An index of the tensile strength of brittle particles

The elementary comminution event can be regarded as a single particle subject to a stress field where the breakage of particle occurs through contact with other particles or with the grinding media, or with the solid walls of the mill. Although the particle is loaded predominantly in compression or impact, substantial tensile stresses are induced within the particle. These tensile stresses are responsible for splitting failure of the particle. In this paper, the state of stress in a spherical particle due to two diametrically opposed forces is analyzed theoretically. A simple equation for the state of stress at the center of the particle is obtained. An analysis of the distribution of stresses along the z-axis due to distributed pressures and concentrated forces, and on diametrically horizontal plane due to concentrated forces, shows that it is reasonable to propose the tensile stress at the center of the particle at the point of failure as an index of the tensile strength of the particle. As the state of stress along the z-axis in an irregular specimen tends to be similar to that in a spherical particle compressed diametrically with the same force, this index of the tensile strength has some validity for irregular particles as well. This index of strength reflects the influences of Poissonʹs ratio, and of the radius of region where the distributed pressures act.