A simple formula for calculating the tensile strength of brittle materials by means of the circular semi‐ring test and the optical method of caustics

Abstract

The tensile strength of brittle materials is here obtained by applying the experimental method of caustics to the circular semi-ring test (CSR). In this context, first the equations of the initial and the respective caustic curves are obtained for the CSR for light reflected from the front and rear face of the CSR as well as for transmitted light, thus covering all cases for both opaque and transparent materials. It is seen that the radii of the initial curves assume complex and real values with only the latter being accepted to form the loci on the CSR to provide the caustics. Then, simple closed-form formulae are provided for determining the critical stresses at the critical points A and B on the inner and outer perimeter of the CSR, in terms of the caustics' horizontal diameter DX.