Relationship between fracture toughness determined by surface crack in flexure and fracture resistance measured by indentation fracture for silicon nitride ceramics with various microstructures

The reliability of the Vickers indentation fracture (IF) method for various types of silicon nitride (Si₃N₄) ceramics was assessed by comparing the fracture resistance, K_R obtained from the IF test with the fracture toughness, K_Ic from the surface crack in flexure (SCF) technique in the same crack depth region. The K_R of a fine-grained and equiaxed Si₃N₄ matched with the K_Ic from the SCF test when Miyoshi's equation was used, while the K_Ic of a bearing-grade Si₃N₄ was found to lie between K_R values calculated with Niihara's equation (higher side) and Miyoshi's equations (lower side). In the case of coarse Si₃N₄ with elongated grains, the K_R determined using Niihara's equation gave the best fit with K_Ic. The inconsistent outcomes were explained by the probable mechanisms, indicating that the K_R from the IF test cannot be correlated directly with the K_Ic unless the effective crack length for the IF test was clarified.     

Fracture resistance estimation of elastic ceramics in edge flaking: EF baseline

The fracture resistance of single-phase oxide and nonoxide ceramics was studied in flaking the specimen edge with a Rockwell indenter (EF test method) and in bar flexure (SEVNB method). The fracture resistance F_R and fracture toughness K_Ic are shown to be proportional, the plot with the F_R–K_Ic coordinates is termed the EF base diagram, in which the EF baseline is constructed. It was revealed that the fracture resistance of ceramics was not influenced by chip scar shapes on the specimen edge. The data points for inelastic ceramics with a lower EF barrier to the onset of fracture lay below the EF baseline in the base diagram, while the data points for glasses and ceramics with a higher barrier were located above it.The EF test method is appropriate for comparative evaluation of fracture resistance of ceramics and verification of estimates obtained by other methods.     

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.     

Fracture Toughness of Advanced Structural Ceramics: Applying ASTM C1421

The three methods of determining the quasi‐static Mode I fracture toughness (K_Ic) (surface crack in flexure—SC, single‐edge precracked beam—PB, and chevron‐notched beam—VB) found in ASTM C1421 were applied to a variety of advanced ceramic materials. All three methods produced valid and comparable K_Ic values for the Al₂O₃, SiC, Si₃N₄, and SiAlON ceramics examined. However, not all methods could successfully be applied to B₄C, ZrO₂, and WC ceramics due to a variety of material factors. The coarse‐grained microstructure of one B₄C hindered the ability to observe and measure the precracks generated in the SC and PB methods while the transformation toughening in the ZrO₂ prevented the formation of the SC and PB precracks and thus made it impossible to use either method on this ceramic. The high strength and elastic modulus of the WC made it impossible to achieve stable crack growth using the VB method because the specimen stored a tremendous amount of energy prior to fracture. Even though these methods have passed the rigors of the standardization process there are still some issues to be resolved when the methods are applied to certain classes of ceramics. It is recommended that, when appropriate, at least two of these methods be employed to determine the K_Ic, especially when a new or unfamiliar ceramic is being evaluated.     

Response of silicon nitride ceramics subject to laser shock treatment

A comprehensive and novel investigation on multiple-layer, square-beam laser shock treatment (“laser peening”) of Si₃N₄ ceramics is reported in this work. Surface topography, hardness, fracture toughness (K_Ic), residual stresses, and microstructural changes were investigated. The evaluation of fracture toughness via the Vickers hardness indentation method revealed a reduction in crack lengths produced by the indenter after laser shock treatment (LST). Upon appropriate calculation, this revealed an increase in K_IC of 60%. This being attributed to a near-surface (50 μm depth) compressive residual stress measured at −289 MPa. Multiple layer LST also induced beneficial residual stresses to a maximum measured depth of 512 μm. Oxidation was evident, only on the top surface of the ceramic, post LST (<5 μm depth) and was postulated to be due to hydrolyzation. The surface enhancement in K_IC and flaw-size reduction was assigned to an elemental change on the surface, whereby, Si₃N₄ was transformed to SiO₂, particularly, with multiple layers of LST. Compressive residual stresses measured in the sub-surface were attributed to mechanical effects (below sub-surface elastic constraint) and corresponding shock-wave response of the Si₃N₄. This work has led to a new mechanistic understanding regarding the response of Si₃N₄ ceramics subject to the LST deployed in this resesrch. The findings are significant because inducing deep compressive residual stresses and corresponding enhancement in surface K_IC are important for the enhanced durability in many applications of this ceramic, including cutting tools, hip and knee implants, dental replacements, bullet-proof vests and rocket nozzles in automotive, aerospace, space and biomedical industries.     

Numerical aspects of the implementation of cubic equations of state in flash calculation routines

It is shown that failures in flash calculations (K₁ → 1.0) when cubic equations of state are used to estimate equilibrium K-values, result from two main deficiencies. One is the well-known problem of guessing good starting values of the phase compositions at high pressure. The other is that regular methods for solving the cubic equation in the compressibility often lead to a wrong “type” of root (i.e. vapour or liquid). An algorithm without these deficiencies is presented.     

Liquid phase sintering and characterization of SiC ceramics

The present study focuses on the sintering of silicon carbide-based ceramics (SiC) by liquid phase sintering (LPS) followed by characterization of the produced ceramics. AlN/Re₂O₃ mixtures were used as additives in the LPS process. In the first step, the LPS-SiC materials were produced in a graphite resistance furnace in the form of discs at different temperatures. The conditions with the best results regarding real density and relative density were taken as reference for sintering in the form of prismatic bars. In the second step, these samples were evaluated regarding fracture toughness (K_IC), by the Single Edge V Notch Beam – SEVNB – method, and flexural strength. K_IC behavior was evaluated according to the depth and curvature radius of the notches. Reliable K_IC values were presented when the ceramic displayed a small curvature radius at the notch tip. When the radius was large, it did not maintain the square root singularity of the notch tip. Tests were carried out to determine K_IC values in atmospheric air and water. K_IC results were lower in water than air, with a decrease ranging between 2.56% and 11.26%. The observations indicated a direct grain size correlation between K_IC values and fracture strength of the SiC ceramics.     

Relationship between the strength and crack resistance of refractory ceramics

Conclusions We established a link between the strength (_tens and _bend) and crack resistance (K_Ic) of brittle and relatively brittle polycrystalline refractory ceramics. The proposed relationships can be used to predict the crack resistance with respect to the strength and average grain size. In the general case the crack resistance is located in direct relationship with the strength and square root of the grain size (d^1/2). Since, in its turn, in the case of brittle finely crystalline refractory ceramic the strength is controlled by the magnitude d^–1/2, then in the final account such ceramic is distinguished by the absence of a clear relationship between the crack resistance and the size of the grain if k_Ic is expressed not through the strength limit but through the physical properties.Comparison of the calculated values of K_Ic with the experimental obtained from the testing of different ceramics indicates the usefulness of equations for predicting the crack resistance.Translated from Ogneupory, No. 5, pp. 9–12, May, 1986.     

Influence of graphite on the low-frequency fatigue behavior of zirconium diboride ceramics

The fatigue behavior of a ZrB₂-based ceramic containing SiC and graphite was compared to a ZrB₂-SiC reference material based on bending testing, quantitative calculations as well as crack growth and fracture characterization. The addition of graphite flake makes ZrB₂-SiC-Graphite ceramics exhibit fatigue failure behavior at very high stress level (93% of the characteristic strength, σ₀), owing to the increased K_Ic promoted by crack deflection, bridging, bifurcation and pull-out of graphite, while the fatigue behavior of ZrB₂-SiC appears when the maximum stress is below ~86%σ₀. However, both the slow crack growth exponents of the graphite containing ceramic, n and nc values, which reflect the fatigue resistance in static and cyclic fatigue conditions, respectively, are only 1/4 as compared to the reference graphite-free ceramic. This may be due to the weak boride/graphite interfaces, which lead to the decrease of the initial critical stress intensity factor (K_c-initial) value from 2.6 to 2.0 MPa m^1/2.     

Relationship between elastic and mechanical properties of dental ceramics and their index of brittleness

The purpose of the study was to verify the effects of a number of materials’ parameters (crystalline content; Young's modulus, E; biaxial flexure strength, σ_i; Vickers hardness, VH; fracture toughness, K_Ic; fracture surface energy, γ_f; and index of brittleness, B) on the brittleness of dental ceramics. Five commercial dental ceramics with different contents of glass phase and crystalline particles were studied: a vitreous porcelain (VM7/V), a porcelain with 16 vol% leucite particles (d.Sign/D), a glass-ceramic with 29 vol% leucite particles (Empress/E1), a glass-ceramic with 58 vol% lithium-disilicate needle-like particles (Empress 2/E2), and a glass-infiltrated alumina composite with 65 vol% crystals (In-Ceram Alumina/IC). Discs were constructed according to manufacturers’ instructions, ground and polished to final dimensions (12 mm × 1.1 mm). Elastic constants were determined by ultrasonic pulse-echo method. σ_i was determined by piston-on-3-balls method in inert condition. VH was determined using 19.6 N load and K_Ic was determined by indentation strength method. γ_f was calculated from the Griffith–Irwin relation and B by the ratio of HV to K_Ic. IC and E2 showed higher values of σ_i, E, K_Ic and γ_f, and lower values of B compared to leucite-based glass-ceramic and porcelains. Positive correlations were observed for σ_i versus K_Ic, and K_Ic versus E^1/2, however, E did not show relationship with HV and B. The increase of crystalline phase content is beneficial to decrease the brittleness of dental ceramics by means of both an increase in fracture surface energy and a lowering in index of brittleness.     

The current detour effect observed on materials with random microstucture: experimental evidence from Li3xLa2/3−xTiO3 studied by impedance spectroscopy

Impedance spectroscopy (IS) has been used to study the influence on the low frequency part of the impedance diagrams of the microstructure of a fast ionic conductor, Li_3xLa_2/3−xTiO₃ with x = 0.10 (named hereafter LLTO). This oxide has been synthesised by sol–gel method. After synthesis, the powder of LLTO displays a large distribution of grain size and agglomerates. The grain size distribution and the porosity of the ceramic have been changed by heat-treatment from 600 °C to 1200 °C in air. The impedance spectra of these ceramics, recorded at different temperatures from room temperature (RT) to 400 °C, show a low-frequency depressed arc, which is characteristic of the grain boundary response of the ceramic. Its shape depends strongly on the heat-treatment of the ceramic, and therefore, on its microstructure. It is a simple arc when the pellet is well sintered but becomes very complex for non-sintered ceramics with high resistive grain boundary and pores. The observed “fish” shape indicates the presence of current “detours effect” in the material. This effect means that current detours around blocking grain boundary and/or pores occur to lower the impedance. Consequently, the brick layer model (BLM), which assumes an ideal microstructure, and then no current “detours effect”, can not be used to analyse these impedance data.     

A new arrangement of SiC particles in reaction bonded Si3N4-SiC ceramic refractory and crack behaviors under thermal shock

High temperature protection brick lining is important for super-charged boilers. In practice, Si₃N₄ bonded SiC ceramics are usually chosen as the raw material of refractory bricks due to their excellent performance under high temperature. In the field of the ceramic refractory material, a main goal is to improve the resistance of ceramics under thermal shock because their inherent brittleness may cause failure under sudden change in temperature. In this paper, we fulfilled this goal by introducing a new particle arrangement called “double dispersion” for the SiC particle-reinforced ceramic refractory material. And we established the micro-structure models for both the original and the modified ceramic refractory material. To study the influence of the particle arrangement on the fracture toughness, we performed simulations of the crack initiation and propagation under the same thermal load for the original and the modified material. The results showed that the “double dispersion” method can improve the thermal shock resistance of the reaction-bonded Si₃N₄-SiC ceramic refractory.     

Fracture toughness of glasses as measured by the SCF and SEPB methods

The fracture toughness, K_Ic, of six glasses was measured by the surface crack in flexure (SCF) and single-edged precracked beam (SEPB) methods. Results depended upon the loading rate as well as the test environment. Environmentally-assisted slow crack growth affects the results for tests done in air. Dry nitrogen testing is preferred. Crack healing may be a severe complicating factor with precracked flexure bar type specimens if the specimens are unloaded between the precracking and final fracture test. Success in K_Ic testing depends to a large degree on upon the ability to make good precracks.     

A new method for the preparation of ultra-sharp V-notches to measure fracture toughness in ceramics

The preparation of an ultra-sharp V-notch on structural ceramics is a prerequisite for reliable fracture toughness assessment. Femtosecond lasers are used to cut ultra-sharp V-notch on the Si₃N₄ and Al₂O₃ ceramics for fracture toughness testing by single-edge V-notched beam method. The radius of the V-notch tip is smaller than 0.5 μm. The K_Ic of Si₃N₄ and Al₂O₃ ceramics determined by this method is much close to the actual fracture toughness. This method exhibits obvious advantage in good reproducibility, high accuracy and precision for reliable fracture toughness testing of structural ceramics.     

Domain Structure of Potassium‐Sodium Niobate Ceramics Before and After Poling

Domain structure and domain wall motion play important roles on the piezoelectric properties of ferroelectric ceramics. In this work, the domain structure of hot‐pressed (K_0.50Na_0.50)NbO₃ (KNN) ceramics before and after poling were studied by observing the domain patterns with an acid‐etching technique, and the extrinsic contribution to the piezoelectric properties were evaluated. It was found that the domain structure of the unpoled KNN ceramic was relatively complicated with many watermark, herringbone and zigzag patterns, while only a single set or few sets of parallel domain stripes were observed in the poled KNN ceramic, due to the domain reorientation and domain wall motion during the poling process. The average domain width changes from 200 (±10) nm before poling to 250 (±10) nm after poling. Domain configurations of “Herringbone‐Zigzag‐Watermark” and “Herringbone‐ Herringbone‐Zigzag” types observed in the unpoled KNN ceramic were then further analyzed. The extrinsic contribution to the piezoelectric properties from the domain reorientation and irreversible domain wall motion in the hot‐pressed KNN ceramic was found to be 71%, slightly higher than that of conventional sintered KNN ceramics ~68%.     

The effect of amine/epoxy ratio on the fracture toughness of tetrafunctional epoxy resin

Summary. The effect of amine/epoxy ratio on the fracture toughness (K_Ic) of tetrafunctional epoxy resin was investigated. K_Ic value was measured by single-edge notch-bend test. The K_Ic value of the tetrafunctional epoxy resin increased with increasing the amount of amine curing agent. This result was explained with the structural viewpoint of the epoxy network. The network structure of the tetrafunctional epoxy was analyzed with dynamic thermomechanical measurement and in-situ near IR technique. Received: 19 June 1997/Accepted: 17 Juli 1997     

Fracture toughness testing of biomedical ceramic-based materials using beams,plates and discs

The testing of fracture toughness becomes problematic when only limited amount of material is available that hinders the production of typical beam specimens to be tested in bending. Here we explore fracture toughness testing methodologies that allow for small discs and plates having surface cracks to be tested in biaxial flexure using the Ball-on-3-balls (B3B) set-up, or sawed notches as in the Compact Tension geometry. The B3B-K_Ic test has shown to be versatile and account for a very small overestimation of the K_Ic-value in the order of 0.8–1.25% due to in-plane crack mispositioning, and a maximum of 4% if a worst-case scenario of additional out-of-plane mispositioning is assumed. The geometrical factor in the standard SCF method, derived by Newman and Raju, resulted in an overestimation of ～8% of the K_Ic-value compared to the new calculation by Strobl et al. for materials with Poisson’s ratio <0.3.     

Relationships between fracture toughness,Y2O3 fraction and phases content in modern dental Yttria-doped zirconias

The relationship between fracture toughness and Yttria content in modern zirconia ceramics was revised. For that purpose, we evaluated here 10 modern Y₂O₃-stabilized zirconia (YSZ) materials currently used in biomedical applications, namely prosthetic and implant dentistry. The most relevant range between 2-5 mol% Y₂O₃ was addressed by selecting from conventional opaque 3 mol% YSZ up to more translucent compositions (4−5 mol% YSZs). A technical 2YSZ was used to extend the range of our evaluation. The bulk mol% Y₂O₃ concentration was measured by X-Ray Fluorescence Spectroscopy. Phase quantification by Rietveld refinement considered two tetragonal phases or an additional cubic phase. A first-account of the fracture toughness (K_Ic) of the pre-sintered blocks is given, which amounted to 0.4 – 0.7 MPa√m. In the fully-densified state, an inverse power-law behavior was obtained between K_Ic and bulk mol% Y₂O₃ content, whether using only our measurements or including literature data, challenging some established relationships. A linear relationship between K_Ic and the fraction of the transformable t-phase was established within the range of 30–70 vol%.     

Elastic properties and fracture toughness of SiOC-based glass-ceramic nanocomposites

Four different SiOC glass ceramics were synthesized and their fracture toughness (K_Ic) and fracture surface energy (γ) were assessed by means of the single-edge precracked beam (SEPB) method. In addition, the elastic moduli were measured and the Vickers indentation behavior (hardness and microcracking) was characterized. In particular, the dependence of K_Ic on the free carbon content and on the fraction of crystallized nanoparticles (SiC, ZrO₂, HfO₂) was investigated. An increase in K_Ic, from about 0.73 to 0.99 MPa √m is observed as the free carbon content is increased from less than 1 to 12 vol%. The addition of Hf and Zr (resulting in 4.5 to 7.8 vol% HfO₂ and ZrO₂ nanoparticles) was found to increase K_Ic to an extent similar to the free carbon content. Moreover, predicted K_Ic values, assuming that the crack travels through all phases accounting for their respective volume fractions, disrupting the weakest links within the structural units, are in agreement with the experimental values.     

Fracture toughness of zirconia from a shallow notch produced by ultra-short pulsed laser ablation

Fracture toughness of submicron grain size tetragonal zirconia polycrystals doped with 3 mol% yttria (3Y-TZP) is measured by the single edge V-notch beam (SEVNB) method from a shallow sharp notch produced by ultra-short pulsed femtolaser ablation (UPLA) on the surface of a bending bar. It is shown that the radius of the notch tip achieved is in the submicron range and the damaged volume in front of the notch tip is characterized by using focus ion beam milling and scanning electron microscopy. It consists of a narrow fully microcracked region less than ∼4 μm wide and ∼15 μm deep in front of the notch. If the extension of this region and the length of the notch are used in the determination of the fracture toughness (K_Ic) in the four bending test, the values obtained for submicron grain size 3Y-TZP are in agreement those obtained by using very sharp cracks. It is concluded that the SEVNB testing method with a sharp notch induced by UPLA may be used for K_Ic testing of submicron grain size ceramics.