The Ball-on-Three-Balls strength test: Effective volumes and surfaces for Weibull strength scaling

Abstract

In order to compare the strength results of brittle materials from various testing methods or use the data for design purposes, it is essential to know the effective volume (Veff) or surface (Seff) for every loading scenario. For the Ball-on-Three-Balls-test (B3B), Veff and Seff have to be determined and investigated through Finite-Element-Analysis due to the lack of an accurate analytical description of the stress field. Through this work, the effective volume and surface of the B3B-test are made available as tabulated data for a wide range of specimen geometries and materials, along with the tools to utilize the data. A fitting model for the dependency of Veff and Seff on the Weibull-modulus for any given specimen geometry is provided. The influence of load-dependent non-linear effects on Veff and Seff is discussed. Finally, the necessity of Veff and Seff for statistical strength analysis is demonstrated through a practical example.