Point load tests and strength measurements for brittle spheres

A multiaxial failure criterion for brittle materials is applied to a stress field analysis of a perfectly elastic sphere subjected to diametrically opposite normal forces that are uniformly distributed across small areas on the sphere's surface. Expressions are obtained for an intrinsic strength parameter of the material, as well as its unconfined compressive strength. An expression for the unconfined tensile strength is obtained by introducing an additional parameter accounting for the microstructural features of the material. The expressions indicate that failure initiates in the sphere where the ratio between the second deviatoric stress invariant and the first stress invariant is a maximum. Such a criterion does not coincide with the location of maximum tensile stress. The expressions are used to reinterpret published point load test results and predict unconfined compressive strengths. The configuration of the point load test as well as surface roughness and elastic properties of the pointer and samples are taken into account to establish the size of the area on which the point loads act. The predictions are in good agreement with measured values obtained directly using unconfined compressive strength tests. It is concluded that the point load test provides a more reliable estimate of the compressive strength than the tensile strength.