Robert Danzer

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.

A general strength distribution function for brittle materials

Abstract A new strength distribution function for brittle materials is developed, which applies to materials with an inhomogeneous distribution of flaws. The probability of failure is F=1− exp [−〈N c,s 〉] where 〈N c , s 〉 is the mean number of critical defects in the specimen of size S. The well-known Weibull statistics are a special case of the new statistics for a special flaw size distribution. Several aspects of the relationships between the Weibull statistics and material structure are analysed in the light of the new formalism. Examples are materials with several different flaw distributions or rising crack resistance. The conditions necessary to get a Weibull distribution as well as the reasons why Weibull distributions are observed so often in the daily material testing practice are discussed. Finally, the minimum number of test specimens necessary to guarantee a reliable prediction of the components reliability using Weibulls theory is given. This number depends on the necessary reliability as well as on the loaded (effective) volumes of the test specimens and components, respectively.

Polished notch modification of SENB-S fracture toughness testing

Abstract In fracture toughness testing it is common for reasons of simplicity and reproducibility to use notches to approximate sharp cracks. However, a dependence of measured fracture toughness (KIc) on notch-root radius is observed. This can be explained as a consequence of the interaction of a distorted stress field with material flaws in front of a notch. A relationship to quantify this effect is presented and examined. It is shown that to measure true fracture toughness sharp notches of the size of microstructural features are required. A simple method to make very sharp notches is presented. Fracture toughness values determined with sharp-notched samples are compared with the results of experiments with conventional sawn-in notches. It is shown that sharp notches deliver considerably lower, more accurate and reproducible values of KIc for materials with fine microstructures. These values are thought to lie at the beginning of any R-curve.

Strategies for fracture toughness, strength and reliability optimisation of ceramic-ceramic laminates

Abstract Layered ceramics are, compared to conventional monolithic ceramics, a good choice for highly loaded structural applications having improved fracture toughness, strength and mechanical reliability. The use of tailored residual compressive stresses in the layers is the key parameter to adjust these properties. In this work two types of ceramics are analysed which have external (ECS-laminates) or internal (ICS-laminates) compressive stresses. The most important factors having influence on the strength and toughness of these laminates are discussed. Clear recommendations on the proper selection of a suitable mismatch strain, volume ratio of the layer materials and thickness and distribution of individual layers are given, either to achieve a high toughness and/or a high lower limit (threshold) for strength.

Chairside CAD/CAM materials. Part 2: Flexural strength testing

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 (12×12×1.2mm3) or round disc (Ø=12mm, thickness=1.2mm) 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 110.9MPa (Vitablocs Mark II) to 1303.21MPa (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.

Calculation of the stress intensity factor of an edge crack in a finite elastic disc using the weight function method

Abstract A closed-form weight function formula is used to calculate the stress intensity factor of an edge crack in a finite elastic disc. The result is applied to the problems of a rotating disc and an infinite long cylinder under thermal shock.

Finite element modelling of the electrical impulse induced fracture of a high voltage varistor

In testing and in service, varistors are subjected to very short (μs range) high current pulses. Due to the inertia effects that appear on rapid Joule heating dynamic stress waves are generated, which can cause brittle failure. An analytical solution for the one-dimensional case was presented recently by Vojta and Clarke. In this work a full three-dimensional analysis of an axisymmetrical varistor has been performed using Finite Element Simulation. The reflections of the stress waves from the bases and the shell of a varistor and their interference are analyzed. The resulting stress field and its development with time is much more complex than in the 1D case. The aspect ratio of the varistor has been shown to have a strong influence on the amplitude of the mechanical stresses and can be varied to minimize the maximum stress level reached. Damping has been considered but found to be negligible in realistic cases.

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.

Edge Toughness of Brittle Materials

In industrial applications edge chipping or flaking is one of the most common reasons for the failure of ceramic components. In this work, a previously presented method, found in literature, to investigate the behaviour of ceramic edges under mechanical loading is further developed. This method, involving loading an edge near region in a sample with an indenter until flaking occurs, can be used to characterize ceramic materials and to rank them with respect to their resistance against edge flaking. It is found that the edge geometry has a significant effect on the measured resistance to edge flaking.

Application of probabilistic fracture mechanics to a dynamic loading situation using the example of a dynamic tension test for ceramics

Every acceleration or deceleration causes inertia forces and as a consequence elastic waves. Of course, such dynamic loading situations often occur in structural applications of materials. The consequences of such dynamic loading on designing with ceramics are considered on the example of a new dynamic tension test. First, the test device is described, and the resulting loading situation is carefully analysed. It is seen that the dispersive character of wave propagation causes an inhomogeneous stress distribution changing with time. Then the influence of the dynamic loading on the stress intensity factors of small cracks, which in general are responsible for failure in ceramic materials, is discussed. Finally, the consequences on fracture statistics are considered. Although the demonstrated procedure is restricted to not-too-steep ramps of the wave front, it is considered to be valid for most cases of dynamically loaded ceramic components. Exceptions are very sharp impact or ballistic loading.