On the diametric compression strength test of brittle spherical particles

Here we revisit, by means of the finite element method, the mechanics that underlie the diametrical compression of a linear elastic sphere between two parallel and planar elasto-plastic platens. We show that the Hiramatsu and Oka equations give valid hoop stress values only when the contact area between the compressed sphere and the platens is less than roughly 5% of the equatorial sphere cross-sectional area. At higher contact areas, when the spheres are more deeply embedded in the platen material and the test can be used to measure the particle hoop strength, the Hiramatsu and Oka solution underestimates the hoop stress. By conducting a parametric study, we provide simple expressions that can be used to quickly, yet accurately to within the ≈5%, compute the hoop stress of compressed spheres in diametric compression tests as a function of the contact area knowing only two parameters, namely the Poisson's ratio of the material making the sphere and the sphere/platen contact friction coefficient.