Proposal of a formula for estimating the tensile strength of solidification with arbitrary particle size distribution

In this study, a formula for estimating the solidification tensile strength caused by interparticle force with arbitrary particle size distributions was proposed based on Rumpf's formula, originally designed for predicting the tensile strength of solidifications comprised of particles with identical diameters. To estimate the capillary force between unequal-sized spherical particles, the approximate solution of Lian et al. was used. The proposed tensile strength equation changes depending on interparticle force, particle size distribution, the packing fraction and average coordination number. Using the proposed formula, the tensile strength according to the difference in particle size distribution was calculated under certain environmental conditions. The results showed that even if the median value of particle size was the same, the tensile strength varied because the packing fraction and surface area of particles per unit volume varied depending on the particle size distribution.