Simple Expressions for the Evaluation of Stresses in Sphere-Loaded Disks Under Biaxial Flexure

Abstract

Abstract In testing ceramic materials, sphere-loaded disk tests are of increasing importance. Three different tests including one, four, and six spheres are addressed. For the first two tests, the maximum stress in the disk center was already studied in several papers. In this note, simple analytical relations for the distribution of the tangential stress will be given. The stress distribution in the center region is, for instance, necessary for the determination of effective surface and volume as used for Weibull statistics. For special applications also, stresses across larger distances from the center are desirable. As an example, strength tests on coarse-grained alumina are mentioned briefly which need a fracture mechanics evaluation for interpretation.