–Molybdenum Composites

The R -curve for mullite–molybdenum (32 vol%) composites, which were obtained at 1650°C under reducing conditions with three different Mo average grain sizes (1.5, 3, and 9 μm), was estimated by the indentation-strength method and compared with that monolithic mullite obtained under similar conditions. The composites material exhibited rising R -curve behavior. The composite with larger grain size, however, displayed better damage tolerance and higher resistance to crack growth. Microscopic observation of the crack path revealed, in the composites, the systematic presence of dispersoids acting as bridging sites in the crack wake. Therefore, the increased fracture toughness of these ceramic-matrix composites with adherent ductile phase can be attributed to clamping forces applied by metal ligaments that bridge the crack faces behind the crack front. These clamping forces retard the crack from opening as an external stress is applied. It was inferred that this superior performance of the larger Mo particle size composite can be attributed mainly to more effective bridging of the metal grains. Because of this, a higher applied stress intensity will be required to propagate the crack tip. These results suggest that the rising R -curve should be proportional to the metal grain size, since the grain bridging area is proportional to the metal grain size.     

In-Situ Determination of bridging stresses in Al2O3/Al2O3-platelet composites by fluorescence spectroscopy

Bridging stresses arising from interlocking and frictional effects in the crack wake have been quantitatively evaluated in an Al₂O₃/Al₂O₃-platelet ceramic, using in-situ microprobe fluorescence spectroscopy. Crack opening displacement (COD) profile has also been quantitatively measured in the scanning electron microscope (SEM), in order to substantiate the reliability of the piezo-spectroscopic measurements of microscopic bridging stresses. Mapping the crack wake (at critical condition for crack propagation) with a laser probe of 2 μm spatial resolution led to determine a discrete map of closure stresses over a crack extension of about 800 μm. Relatively high bridging stress values ≈350 MPa were revealed due to platelet interlocking in a near-tip bridging zone <100 μm, whereas frictional sites of lower stress magnitude <100 MPa were monitored in the crack profile farther away from the crack tip. The availability of microscopic fracture parameters like as the bridging stress distribution and the near-tip COD profile enables to quantitatively explain the rising R-curve behavior of the Al₂O₃/Al₂O₃-platelet material. Bridging stress distribution, COD profile and R-curve data are discussed in comparison with those collected in previous studies on equiaxed Al₂O₃ and toughened Si₃N₄. The present study supports the notion that crack bridging is by far the most important toughening mechanism in non-transforming ceramics.     

Cyclic Fatigue Crack Propagation Behavior of 9Ce-TZP Ceramics with Different Grain Size

Cyclic fatigue crack growth behavior has been investigated in 9 mol% Ce-TZP ceramics with grain sizes varying from 1.1 to 3.0 μm. To ascertain the interaction between crack resistance curve behavior and cyclic fatigue crack growth, cyclic fatigue tests were conducted with short double-cantilever-beam specimens in two conditions: (a) with a sharp precrack without preexisting t - m transformation and (b) with a sharp crack after R -curve measurements, i.e., with preformed t - m transformation in the crack region. Fatigue crack propagation occurs at applied stress intensity factor values as low as about 40% of the K _I,∞ values measured in the R -curves. The size and shape of the t - m transformation zones are found to be different for specimens obtained in monotonic loading R -curve measurements and in cyclic fatigue tests. For the specimens without preexisting t - m transformation the overall crack growth behavior can be described by the Paris power law relation: d a /d N = AδK^m _I with m values of 15 for the 1.1-μm grain size and between 8 and 9 for the material with larger grain sizes. For the specimens with the preformed transformation zone, a "V"shape d a /d N versus Δ K _I relation is obtained. Explanations for these different results in the two conditions are discussed in terms of crack tip shielding effects.     

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.     

R-curves determination of ordinary refractory ceramics assisted by digital image correlation method

As a figure-of-merit, the rising ratio of crack propagation resistance to fracture initiation resistance indicates a reduction of the brittleness and enhances the thermal shock resistance of ordinary refractory ceramics. The significant nonlinear fracture behaviour is related to the development of a fracture process zone (FPZ). The universal dimensionless load–displacement diagram method is applied as a promising graphical method for the determination of R-curves for magnesia refractories showing different brittleness. By applying digital image correlation (DIC) together with the graphical method, the problems arisen with accurate determination of the fracture initiation resistance and the crack length are overcome. Meanwhile, the R-curve is subdivided with respect to the fracture processes, viz the fracture initiation, the development of FPZ and the onset of traction free macro-crack. With the simultaneous crack lengths evaluated from DIC, the contribution of each fracture process to the crack propagation resistance at certain loading stage is quantitatively presented.     

Morphology and crack resistance behavior of binary block copolymer blends

Fracture behavior of binary blends comprising of styrene-butadiene block copolymers having star and triblock architectures was studied via instrumented Charpy impact test. The toughness of the ductile blends was characterized by dynamic crack resistance curves (R-curves).This study represents a systematic investigation of crack resistance behavior of nanometer structured binary block copolymer blends and the development of a new material with a combination of high toughness and transparency, usually not observed in incompatible polymer blends. While the lamellar star block copolymer shows an elastic behavior (small-scale yielding and unstable crack growth), adding of 20 wt% of the triblock copolymer leads to a stable crack growth and at 60 wt% of the triblock copolymer the strong increase of toughness values indicate a tough/high-impact transition, demonstrating the existence of novel toughening concepts for polymers based on nanometer structured materials.     

Subcritical Crack Growth of Macrocracks in Alumina with R-Curve Behavior

Subcritical crack growth of macroscopic cracks in two Al₂O₃ ceramics is investigated with single-edge-notched bending specimens under constant load. The resulting v - K _I-curves are in complete contrast to the behavior of natural cracks. In spite of the monotonic increase of the externally applied stress intensity factor due to crack extension, the crack growth rates first decrease. This behavior is caused by crack shielding due to crack border interaction and can be described by a rising crack growth resistance. Two methods are applied to determine the R -curve under subcritical crack growth conditions.     

R-curve behavior,mechanical properties and microstructure of sintered ZrB2–SiCp–ZrO2f ceramics

In this paper, zirconium diboride based ceramics added with 20 vol.% silicon carbide particle and 15 vol.% zirconia fiber (Z20S_p15Z_f) were prepared by hot-pressing at 1850 °C for 60 min under a uniaxial load of 30 MPa in Ar atmosphere. R-curves for Z20S_p15Z_f ceramics were studied using the indentation-strength in bending technique and the envelope method. The results indicated that these two testing methods were consistent and viable for estimating R-curve. Z20S_p15Z_f ceramics had high resistance to crack growth and damage tolerance with the 6.8 MPa m^1/2 of steady-state toughness. The toughening mechanism was fiber debonding, fiber pull-out, crack bridging, crack branching, crack deflection and transformation toughening.     

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

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

Improved Resistance to Damage of Silicon Carbide-Whisker-Reinforced Silicon Nitride-Matrix Composites by Whisker-Oriented Alignment

The effects of whisker-oriented alignment on resistance to damage of SiC( w )/Si₃N₄ composites have been investigated by the Vickers indentation method and R -curve behavior. It is shown that increasing the degree of whisker-oriented alignment decreases the lengths of Vickers impressions and indentation cracks. The results exhibit rising R -curve behaviors for the SiC( w )/Si₃N₄ composites with different degree of whisker-oriented alignment. Moreover, the initial crack length c _i, the threshold of crack growth resistance K _i, and the upper bound of crack growth resistance K _∞ change regularly with increasing degree of whisker-oriented alignment. All results suggest that the whisker-oriented alignment improves the resistance to damage of the composites, resulting in a more reliable and usable composite.     

Comments on “Thermal shock resistance of yttria-stabilized zirconia with Palmqvist indentation cracks” by G. Fargas,D. Casellas,L. Llanes,M. Anglada [J. Eur. Ceram. Soc. 23 (2003) 107–114]

In a recent paper, Fargas et al. [Fargas, G., Casellas, D., Llanes, L. and Anglada, M., Thermal shock resistance of yttria-stabilized zirconia with Palmqvist indentation cracks. J. Eur. Ceram. Soc., 2003, 23, 107–114] make use of the Vickers indentation technique to characterise the thermal shock resistance of brittle materials exhibiting the Palmqvist indentation crack system. They claim that their approach can provide a measurement of Hasselman's R⁗ thermal shock resistance parameter. It is here demonstrated that the obtained parameter is in fact different from R⁗. In parallel, it is shown that a previously developed approach, which is both consistent with the concepts of R⁗ and of the critical quenching temperature difference, ΔT_C, can be used in the case of the Y-TZP ceramics of Fargas et al. This approach also allows an estimation of the maximum thermal stresses and of the coefficient of heat transfer at the fluid–solid interface as a function of the quenching temperature difference.