Search

The strength distribution of Zerodur® (Schott AG) prepared by grinding and etching is determined through statistical analysis to be best described as normal. Although a 3-parameter Weibull appearance is exhibited when multiple specimen batches are combined and analyzed together, this appearance is the result of mixing of components of variation. As a result of the particular type of flaw population, little effect of scale is exhibited. Caution is advised when assuming a 3-parameter Weibull distribution and associated threshold solely based on distribution shape. Fractography to understand the flaw distribution should be employed.

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-KIc test has shown to be versatile and account for a very small overestimation of the KIc-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 KIc-value compared to the new calculation by Strobl et al. for materials with Poisson’s ratio

A new method for fracture toughness determination of ceramic balls is presented. The starter crack is introduced into the surface of the ball by a Knoop indentation followed by grinding off the deformed zone. The loading through surface tensile stresses is realized by water quenching, i.e. dropping the heated ball into water. The temperature difference is stepwise increased to find the critical temperature difference for the initiation of crack growth. The geometric factor is calculated in a parametric finite element study, whereas the temperature distribution in the ball was previously determined by using the Biot concept. Combining experimentally measured critical temperature differences for different cracksizes and ball diameters with numerical results of the geometric factor, the fracture toughness of the silicon nitride balls is evaluated. For the evaluation, the knowledge of several material properties (e.g. the CTE) and other parameters is necessary, which have influence on the precision of the measurement. The overall measurement uncertainty is estimated to be about ± 10 %, what roughly corresponds to the value determined with standard measurement procedures. There is an excellent agreement with published fracture toughness results of these balls determined by the modified Surface Crack in Flexure procedure.

In high performance hybrid bearings the balls are conventionally made of silicon nitride ceramics. There are some disadvantages such as costs or the higher stiffness of silicon nitride compared to steel. Therefore, alternative materials are under investigation. The surface strength is one of the most important criteria for the qualification of the spherical components in the application. It has to be evaluated for each new material (or new surface finish). The recently standardised Notched Ball Test (NBT) enables one to determine the surface strength (tensile strength) of balls, which is strongly influenced by the surface finish and volume flaw populations. In this paper the NBT strength of five candidate materials for rolling elements (silicon carbide, silicon nitride, alumina, zirconia and zirconia toughened alumina) is investigated. Fractography is performed to evaluate the direct correlation between the defects found at the surface and the measured strength.

Zerodur ® is a well-known glass-ceramic used for optical components because of its unequalled dimensional stability under changing temperature. For example, it is used for mirrors of space telescopes. Due to the large amount of material that has to be removed during fabrication of the mirrors a rather coarse grit is used for grinding. Strength limiting defects introduced by this procedure are eliminated by removing the damaged surface layer by etching to achieve a high strength. Through a large test campaign comprising a high number of strength specimens (>160) of various types and sizes, the validity of the Weibull strength statistics was investigated. The purpose was to accurately determine the parameters of the Weibull law for Zerodur ® when treated in the same conditions as mirrors. As a rule of thumb the average strength of Zerodur ® is assumed to be around 10 MPa. The measured strength is much higher. The strength distributions showed unexpected results, especially the absence of the expected size effect. Through a thorough fractographic analysis it was shown what kind of defects were responsible for failure of etched Zerodur ® and why the prerequisites for the validity of the Weibull theory were not fulfilled in the investigated specimens.

In this study, fatigue life predictions were made for silicon nitride components undergoing hybrid ceramic-steel rolling contact. Three-dimensional stress fields were extracted using a bespoke finite element model and subsequently used to calculate stress intensity factors by means of the weight function method. Crack-growth rates were estimated by assuming crack growth to follow a Paris power-law expression whose material parameters were obtained from four-point bending fatigue experiments under fluctuating tensile load (R = 0.1) and fully-reversed alternating load (R = −1). The crack-growth behavior obtained from the calculations was compared with experimental results obtained from twin-disk-type RCF experiments. The calculated lifetime predictions were in accordance with the experimental results. Crack formation and propagation was found more likely to occur in locations undergoing alternating load rather than those undergoing pure fluctuating tensile load.

Objective Strength is one of the preferred parameters used in dentistry for determining clinical indication of dental restoratives. However, small dimensions of CAD/CAM blocks limit reliable measurements with standardized uniaxial bending tests. The objective of this study was to introduce the ball-on-three-ball (B3B) biaxial strength test for dental for small CAD/CAM block in the context of the size effect on strength predicted by the Weibull theory. Methods Eight representative chairside CAD/CAM materials ranging from polycrystalline zirconia (e.max ZirCAD, Ivoclar-Vivadent), reinforced glasses (Vitablocs Mark II, VITA; Empress CAD, Ivoclar-Vivadent) and glass-ceramics (e.max CAD, Ivoclar-Vivadent; Suprinity, VITA; Celtra Duo, Dentsply) to hybrid materials (Enamic, VITA; Lava Ultimate, 3M ESPE) have been selected. Specimens were prepared with highly polished surfaces in rectangular plate (12 × 12 × 1.2 mm3) or round disc (O = 12 mm, thickness = 1.2 mm) geometries. Specimens were tested using the B3B assembly and the biaxial strength was determined using calculations derived from finite element analyses of the respective stress fields. Size effects on strength were determined based on results from 4-point-bending specimens. Results A good agreement was found between the biaxial strength results for the different geometries (plates vs. discs) using the B3B test. Strength values ranged from 110.9 MPa (Vitablocs Mark II) to 1303.21 MPa (e.max ZirCAD). The strength dependency on specimen size was demonstrated through the calculated effective volume/surface. Significance The B3B test has shown to be a reliable and simple method for determining the biaxial strength restorative materials supplied as small CAD/CAM blocks. A flexible solution was made available for the B3B test in the rectangular plate geometry.

The present work focuses on the determination of the effective thermoelastic properties and the statistical characterization of stress fluctuations in silicon nitride's local phases. For that purpose, full field finite element solutions have been considered, based on 3D electron backscatter diffraction (EBSD) data of silicon nitride. A second-order mean field homogenization scheme, consisting in Hashin–Shtrikman bounds, has been also considered. Ab-initio simulations have been performed in order to determine the temperature-dependent elastic properties of the local phases. The isotropic material microstructure has been checked based on both experimental results and full field solutions. The effective thermoelastic properties have been assessed with the newly obtained experimental results. The stress fluctuations within silicon nitride's local phases have been examined under mechanical and thermal loadings. It has been shown that the amorphous phase is the most vulnerable to fracture and to micro-cracks initiation.

Silicon nitride rolling elements for hybrid bearings (rollers, two sizes of balls and plate material as a reference) made from the same material lot and using the same sintering route are investigated in regard to their microstructure and their mechanical properties. For the first time, a direct comparison of the surface strength of the components as well as of their fracture toughness is enabled by recently developed testing methods for balls and rollers. It was found that the microstructure of these material variants influences the fracture toughness up to about 10%. In addition, due to the different surface finish, the surface strength of the different rolling elements (made of the same material) is very different. The differences may reach up to 100% and more.

The “Surface Crack in Flexure” method is widely used for fracture toughness (KIc) determination of ceramics. In part I of the paper we developed the theoretical fundamentals to apply this procedure to ceramic balls by using the stress application as developed for the so-called “Notched ball test”. The new test (SCF-NB) can be used to test spherical components without the need to cut out special specimens such as bending bars. In this work the practical part is presented including suggestions for crack introduction and specimen preparation and possible measurement errors are discussed. It is concluded that a measurement error less than ±5% is possible. Experiments on balls and bars made from the same silicon nitride ceramic indicate that SCF-NB delivers the same KIc-values as standardised measurements on bars. Additionally, KIc-values obtained for silicon carbide, alumina and zirconia ceramics are presented. They coincide with KIc-data from the literature.

A new fracture toughness test for discs and plates is presented, which can be applied to small specimens (>5 mm diameter). A semi-elliptical surface crack is made into the centre of the top plane using a Knoop intender. Then the layer containing the plastically deformed zone is ground off and the crack is loaded in tension using the Ball-on-3-Balls test. Applied to five different ceramic materials the results gained with the new method agree well with those of standardised methods.

The strength and fracture toughness of small ceramic discs under biaxial flexural load are investigated with two different miniaturized test methods: the small punch test (SPT) and the ball-on-three-balls test (B3B). An alumina ceramic was chosen as sample material. While the specimen geometries are identical for both tests, the experimental set-ups and the stress fields are different. First, the Weibull parameters of strength have been estimated. Second, the fracture toughness is evaluated with an adaption of the surface crack in flexure (SCF) method. The discs are prepared with artificial surface cracks whose sizes have to be measured. The evaluation of stresses and stress intensity factors is based on finite element calculations.

The Newman and Raju formula for the stress intensity factor of a semi-elliptical surface crack loaded in uniaxial tension or in bending has been developed about 30 years ago using an FE-analysis for several geometric parameters and fitting an empirical equation to the data points. The Poisson's ratio analyzed was 0.3. In this paper a reassessment of the Newman and Raju formula is made, where all relevant geometric parameters of crack and specimen and the Poisson's ratio are considered. The deviations of the old formula from the new results are up to 21%, if the full range of Poisson's ratio is taken into account. Furthermore the influence of the crack-surface intersection angle is discussed. The results of this work are important for more precise fracture toughness measurements in brittle materials and give a practical guidance for appropriate specimen preparation for fracture toughness measurements, which is also considered here.

A new toughness test for ball-shaped specimens is presented. In analogy to the “Surface Crack in Flexure”-method the fracture toughness is determined by making a semi-elliptical surface crack with a Knoop indenter into the surface of the specimen. In our case the specimen is a notched ball with an indent opposite to the notch. The recently developed “Notched Ball Test” produces a well defined and almost uniaxial stress field. The stress intensity factor of the crack in the notched ball is determined with FE methods in a parametric study in the practical range of the notch geometries, crack shapes and other parameters. The results correlate well with established calculations based on the Newman–Raju model. The new test is regarded as a component test for bearing balls and offers new possibilities for material selection and characterisation. An experimental evaluation on several ceramic materials will be presented in a consecutive paper.

Layered ceramics have been proposed as an alternative choice for the design of structural ceramics with improved fracture toughness, strength and reliability. The use of residual compressive stresses, either at the surface or in the internal layers, may improve the strength as well as the crack resistance of the material during crack growth. In this work, two alumina–zirconia laminates designed with external (ECS-laminates) and internal (ICS-laminates) compressive stresses have been investigated using a fracture mechanics weight function analysis. An optimal architecture that maximises material toughness and strength has been found for each design as a function of geometry. From a flaw tolerant viewpoint, ECS-laminates are suitable for ceramic components with small cracks or flaws which are embedded in or near the potential tensile surface of the piece. On the other hand, the existence of large cracks or defects suggests the use of ICS-laminates to attain a more reliable response.

Ceramic multilayer composites have been developed in recent years to enhance toughness and reliability of ceramics. It has been demonstrated by theoretical as well as experimental means, that surface compressive stresses protect the composite against the negative action of surface flaws. The behaviour of an alumina–alumina/zirconia laminate having significant compressive residual stresses at its alumina surface is investigated. Compared to alumina specimens its strength is increased by the amplitude of the residual compressive surface stress, which is also a lower threshold value for strength. The consequences of that behaviour for the fracture statistics and reliability are discussed.

It is claimed in almost every experimental work on ceramics that the strength is Weibull distributed. The literature demonstrates that this is not valid in any case, but it is up to now the backbone in the design of brittle components. An overview on situations that deviate from Weibulls statistics is presented (multi-modal flaw distribution, R-curves, etc.). It is also shown that testing specimens with different volumes may help to understand the real strength distribution. Inaccuracies that arise from using the Weibull’s theory are presented. Monte Carlo simulations on the basis of the standardised testing procedure (30 specimens) clearly reveal that these deviations can be hardly detected on the basis of small samples.

Silicon nitrides with sufficient strength for structural applications have been developed 20 years ago. A break-through in the use of these ceramics for structural applications did not yet take place. Most probably, the reason for this is a significant lack of design relevant data. TC 6 “Ceramics” of the European Structural Integrity Society (ESIS) has established a research program in order to determine a complete set of material properties and data indispensable for design for a commercially available silicon nitride ceramic. The material chosen as the ESIS Silicon Nitride Reference Material is a gas pressure sintered silicon nitride containing ∼3 wt.% Al2O3 and ∼3 wt.% Y2O3. The results available to the present indicate that this specific material has a good mechanical performance at room temperature and up to ∼800 °C. Above this temperature the large amount of amorphous grain boundary phase causes a detrimental influence on the environmental assisted crack growth properties and the creep performance.

The ball on three balls (B3B) test is a new method for biaxial strength testing of brittle materials. A detailed analysis of the stress field in the specimens and of possible measuring errors has been made recently. The B3B-testing method has several advantages compared to common three- or four-point bending tests: for example, the edges of the specimen have no influence on the testing results, small geometrical inaccuracies of the specimens or of the test jig have only a little effect on the maximum tensile stress and friction is of minor significance. Therefore the B3B-test seems to be suitable for miniaturisation. In this paper the practical applicability of the B3B-test is investigated by measuring the strength of three ceramic materials having a low (electro ceramics), an intermediate (alumina) and a high (silicon nitride) strength. Specimens of different size (the smallest specimens had a volume of less than 1 mm 3 ) with polished or with as-sintered surface were tested. The results are compared with bending test results. In total more than 600 strength tests were performed. A pronounced size effect on strength could be observed, which is discussed in the framework of fracture statistics (Weibull theory). In summary the B3B-test has been proven to be a cheap and easy new testing method, which can be used to determine the biaxial strength of brittle materials and which is particularly well suited for the testing of very small specimen.

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

In this paper, a commercial liquid phase sintered silicon nitride with Y 2O3 and Al2O3 additives is investigated. The material is characterised by a large, and stable, internal friction peak near 1150 ◦ C. The peak is linked with the glass transition in intergranular amorphous volumes, whose presence is confirmed with transmission electron microscopy. An estimate of the volume fraction of the amorphous phase is calculated from the difference in stiffness below and above the glass transition temperature. The procedure relies on accurate Young’s modulus data, which were obtained with the impulse excitation technique (IET). The amount of amorphous pocket phase was estimated at 12.4 vol.%. For the first time, microstructural evidence supporting this estimate is obtained, using analysis of scanning electron microscopy (SEM) images. The rather large amount of amorphous matter explains the limited high temperature potential of the material, which was primarily and successfully developed for wear applications. © 2003 Elsevier B.V. All rights reserved.

The aim of the present contribution was to study the delayed failure of a commercially available Si3N4. Static flexure tests at different stresses (150, 200, and 300 MPa) were carried out at 1200 °C in air. The strain and the lifetime of the specimens were recorded, and fracture surfaces were investigated. In all specimens, some creep deformation occurred (more at lower stresses). At the lowest stress, some indication for creep damage (multiple crack growth) could be detected. The lifetime of the specimens is proportional to an inverse power of the applied stress. The stress exponent was determined as n=7. The low value of this exponent is an evidence that a long-time use of the material at high mechanical loads is only possible at temperatures below 1200 °C. The work was done in the frame of the European Structural Integrity Society (ESIS) Technical Committee for Ceramics (TC6) Reference Material Testing Program (RMTP).

Indentation crack profiles that form under Vickers and Knoop indentations in silicon nitride were investigated. Two different experimental techniques were used to obtain a complete representation of the radial/median as well as the lateral crack system and the plastic deformation zone as a function of indentation load. Vickers indentation cracks exhibit a load dependent shape. At low loads two seperate radial cracks form per median plane, at high loads these cracks merge beneath the hardness impression to form an annular crack. Lateral cracks appear much closer to the surface than frequently assumed. Knoop cracks are nearly semielliptical. The crack aspect ratio and the aspect ratio of the elongated wedge-shaped plastic deformation zone are load dependent.