Approach to the Weibull modulus based on fractal fragmentation of particles

Abstract Particle fragmentation results in a fractal distribution of progeny fragments. Based on the fractal distribution, a statistical approach is proposed to interpret the scaling characteristics in tensile strength of brittle particles. It is found that the relationship between the cumulative survival probability of the particles and the tensile strength follows the Weibull distribution reasonably well. The Weibull statistical theory was commonly applied to calculate the size effect on tensile strength observed in brittle particles. The scaling law between the tensile strength and the particle size is a connector between the fractal distribution and the Weibull statistical theory. The Weibull modulus ( m ) can be calculated from the fractal dimension ( D ) of the particle size distribution, as m  =  D  / (3 −  D ). It is extensively verified by uniaxial compression experiments on rock particles.