Tensile Strength of Granular Materials

Abstract

RUMFF¹ has calculated the tensile strength of an ideal granular material; he suggests that: where σ is the tensile strength, B is the interparticle force and D is the diameter of the particles. The ideal material is a completely random pack of equal spheres with the bonding force concentrated at the point of contact. Some of the postulated relationships in the early part of Rumpf's calculation may appear to be dimensionally anomalous, and the strength has been re-calculated to investigate the effect of these anomalies. The whole aggregate has a volume V_a; a thin section of thickness t and volume V_s, perpendicular to the tensile stress direction, is considered. The average number of particles contributing to this section: where V_p is the mean crossed volume of one particle and ρ is the fractional packing density. The section is very thin and it is assumed that : where A_p is the mean crossed area for an average particle. If the cross-sectional area of the whole aggregate is A_a: Substitution in equation 4 gives: