Statistical analysis of the strength reliability of the MAX phases

A good comprehension of the mechanical property stability is crucial in promoting the structural applications of the MAX phases. This study aims to determine the most suitable intensity distribution for the experimental flexural strength of present Ti₃AlC₂ and previous Ti₃SiC₂, optimize the fitting parameters, and explore the error sources. After comparing two-parameter Weibull, three-parameter (3P) Weibull, and other three distributions, the 3P-Weibull distribution is the most suitable for the MAX phases. The different parameter estimation methods, rank estimators, and minimum used sample numbers of 3P-Weibull were tested to determine safe and accurate parameter values for engineering application. Furthermore, the 3P-Weibull modulus (2.32 for Ti₃AlC₂ and 2.04 for Ti₃SiC₂) indicates that the MAX phases occupy a middle ground between typical metals and ceramics, attributing to their high fracture toughness and the R-curve behavior. These findings would open up prospects for the standardization of testing methods for the Weibull statistics of the MAX phases.     

Fracture statistics of dental ceramics: Discrimination of strength distributions

The Weibull distribution is the most widely used function in the reliability analysis and structural design of dental ceramics; however, it is still unclear whether Weibull distribution is always the most suitable one. With wide applications of dental ceramics, a special attention has been paid in discriminating their strength distributions. In this paper, three versatile functions, involving normal, log-normal and Weibull distributions, are applied to the analysis of ten strength data sets of dental ceramics with different compositions and the results are compared in terms of the Akaike information criterion and the Anderson–Darling test. It reveals that various microstructures and compositions in the investigated dental ceramics cause their strength distributions deviated from the Weibull distribution. The influence of microstructure induced fracture properties (multiple-modal flaw size distribution, R-curve behavior and subcritical crack growth) on strength distributions is discussed.     

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.     

Crack-location-dependent R-curve behavior in Si3N4

The rising crack resistance (R-curve) behavior in a hot-pressed Si₃N₄ with an elongated grain structure was studied by observing the stable growth of annealed indentation-induced cracks during the bending test. The experimental data corresponding to each individual crack were analyzed according to an exponential function proposed by Ramachandran and Shetty. [Ramachandran, N. and Shetty D. K., Rising crack growth-resistance (R-curve) behaviour of toughened alumina and silicon nitride. J. Am. Ceram. Soc., 1991, 74, 2634–2641]. It was found that the measured R-curve is strongly dependent on the crack location. Due mainly to the existence of a microstructural driving force for crack growth, all cracks may start to propagate at nearly the same level of the applied stress intensity. During the subsequent stable growth, however, the variations of crack resistance with crack extension may be different for different cracks located in different sites of the surface of material. The effect of the random orientation of the elongated grains within the material on the interaction between the bridging grain and the propagating crack was suggested to be the main cause of the crack-location-dependence of the measured 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.     

Microstructure, Flaw Tolerance, and Reliability of Ce-TZP and Y-TZP Ceramics

Ce-TZP and Y-TZP ceramics were heat-treated for various times and temperatures in order to vary the microstructure. Flaw tolerance was investigated using the indentation–strength test. Reliability was quantified using conventional two-parameter Weibull statistics. Some Ce-TZP specimens were indented at slightly elevated temperatures where no transformation was observed. Results indicated that the Ce-TZP specimens were extremely flaw tolerant, and showed a relatively high Weibull modulus that scaled with both R -curve behavior and flaw tolerance. Y-TZP, on the other hand, with very little if any R -curve behavior or flaw tolerance, had a low Weibull modulus. The results also show that flaw history, i.e., whether or not a transformation zone exists along the wake of the crack, has a significant influence on strength. Strength was much less dependent on initial crack size when the crack had an associated transformation zone, whereas strength was highly dependent on cracks typical of natural processing defects. It is argued that the improvement in reliability, flaw tolerance, and dependence on flaw history are all ramifications of pronounced R -curve behavior.     

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.     

MAS-content dependence of the texture and fracture behavior of h-BN-MAS composite ceramics

Texturing was employed to tailor the mechanical properties of h-BN ceramic with MAS as liquid texturing aid. Effects of MAS content on the texture behavior, densification behavior, bending strength, fracture toughness and the fracture behavior of the h-BN ceramics were studied. Moderate MAS of 30 wt% can significantly facilitate the orientation of h-BN grains in the direction perpendicular to the hot-pressing direction. MAS is also in favor of the densification behavior of h-BN as sintering aid. In-situ mechanical testing shows that texturing can greatly improve the mechanical properties and avoid the catastrophic fracture of the h-BN ceramics, and the textured h-BN ceramics exhibit distinct rising R-curve behavior, which is primarily attributed to the effect of parallel-aligned h-BN grains to the crack propagation under loading.     

R-Curve Behavior and Flaw Insensitivity of Ce-TZP/Al2O3 Composite

A ceria-partially-stabilized zirconia-aiumina (Ce-TZP/Al₂O₃) composite optimized for transformation toughening was used to demonstrate its flaw insensitivity due to R -curve behavior. Four-point bend specimens fabricated with a controlled distribution of spherical pores showed nearly the same characteristic strength and strength variability (Weibull modulus) as specimens fabricated without the artificial pores. In situ observations confirmed stable growth of cracks initiated at pores and the crack lengths at fracture instability were much greater than the pore sizes, thus resulting in fracture strengths insensitive to the pores. The small variability in the fracture strength was found to be associated with variability in the R -curve and the instability crack lengths. An analysis based on the fracture instability criterion for rising crack growth resistance accounted for the strength variability due to variability in the R -curve. Comparable four-point bend experiments were also conducted on a sintered yttria-partially-stabilized zirconia (2Y-TZP) ceramic. This ceramic showed significant degradation of strength due to the presence of the pores. This flaw sensitivity is attributed to its steep rising R -curve over short crack lengths.     

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.     

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.     

Effect of hot isostatic pressing on the mechanical properties of aluminum oxide ceramics

The influence of the conditions of hot isostatic pressing (HIP) on the mechanical properties of presintered ceramics containing 94, 97, and 99% Al₂O₃ is studied. It is shown that HIP treatment provides the possibility of increasing substantially the strength, the crack resistance, and especially the modulus of the Weibull function for the statistical strength distribution. The optimum HIP parameters depend on the composition and previous technological history of the ceramics. Translated from Ogneupory i Tekhnicheskaya Keramika, No. 1, pp. 8–11, January, 1997.     

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 Behavior in a Silicon Carbide Whisker/Alumina Matrix Composite

R -curve measurements were performed on a SiC whisker/Al₂O₃ matrix composite. A controlled flaw/strength technique was utilized to determine fracture resistance as a function of crack extension. Rising R -curve behavior with increasing crack extension was observed, confirming the operation of wake toughening effects on the crack growth resistance. Observations of crack/microstructure interactions revealed that bridging by intact whiskers in the crack wake was the mechanism responsible for the rising R -curve behavior.     

Influence of sample size on strength distribution of advanced ceramics

Strength distribution of advanced ceramics is mostly characterized by Weibull distribution function. The question whether the Weibull distribution always gives the best fit to strength data has been being considered in the last years. The sample size affects the reliable decision of discrimination of different distribution functions (e.g. normal, log-normal, gamma or Weibull). In this paper, 5100 experimental alumina strength data and virtual strength data generated by Monte Carlo simulations are used in order to investigate the effect of sample size on strength distribution of advanced ceramics. It is suggested that, at least 150–200 samples should be used for determination of best fitting distribution function with a statistical fallibility of 10%. Extreme Value Analysis performed with the experimental strength data showed that the Weibull distribution fits the data best and difference between the Weibull and Gumbel distributions appear at the tails.     

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.     

Transformation Toughening in ZrO2-Containing Ceramics

Transformation toughening in ZrO₂-containing ceramics is discussed. Specifically, microstuctures of the three distinct types of ZrO₂-toughened ceramics are presented, after which microstructural evolution in MgO-partially-stabilized ZrO₂ Mg-PSZ) is reviewed. The mechanical properties of such transformation-toughened ceramics are dominated by "resistance-curve" ( R -curve) behavior, wherein the crack resistance increases during the course of crack propagation. Ceramics subject to R -curve behavior require a more detailed failure criterion than those subject to the usual linear elastic fracture mechanics criterion involving a critical stress intensity factor, K_IC.R -curve-controlled fracture in ceramics provides a degree of very desirable flaw insensitivity, but can lead to counterintuitive relationships concerning strength, toughness, and initial flaw size. Examples of R curves of Mg-PSZ with different thermal histories are given.     

Crack healing behavior of a MAB phase: MoAlB

Self-healing property of ceramics is highly attractive in meeting the safety and durability requirements of high temperature structural components. This work reports on the crack healing behavior of MoAlB, together with its oxidation resistance. The MoAlB material showed a good oxidation resistance due to the formation of a dense and thin Al₂O₃ scale in the temperature range 1200–1300 °C for 10 h. The crack healing behavior as a function of temperature and healing time was studied. For the healed samples, the strength recovery almost returned to the initial strength. Healing is accomplished by the formation of only Al₂O₃ in the site of damage. The microstructure and the phase composition of samples before and after healing were characterized with scanning electron microscopy and x-ray diffraction method, respectively.     

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.     

Flexural fracture mechanisms and fatigue behaviors of Bi4Ti3O12-based high-temperature piezoceramics sintered at different temperatures

In this paper, a series of Aurivillius phase Bi₄Ti_2.95W_0.05O_12.05 +?0.2?wt% Cr₂O₃ (ab. BTWC) ceramics were prepared by a solid-reaction process and sintered at different temperatures (1050?℃~1150?℃), their microstructures, fracture mechanisms and fatigue behaviors were investigated under three-point-bending mode. The results show that the grain size of BTWC ceramics increases with increasing the sintering temperature. The typical transgranular mode dominates the fracture behavior of the samples sintered at lower temperatures, while the intergranular fracture can be also observed in the samples sintered at higher temperatures. Besides, the storage modulus (E’) and mechanical loss (tan_mδ) of BTWC ceramics have a subtle variation with the increase of sintering temperature. In addition, the high-temperature environment could not only decrease the fracture toughness and bending strength of ceramics but also change their fracture mode. On the other hand, the bending strength also decreases with the decrease of loading rates, which could be attributed to the slow crack growth referring to the dynamic fatigue behavior of brittle materials. The slow crack growth parameter (n) of BTWC ceramics shows a downtrend with increasing their sintering temperature, indicating that those high temperature sintering samples possess a higher susceptibility when subjected to the long-term stress corrosion. Furthermore, the sample sintered at 1125?℃ exhibits an excellent fatigue resistance when subjected to the cyclic stress. The corresponding fatigue mechanism is not only related to the ferroelectric domain configuration but also involved with the pores or impurities.