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.