Peter Supancic

The ball on three balls test for strength testing of brittle discs: stress distribution in the disc

Biaxial strength testing of brittle materials is claimed to have some benefits compared to uniaxial testing, e.g. the much simpler specimen preparation, the avoiding of tensile loaded edges, the similarity of the stress state to those from typical loading (e.g. during a thermal shock loading) and the fact, that biaxial stress states are more revealing of defects than uniaxial stress states. The experience of the past showed, that biaxial strength testing has its own problems, to avoid these led to the development of several variants. One of these variants, the ball on three balls test, seems to be extremely simple: a disc is supported by three balls and then axially loaded from the opposite side via a fourth ball. In this system small deviations from the requested geometry, especially some out of flatness of the disc, are mentioned to be tolerable, but the threefold bending symmetry makes an exact analytical assessment of the stress state in the loaded disc extremely difficult. A numerical approach has yet not been performed. In this paper a FE analysis of the stress state in a ball on three balls tested disc is performed. The stress field scales with the maximum principle stress, which occurs in the centre of the tensile surface. For this stress an analytical approximation (which has been fitted to the numerical results) is given, which accounts for the influence of all relevant geometrical and material parameters. The investigated range of parameters considers the values typical for testing of brittle materials.

Thermal Shock Behavior of an Al2O3/ZrO2 Multilayered Ceramic with Residual Stresses due to Phase Transformations

In this work, the thermal shock behavior of an Al2O3-5%tZrO2/Al2O3-30%mZrO2 multilayer ceramic is studied. On these materials, a tetragonal to monoclinic phase transformation within the Al2O3-30%mZrO2 layers takes place when cooling down from sintering. The latter induces an increase in volume and therefore compressive residual stresses arise in these layers. The residual stress distribution profile in the laminate influences the thermal shock response of the material. A finite element model has been developed to estimate both the thermal strain effects during the sintering process as well as the temperature distribution and stress profile within the laminate during thermal shock testing. Experimental tests on the monoliths and laminates were carried out and compared to the model. It is observed that the presence of the compressive layers within the laminate inhibits the penetration of thermal shock cracks into the body at even more severe conditions than in the monolithic material.

Mechanical stability of BaTiO3-based PTC thermistor components : experimental investigation and theoretical modelling

Barium titanate based positive temperature coefficient (PTC) thermistors, especially high power switching devices, can suffer major mechanical damage if inhomogeneous heating occurs under an applied electrical voltage. The main mode of mechanical failure, known as delamination fracture, manifests itself by cracking of the ceramic disc along a plane approximately parallel to the electrodes. This damage results from the build-up of thermal stresses, the amplitude of which is governed by a large number of geometrical, electrical and thermo-elastic parameters. For an experimental investigation, a measurement device was set up to observe the electrical behaviour of PTC-components during the switching process. To interpret specific aspects of the observations, a mathematical model was developed to simulate the electrical, thermal and thermo-elastic behaviour. In addition to the resistance/temperature characteristics considered by other authors, the varistor-effect (i.e. the non-linear isothermal current-voltage behaviour which is thought to make a significant contribution to the development of the mechanical stresses inparticular) is also taken into account. By doing a non-linear analysis with one and two dimensional models, and taking all relevant temperature dependencies of the material properties into account, a qualitative and quantitative agreement with the experimentally determined electro-thermal and failure statistical behaviour could be achieved. It is shown that in addition to the resistance/temperature characteristics, it is very important to account for the varistor-effect when modelling the build-up of the mechanical stresses during the switching process.

Precise determination of phonon constants in lead-free monoclinic (K0.5Na0.5)NbO3 single crystals

A polarized Raman analysis of ferroelectric (K0.5Na0.5)NbO3 (KNN) single crystals is presented. The Raman modes of KNN single crystals are assigned to the monoclinic symmetry. Angular-dependent intensities of A′, A″, and mixed A′ + A″ phonons have been theoretically calculated and compared with the experimental data, allowing the precise determination of the Raman tensor coefficients for (non-leaking) modes in single-domain monoclinic KNN. This study is the basis for non-destructive assessments of domain distribution by Raman spectroscopy in KNN-based lead-free ferroelectrics.

Piezotronically Modified Double Schottky Barriers in ZnO Varistors

Double Schottky barriers in ZnO are modified piezotronically by the application of mechanical stresses. New effects such as the enhancement of the potential barrier height and the increase or decrease of the natural barrier asymmetry are presented. Also, an extended model for the piezotronic modification of double Schottky barriers is given.

Strength Tests on Silicon Nitride Balls

For some years ceramic bearing balls based on silicon nitride have been routinely used in technical practice. An important property of bearing balls is their strength, but appropriate testing methods are still missing. In this paper four different methods for strength testing are applied to commercial bearing balls. Each of the tests needs a different type of specimen, their preparation needs a very different effort, and the stress state applied to the specimens is also very different. This causes pros and cons, which are discussed in detail. The conventional 4-point bending test characterises the material in the interior of the balls. The applied stress state is uniaxial. The machining of the bending bars out of the balls is time intensive and costly. The ball on three balls test also characterises interior of the balls. The stress state is biaxial. The machining of the disc shaped specimens out of the balls is less expensive than the production of bending bars, but the finish of the tensile loaded surface needs special care. The data of both types of tests can be converted into each other using Weibull theory. The specimens in the triple ball crush test are as-received bearing balls, which are squeezed together. This causes some kind of contact loading, as will also occur in service. Failure is caused by the creation and growth of contact cracks, followed by a collapse of the compressed and cracked material. A detailed analysis of test results is complicated. It can be speculated that the component’s behaviour is mainly influenced by the toughness of the material and that the flaws in the material or at the component’s surface are of less significance. In the newly developed notched ball test the highest stressed region is a part of the original surface of the balls. Machining of the notch is straightforward. The stress state is almost uniaxial. The strength depends on size of flaws in the surface region. Therefore the notched ball test is a relevant measure to characterize the quality of the bearing balls.

Varistor piezotronics: Mechanically tuned conductivity in varistors

The piezoelectric effect of ZnO has been investigated recently with the goal to modify metal/semiconductor Schottky-barriers and p-n-junctions by application of mechanical stress. This research area called “piezotronics” is so far focused on nano structured ZnO wires. At the same time, ZnO varistor materials are already widely utilized and may benefit from a piezotronic approach. In this instance, the grain boundary potential barriers in the ceramic can be tuned by mechanical stress. Polycrystalline varistors exhibit huge changes of resistivity upon applied electrical and mechanical fields and therefore offer descriptive model systems to study the piezotronic effect. If the influence of temperature is contemplated, our current mechanistic understanding can be interrogated and corroborated. In this paper, we present a physical model based on parallel conducting pathways. This affords qualitative and semi-quantitative rationalization of temperature dependent electrical properties. The investigations demonstrate that narrow conductive pathways contribute to the overall current, which becomes increasingly conductive with application of mechanical stress due to lowering of the barrier height. Rising temperature increases the thermionic current through the rest of the material with higher average potential barriers, which are hardly affected by the piezoelectric effect. Hence, relative changes in resistance due to application of stress are higher at low temperature.

Influence of internal architectures on the fracture response of LTCC components

Low Temperature Co-fired Ceramics (LTCCs) are layered ceramic based components, which – in recent years - are increasingly used as high precision electronic devices (e.g. mobile and automotive technologies) in highly loaded (temperatures, inertia forces, etc.) environments. They consist of a complex three-dimensional micro-network of metal structures embedded within a glass-ceramic substrate. Even though LTCCs have been used for more than 20 years, there is insufficient understanding of the mechanical loads during processing. In this regard, different types of failure of the end component during service have been reported, coming from different parts within the part. In this work, the influence of the internal architectures in the fracture response of LTCC components during bending has been investigated. Strength has been determined in 10 × 10 mm2 specimens using the ball-on-three-balls test (biaxial loading) and evaluated using Weibull statistics. Fractography of broken specimens has been performed to determine the mode of fracture of the components and the role of the internal architecture in the crack path. Results show strength dependence as a function of the testing position within the part. The influence of the internal architecture and residual stresses is also discussed.

Strength and Fractography of Piezoceramic Multilayer Stacks

Modern low-voltage piezoelectric actuators consist of a stack of piezoceramic layers (PZT) with metallic electrodes in between. Due to the use of these parts in automotive applications, a big but sensitive market is opened. During application mechanical stresses are an inherent loading of these electro-mechanical converter components. Therefore some strength of the actuators is necessary to guarantee a demanded life time. Bending and tensile tests were performed on commercial components to measure the strength in axial direction. Fracture surfaces were investigated with the methods of fractography to get information about the weakest links in the microstructure.

Mechanical properties of ceramics

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.