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Many substrates for microelectronic systems contain ceramic/glass layers and metal features (e.g. electrodes, vias, metal pads) built up in a complex 3D architecture. The combination of different materials with distinct thermo-elastic properties may yield significant (local) internal stresses, which are to be superimposed to external thermo-mechanical loads in service. Due to the various material junctions, interfaces, etc, failure of these multilayer systems can hardly be predicted. In this work, a strategy is proposed to quantify the effect of architecture and loading conditions on the mechanical reliability of ceramic-based substrates. Model ceramic structures containing important design features (e.g. inner electrode, via, top metallization) were fabricated and tested in different environments (i.e. humid or dry conditions) under uniaxial as well as biaxial bending. Significant difference in the characteristic strength between ∼260 MPa and ∼620 MPa were measured, associated with the particular architectural feature, type of loading, and/or environment.

Ceramic varistors are electronic components which have a sharp change (over several orders of magnitude) of their electrical resistance at a well-defined voltage (switching voltage). Starting at low voltages, the resistance is large. But by exceeding the switching voltage the resistance drops dramatically and the component acts as a good conductor. Mounted parallel to a consumer, they are used as protection devices against over voltage loading. In the technical routine yearly billions of varistors are used to protect power lines, transformation stations, electronic devices, microelectronic systems or even LEDs. In service large temperature differences may come into existence, which cause severe mechanical stresses that even may destroy the components. The basic principles of the varistor behaviour are explained and examples of mechanical failure are discussed.

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.

This study examines ceramic varistors made from zinc oxide whose electrical resistance drops by many orders of magnitude within a few nanoseconds when a critical voltage threshold is exceeded. These unusual properties are caused by charges which are build into grain boundaries or accumulate near the grain boundaries. Zinc oxide crystals are polar and piezoelectric. Therefore, the charges in the grain boundary area and thus the electrical properties of the varistor depend on the orientation of the crystals towards the grain boundaries and on the mechanical tensions in the individual crystals. In this study, the microstructures of ZnO varistors, particularly the size and distribution of the grains and their orientation towards the grain boundaries will be examined. Among other things, lock-in thermography with a target preparation of strongly active grain boundaries and EBSD analyses in combination with SEM examinations, ion-etching and wet-chemical etching for the determination of crystal orientations are used. For selected grain boundaries, the electrical resistance in dependence of the applied voltage is determined via Micro-4 pole measurements.

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.

Subcritical crack growth (SCCG) in glasses and ceramics causes a decrease of strength with time under applied load. The dependence of the crack growth rate with the stress intensity factor can be approximated by a power law, with n being the SCCG exponent. In this work the effect of the inherent scatter of strength as well as measurement uncertainties on the determination of n is analysed. Constant stress rate tests as proposed in the EN 843-3 standard are simulated using Monte Carlo techniques. It is shown that the large scatter of strength causes large uncertainties on the determination of n , yielding a significant influence of the sampling procedure especially for small samples. Measurement uncertainties have a surprisingly low influence on the determination of n with exception of a special situation that may arise during long time testing campaigns.

The strength of Low Temperature Co-fired Ceramics (LTCC) can be affected by the environmental conditions under which the material is loaded. In this work, the strength degradation associated with Subcritical Crack Growth (SCCG) mechanisms is investigated in several multilayer LTCC architectures designed with surface compressive residual stresses. The magnitude of the residual stresses was tailored combining two different LTCC materials. Biaxial strength measurements using the ball-on-three-balls method performed at room temperature in water (as reference environment) showed a clear increase in the characteristic strength with the compressive residual stress in the surface layer. The strength distribution in dependence of the surface stresses in the outer layer can be represented by a three-parameter Weibull distribution, thus providing a “threshold strength” (i.e. minimum strength) for the material. In addition, the use of compressive stresses in LTCCs introduces a threshold intensity factor for the SCCG behaviour, below which no environmental assisted cracking can occur.

Ceramic materials fail from defects which are distributed on the surface or in the bulk of specimens and components. The more dangerous surface flaws are often caused by improper machining or handling. In this investigation two possible ways to improve the surface quality and, as a consequence, increase the strength of a commercial silicon carbide ceramic are shown. In bending tests which apply a uniaxial stress state on the specimens only cracks perpendicular to the stress direction are dangerous but in biaxial tests cracks of any orientation may become fracture origins. Therefore, for this investigation, the biaxial Ball-on-Three Balls (B3B) test was used for the strength tests. To investigate the influence of surface finishing 6 samples of specimens were machined in different ways and tested with the B3B-test afterwards. It could be shown that a better surface finishing leads to a higher strength. In order to heal surface defects and to find the best healing conditions 5 samples of specimens were heat treated under different conditions and then tested with the B3B-test. For a better comparison of the obtained results all heat treated samples had the same surface finishing (ground with a grit size of 46 μm). Microscopic investigations showed that defects are healed by the formation of a glassy layer. The layer fills cracks and pores (at least partially) and causes a significant increase of strength.

The strength of materials suffering from subcritical crack growth (SCCG) can be affected by the loading conditions and environment. This crack growth can also occur during the measurement of the material’s fracture toughness, K Ic , yielding lower measured (apparent) values. In this work the K Ic measurements of two different brittle materials was compared in different environments ( i.e., water, ambient air and argon) using three testing methods: (i) Single Edge V-Notch Beam, (ii) Chevron Notch Beam, and (iii) Ball-on-three-Balls-KIc. A strong effect of the environment was found on the measured K Ic values using all three methods. Low “ K Ic values” were measured in water, i.e., ∼1.3–1.7 MPa m 1/2 depending on the material, whereas higher “toughness values” were obtained in argon, i.e., ∼2.0–2.3 MPa m 1/2 . This is explained with a model accounting for the SCCG during the fracture toughness experiment. Recommendations on the assessment of fracture toughness in brittle materials are given.

Functional components are commonly fabricated combining a ceramic substrate with external and/or internal metallization (e.g. metal electrodes, vias, contact pads, etc.) using a tape casting process. Different layers are printed and/or fired (e.g. up to 800°C) onto the ceramic part to provide the component with a (certain) functionality. As a result of the combination of different materials (e.g. ceramic, glass, metal alloys) with different coefficients of thermal expansion, internal stresses may arise during the different fabrication steps. Although some of these tensile residual stresses may relax due to plastic deformation of metallic materials, stress concentrations generated in material junctions or terminations (imposed by geometrical constrains) may lead to cracks and/or reduce the component strength.In this work different architectures combining metal and glass layers on the surface of ZnO substrates were investigated experimentally and numerically in order to identify weak points in commercial components. Mechanical testing using three-point-bending was performed on samples taken after different steps. A FE model was developed to (i) calculate residual stresses generated during the manufacturing process, and (ii) simulate the propagation of initial crack/defect during manufacturing. Experimental results were compared with numerical predictions. These results in combination with fractographic analyses were used to validate the finite element model in order to assess location of failure.

In many ceramic components for electric applications, small defects in the microstructure may cause an anomalous current flow. Especially in components exhibiting nonlinear electro-thermal properties, such as varistors, PTC or NTC resistors, inhomogeneities lead to high concentrations of current and localized heat generation due to positive feedback effects. While the integral behavior of those components is often nearly not affected by these defects, the local load at these hot spot regions is considerably high and can even lead to the complete failure of the device. In this work micro-analytical tools are combined to identify the location and type of defects which may cause leakage currents, overheat or other reasons for inhomogeneous current distributions in functional ceramic components. Lock-in thermography is used to localize dominating current paths. This is even possible if the heat sources are in the micrometer range or less. Additionally, micro-sectioning techniques (e.g. Focus Ion Beam) are utilized to expose such regions to investigate features of the microstructure and causes for the enhanced current flows. Examples are shown in PTC resistor components as well as in LTCC based modules.

Functional components such as multilayer low temperature co-fired ceramics are examples of the combination of a ceramic-based substrate with internal electrodes as well as surface features (e.g. metallization, contacting pads, cylindrical vias, etc) employed to provide the component with a given functionality. Another example is that of functionalized silicon chips to be embedded into polymer circuit boards in order to enhance integration and save costs. The functionality of the system can be influenced by the mechanical reliability of the different components. Due to miniaturization and design complexity, no standard methods for mechanical testing can be applied for the characterization of these brittle components. In this work, an experimental approach is presented, which enables determining the strength distribution in functional components (e.g. rectangular plates as small as 2 × 2 × 0.1 mm3) in different environments at different temperatures. The method is based on localized biaxial testing using a ball-on-three-balls fixture. The high accuracy of the test allows quantifying the effect of surface quality, surface features and/or metallization (e.g. contact pads or cylindrical vias) on the component strength distribution. Experimental findings show that the strength distribution of ceramic components can be affected by environmental degradation, whereby subcritical crack growth phenomena can be enhanced in environments with high relative humidity. In addition, metallization at the surface subjected to tensile stresses can even raise the strength of the component, acting as a protective layer against environmental degradation, whereas cylindrical vias can become weak points in the design. It is shown that functionalized layers such as those used in silicon chips can have a significant effect on the strength parameters, thus influencing the lifetime of the device.

Strength degradation in glass and ceramic materials is related to subcritical crack growth mechanisms acting at the crack tip during mechanical loading. In this work the effect of humidity and temperature on the strength of a commercial low temperature co-fired ceramic was investigated using a biaxial testing procedure. Experiments were performed in argon and in air at different stress rates between 25 and 125 °C. The effect of humidity on strength was assessed at room temperature varying only the relative humidity. The sole effect of temperature was evaluated in argon at high stress rates. The combined effect of humidity and temperature was determined in air, testing at different temperatures. Results showed the existence of an inert strength of the material at room temperature. Measurements in ambient air showed a counterbalance effect of temperature and humidity yielding an almost constant strength for this material between 25 and 125 °C.

Solid-Oxide-Fuel-Cell systems are efficient devices to convert the chemical energy stored in fuels into electricity. The functionality of the cell is related to the structural integrity of the ceramic electrolyte, since its failure can lead to drastic performance losses. The mechanical property which is of most interest is the strength distribution at all relevant temperatures and how it is affected with time due to the environment. This study investigates the impact of the temperature on the strength and the fracture toughness of different zirconia electrolytes as well as the change of the elastic constants. 3YSZ and 6ScSZ materials are characterised regarding the influence of sub critical crack growth (SCCG) as one of the main lifetime limiting effects for ceramics at elevated temperatures. In addition, the reliability of different zirconia tapes is assessed with respect to temperature and SCCG. It was found that the strength is only influenced by temperature through the change in fracture toughness. SCCG has a large influence on the strength and the lifetime for intermediate temperature, while its impact becomes limited at temperatures higher than 650 °C. In this context the tetragonal 3YSZ and 6ScSZ behave quite different than the cubic 10Sc1CeSZ, so that at 850 °C it can be regarded as competitive compared to the tetragonal compounds.

During the last fifty years the mechanical properties of ceramic materials have been greatly improved, their toughness and strength have been increased and the scatter of strength decreased. Adequate statistical design procedures for brittle materials exist but cracking and brittle fracture of ceramic components still occur very often. In this review the theory of brittle fracture and the underlying assumptions are critically discussed and the measurement procedures of strength are reviewed. It is shown that the strength of materials, the strength of specimens and the strength of components are often quite different properties. Three main factors are identified which – in order to avoid unexpected failure of components – have to be considered much more than in the past: (i) hidden stresses, i.e. stresses caused by thermal strain mismatch, by contact (for example in joints) and internal stresses, (ii) the quality of the component's surfaces and edges and (iii) proper handling of ceramic materials and components. It can clearly be stated that the mechanical properties of many ceramic materials are appropriate even for applications under severe loading conditions but bad or incomplete mechanical design, insufficient surface finish and mishandling are the main reasons for unexpected failure of ceramic components.

A new tensile strength test for ceramic rollers (cylinders) is presented, following the idea of the previously published and since that time standardized notched ball test. The specimen is prepared by cutting a long narrow notch along the symmetry plane of the roller, perpendicular to the end faces. By applying compressive forces perpendicular to the notch, tensile stresses are induced in the outer surface region of the roller opposite to the notch, mainly pointing in tangential direction with respect to the roller axis. The stress amplitude is proportional to the applied force and depends also on the test geometry and the Poisson’ ratio, which has been analyzed carefully with FE methods. Strength tests have been performed on two different qualities of commercial silicon nitride rollers of 10 mm diameter and length. According to their specification a significant difference in the strength has been obtained.

The varistor effect in ZnO ceramics is triggered by the behavior of the grain boundaries. To understand this effect in detail we have electrically characterized individual grain boundaries. Here, we apply the micro four-point probe method to measure the electrical properties of individual grain boundaries in a polycrystalline ZnO varistor ceramic with a mean grain size of 10 μm. The investigation revealed a wide spread in electrical properties, like nonlinearty exponents from 10 to 150 and switching voltages from 2.3 V to 3.6 V.

The biaxial strength of Low Temperature Co-fired Ceramics was determined using the ball-on-three-balls test in several environments (dry oil, air and water). Subcritical crack growth phenomenon was observed, activated by the prolonged presence of humidity at the specimen surface. Whereas high strength values were reached during high-rate testing in dry oil, up to a 50% lower strength was measured on specimens immersed in water tested for longer periods. Experiments in a relative dry environment have shown for the first time evidence of two different crack growth mechanisms in this material. A model has been implemented to interpret the experimental results.

An experimental approach is proposed, based on localized biaxial testing of brittle samples at several locations under different environments, to quantify the effect of surface features or metallization (e.g. contacting pads or cylindrical vias) on the strength distribution of functional ceramic components. It is found that cylindrical vias can act as weak points in the design (i.e. lower strength and reliability), whereas contacting pads can raise the strength of the component acting as a protective layer against environmental degradation.

Failure of brittle materials starts in general from defects which exist in the volume or on the surface of the specimens. Surface flaws, which are more dangerous than volume flaws, can be introduced by machining. They decrease the strength of specimens and components. For this investigation silicon nitride specimens were produced using different machining conditions. About half of them were strength tested by use of the biaxial ball-on-three balls (B3B) test. It has been shown that better (more gentle) machining increases the strength but may also cause an increased scatter of strength data. The remaining specimens were heat treated (annealed) at 1000 °C in air and afterwards also strength tested using the B3B test. Compared to the non heat treated specimens a significant increase in strength could be proven, which was – depending on the machining conditions – between almost 300 MPa and more than 500 MPa. The scatter of strength data was largely decreased. The improvement was caused by the formation of a thin (0.5–2 μm) glassy layer which filled surface cracks and surface related pores during annealing.

Details of surface finish affect significantly the surface quality of ceramic specimens (e.g. surface roughness, residual stress). To analyse the influence of surface quality on strength five samples of silicon nitride specimens were machined applying different surface finishing procedures. Then they were strength tested using the biaxial Ball-on-three Balls (B3B) test. The test results were compared to those of conventional bending tests. A fractographic analysis was performed on selected specimens to identify the fracture origins. It could be shown that a better surface quality leads to an increased strength but increases the scatter of strength data too.

Low temperature co-fired ceramics (LTCCs) are multilayered ceramic based components, which can be used as high precision electronic devices in highly loaded environments. In many applications, LTCC end components are exposed to mechanical stresses, which may yield different types of failure coming from different locations, thus decreasing the mechanical reliability of the device. The aim of this work is to assess the mechanical strength of LTCC parts and investigate the influence of the metal internal structure (supporting the maximum load) on the local fracture response. Strength of different positions (e.g. near vias, metal-pads, ceramic layers) has been measured under biaxial loading and compared with a reference bulk LTCC. The strength results were interpreted in the framework of Weibull theory. Fractographic analyses revealed a significant effect of the first metallisation layer below the tensile surface on the strength reliability of the structure, which should be considered to optimise LTCC designs.

Rolls for rolling of metal wires are traditionally made from cemented carbides, but they suffer from roughening of the working surfaces and severe wear which restrict the roll lifetimes. Silicon nitride ceramics are feasible alternative materials for rolls (and other components in rolling mills) due to their good combination of properties, e.g. high strength and hardness, excellent high-temperature properties, oxidation resistance and good thermal shock behaviour. Increasingly the switch is being made to such ceramics for extension of life and improvements in surface quality of the rolled product. In a collaborative project between universities, industrial partners and research centres, rolls made of silicon nitride, supported and clamped by steel rings were tested at the rolling mill of Bohler-Edelstahl in Kapfenberg, Austria. Under low and medium hard loading conditions the suitability of these composite rolls has been very satisfactorily demonstrated. However, under very severe loading conditions one pair of silicon nitride rings failed. In this paper, the failure of these ceramic rings is analysed, and suggestions for further improvements are presented.

Direct inkjet printing (DIP) allows the production of small ceramic specimens with special geometries starting from high solids content suspensions. In this work, thin (300m thickness) 3Y-TZP specimens were produced with the DIP technique as model materials for microelectronic applications. The mechanical strength of the printed specimens was evaluated under biaxial loading, and the results were interpreted within the framework of the Weibull theory. Hot-pressed 3Y-TZP specimens with the same geometry and dimensions were tested for comparison. The fracture surfaces were subsequently examined using scanning electron microscopy (SEM). The inkjet printed materials revealed high mechanical reliability (m ≈ 10 for σ0 ≈ 1400 MPa), which was ascribed to the uniform and defect free microstructure generated by the DIP technique. © 2010 Elsevier Ltd. All rights reserved.

Layered ceramics designed with weak interfaces favour interface delamination, while laminates with strong interfaces show higher strength and enhanced mechanical reliability. In this paper, conditions are reviewed aiming to combine crack bifurcation and interface delamination mechanisms in a unique architecture to design layered ceramics with high failure resistance. Based on a bi-material theoretical approach supported by experiments it is found that interface delamination can be favoured if crack bifurcation occurs in the compressive layers with a low inclination angle. The thickness and stresses of the compressive layers are the key features to optimise the mechanical behaviour in layered ceramics.

For failure assessment of natural cracks caused by surface treatment, the crack resistance for very small crack extensions is necessary. In ceramics with strongly rising R curves, the initial part of a few micrometer crack propagation is of special interest. For this purpose, the use of very small sharp starter notches introduced by a focused ion beam is recommended. As an example, the initial R curve for gas-pressure-sintered silicon nitride at high temperature will be estimated. Whereas for V-notched bending bars a fracture toughness of about 6-6.3 MPa·m 1/2 was determined, the toughness for small strength-relevant cracks was found to be K Ic ≅5.1 MPa·m 1/2 .

For hot rolling, tools are nowadays made of cemented carbides. In service, these rolls suffer from wear and thermal fatigue. Due to the properties of ceramics, their use could cause improvements in tool behaviour. In field tests – when rolling materials with high deformation resistance – cracks developed in the silicon nitride rolls, which grew for a long time period before large parts of the rolls broke apart. In more moderate rolling conditions the rolls operated safely. A FE model is used to analyse the in-service behaviour of cracks in the silicon nitride rolls. For the observed crack path the stress intensity factor of the cracks is determined using the weight function method. It increases up to a crack depth of around 0.35 mm and then decreases again with increasing crack depth. This explains the observed pop-in-type growth of cracks after an overload. Depending on the rolled materials, the popped in cracks have a length of up to 1.2 mm. The further growth of the cracks to a length of several millimetres, which is caused by a fatigue growth mechanism, needs several thousand additional revolutions.

A new strength test for ceramic spheres (balls) is presented. A long narrow notch is cut in the equatorial plane of the ball and the ball is then loaded in compression perpendicular to the notch. This causes tensile stresses in the outer surface region of the ball opposite to the notch, which are analysed carefully with finite element (FE) methods. The tensile stress amplitude depends on the bending moment in the notch ligament – given by the applied force – and on details of the notch geometry. The stress state in the highly stressed surface is almost uniaxial showing only a slight influence of Poisson's ratio. Numerical solutions for balls with quite different notch geometries are given. Strength tests have been performed on commercial silicon nitride balls of 5 mm diameter. Two sets of specimens having notches of different length have been tested. Although the typical fracture loads in both sets of data are quite different, the tensile strengths are closely similar. This indicates the validity of the data evaluations. Experimental details are discussed and an analysis of the experimental uncertainties on the test results is made. For balls with 5 mm the uncertainties are estimated to be less than ±3% (of the measured value). For balls having a diameter of 10 mm or more the uncertainties are less than ±1%.

Laminates with strong interfaces and having compressive residual stresses in the outer layer are designed to have high strength and high reliability. Bending strength tests on such laminate specimens were performed and compared with tests made on monolithic specimens made from the outer layer material. In both types of specimens fracture started from similar flaws, but the laminate specimens showed a higher strength and Weibull modulus. In the case of the monolithic material the toughness is constant but in the case of the laminates it increases – due to the action of the residual stresses – with crack extension (i. e. it is an apparent toughness). The influence of the apparent toughness curve on the fracture statistics is discussed. It is also shown that the statistics of the laminate can be determined using the statistics of the monolithic material, if the influence of the residual stresses on the toughness and strength is properly taken into account.

The paper reviews the current state of art of the fracture of brittle ceramic materials. Typical loading situations (thermal shock, contact damage) are analysed and the resulting fracture modes are discussed. In focus of the paper are the brittle fracture and the resulting probabilistic aspects. The delayed failure of brittle materials (sub critical crack growth and cyclic fatigue) is also discussed.

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.

For the hot rolling of wire, tools are nowadays made of cemented carbides. In service, these rollers suffer primarily from wear. Due to the properties of ceramics, improvements in tool behaviour could be expected. In a recent paper the thermal and mechanical stresses in silicon nitride rollers were analysed. In field tests – when rolling materials with high-deformation resistance – cracks developed in the ceramic rollers, which grew for a long-time period before large parts of the rollers broke apart. In more moderate conditions the rollers operated safely. In this paper a FE model is used to analyse the in-service behaviour of cracks in the silicon nitride rollers. For the observed crack path the stress intensity factor of the cracks is determined using the weight function method. It increases up to a crack depth of around 0.35 mm and then decreases again with increasing crack depth. This explains the observed pop-in-type growth of cracks after an overload. Depending on the rolled materials, the popped in cracks have a length between approximately 0.35 and 1.2 mm. The further growth of the cracks to a length of several millimetres, which is caused by a fatigue growth mechanism, needs several thousand additional revolutions.

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.

A procedure to predict the fracture toughness of a ceramic multilayer composite made of different phases is presented. The procedure requires experiments to measure the intrinsic fracture toughness of the phases and to determine the required material data. The numerical modeling includes a conventional finite element stress analysis and the calculation of the crack driving force based on the concept of configurational (material) forces. The procedure yields the fracture toughness of the composite as a function of the crack length. A bending bar consisting of layers made of alumina and an alumina–zirconia composite is investigated. The bar has a crack perpendicular to the interfaces. The spatial variations of both the thermal residual stresses and the elastic modulus induce shielding and anti-shielding effects on the crack, which are quantified. The numerically predicted fracture toughness is compared with the experimental values.

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.

Because of their high yield strength and hardness as well as their brittle fracture characteristics the behavior of cracks in ceramics can be described within the framework of linear elastic fracture mechanics. For fracture toughness (K Ic) measurements the test techniques which were developed for metallic materials are unfavorable, as an economical preparation is impossible in the case of ceramic materials. Therefore simple geometries e.g. bend bars became a preferred specimen shape for K Ic measurements. A major difficulty arises when sharp and well-defined pre-cracks for crack propagation studies have to be created. Several methods to overcome this problem are introduced. Additionally, methods to investigate small amounts of material are discussed.

Strength data of brittle materials show a significant scatter. Therefore probabilistic methods have to be used for designing with these materials. So far this has been done on the basis of the Weibull statistics. The Weibull statistics (implicitly) implies a particular type of defect distribution, which can be observed in many (but not in all) ceramic materials. The correlation between the strength and the flaw size distribution is discussed in some simple examples. Then the situation for very small specimens is discussed. This case will be of high relevance for the testing of miniaturised electroceramic components and materials of the microsystem technique. It is shown that the Weibull theory gets inconsistent and should overestimate the strength of the specimens (components), due to the fact that the effective volume becomes smaller than the fracture origin.

Silicon nitride rolls for wire hot rolling have been tested in the rolling mill. After short employment for processing of ultra-high strength materials, cracks appeared in the roll calibre, which limited further application of the rolls. In order to find out possible causes for the damage, relevant mechanical properties of the roll have been determined and thermally and mechanically induced stresses were assessed by numerical simulation. It has been found that thermal stresses are of little relevance, whereas mechanically induced stresses are high enough to enhance subcritical crack growth resulting in the development of the macroscopic cracks, so that the observed damage of the rolls could have been adequately explained. One further result of the analysis was that flaws induced by grinding are decisive for the service time of ceramic rolls, so that special attention has to be paid to the machining of the roll calibre.

Electroceramic varistors, typically based on ZnO, show a strong non-linear currentvoltage characteristics. Actually they can be considered as electrical isolators below a critical field strength and highly conductive above. These components are used as over voltage protection elements in various fields of electric and automotive industry. In testing and in service high power varistors are loaded with µs-voltage pulses and suffer high mechanical loads due to thermal shock and inertia effects. Therefore the reliability in terms of mechanical strength becomes a crucial mark of quality. In this work the microstructure and the strength of commercial high power varistors of three different producers are presented. By a subsequent fractographic analysis fracture initiating defects are identified. It is shown, that defects in the microstructure, which result from the processing of the varistor components, play a significant role for the strength of the ceramics and of course also for the service performance of the components.

Recent experiments on the fracture strength of zinc oxide (ZnO) ceramics showed that the size of specimens has almost no influence on their mean strength although strength data of a set of nominally identical specimens are still found to scatter. It is suspected that the complex nature of defect–microstructure interaction and the high density of porosity in ZnO ceramics are possible reasons for this insensitivity to strength scaling. In the paper, numerical results obtained by finite element analysis show that the fracture strength of ZnO is more influenced by the pore/grain-size interaction than only by the size of a pore or its shape. As a consequence, the pore/grain-size interaction will increase the fracture probability of small pores and lead to a homogenisation of critical flaw sizes. Furthermore, the high degree of porosity, especially the heterogeneous distribution and clustering of pores, could favour further homogenisation of critical crack sizes. This implies that the fracture strength of ZnO is insensitive to the size of specimens as corroborated by experiments. Finally a simple statistical explanation is given.

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).

Brittle material behavior and mode of failure are contrasted with those characteristics of ductile materials. The stochastic nature of brittle fracture, which results from the random occurrence of fracture-initiating microstructural imperfections, necessitates a probabilistic fracture mechanics approach to design with brittle materials. It is also clearly shown which main properties of brittle materials have to be optimized to improve the reliability of mechanically loaded components made of brittle materials. Important features of designing with brittle materials are elucidated and illustrated by an exemplary design calculation of a ceramic disc spring. It is shown how even environmentally induced subcritical crack growth, characteristic of ceramic materials, can be adequately accounted for in the assessment of reliability.

— Strength measurements are becoming increasingly important for electroceramics. Bending of specimens small enough to be cut out of small electroceramic components may be one possibility. Therefore the miniaturisation of the 4-point bend-test for ceramic specimens is now being attempted. In this paper the errors in determining the flexural strength arising from the test principle itself, plus the geometry and measuring inaccuracies are calculated and expressed as a function of the outer span length. Contact pressure and a tolerable total measuring inaccuracy determines the dimensions of miniature specimens and fixtures. The possibilities of appropriate specimen preparation are also investigated. Ceramic materials show a volume (i.e. a specimen size) dependence of strength which is described by Weibull's statistical theory. The applicability of the miniature bend-fixtures is demonstrated by measuring this volume effect.

Advanced ceramic materials have unique properties that make them key elements of current and future technologies. Not only do some forms of ceramic have advantageous refractoriness, hardness, wear resistance, and resistance to corrosion but others also have what is often described as ‘functional’ properties. For example, the high oxygen ion conductivity of zirconia is exploited for high-temperature fuel cells. Some ceramics with perovskite crystal structure can be switched between electrical conducting and nonconducting conditions, triggered by a phase transformation, a feature commonly used in electric circuit protectors. In other perovskite structure ceramics, a strong piezoelectric effect can be developed, and this is exploited in force measurement, for example, load cells, and for displacement control, such as in positioning devices and even as fast-acting valves for diesel injection in vehicle engines.

This paper reviews current activities at the Montanuniversitat Leoben on the hierarchical design of flaw-tolerant brittle materials in the fields of layered ceramics, hard coatings, fibre reinforced laminates, and biomimetic functional systems. Different examples of reinforcement mechanisms are presented acting at different length scales. Novel strategies are analyzed that make use of tailored residual stresses, textured microstructures, compositional heterogeneity and spatial variations in properties, fiber arrangement and laminate stacking, or functionalization of hierarchical materials from brittle constituents. Potential implications of hierarchical structures combining different materials science approaches for future engineering designs are discussed.

Tools for rolling steels and super alloys, which are nowadays in general made from steel or cemented carbides, suffer from wear and/or from surface cracking caused by thermal fatigue. New tools made from silicon nitride show improved performance in respect to thermal shock loading and wear. But their low toughness manifests also a high risk of brittle failure. Nevertheless the successful use of silicon nitride rolls with having more than a manifold lifetime (compared to the conventional solutions) has been reported in the last years [1 -3]. In this paper earlier work of the Institut für Struktur- und Funktionskeramik at Montanuniversität Leoben on highly loaded silicon nitride rolls is summarized, where the limits of the Application of silicon nitride rolling tools are discussed. On the extreme example of rolls for super alloy wire rolling the behaviour of small surface cracks in the roll track is discussed. It is shown that – for the investigated conditions - rolling high strength steel wires is manageable but rolling of super alloy wires will cause the growth of fatigue cracks, which may destroy the rolls after some tons of rolled wire. A not trivial problem to be solved is the connection of the ceramic tool with the metal parts of the roll stand. Thermal strains of the metal parts can be several times larger than those of the silicon nitride ceramic and can therefore cause very high thermal misfit strains, even if the heating of metal parts seems to be modest. This case is discussed on the example of a catastrophically failed ceramic tool. This clearly shows that not only the tool but also the joint of the tool to the rest of the machinery has to be designed carefully. In summary this work demonstrates that a successful use of silicon nitride ceramic tools for cold and hot forming of metals and alloys is possible.