Tensile strength for splitting failure of brittle particles with consideration of poisson's ratio

Abstract

The core mechanism of comminution could be reduced to the breakage of individual particles that occurs through contact with other particles or with the grinding media, or with the solid walls of the mill. When brittle particles are loaded in compression or by impact, substantial tensile stresses are induced within the particles. These tensile stresses are responsible for splitting failure of brittle particles. Since many engineering materials have Poisson's ratios very close to 0.3, the influence of Poisson's ratio on the tensile strength is neglected in many studies. 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 tensile stress at the centre of the particle is obtained. It is found reasonable to propose this tensile stress at the instant of failure as the tensile strength of the particle. Moreover, this tensile strength is a function of the Poisson's ratio of the material. 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 tensile strength has some validity for irregular particles as well. Therefore, it could be used as the tensile strength for brittle particles in general. The effect of Poisson's ratio on the tensile strength is discussed.