Void initiation in a random distribution of spherical particles

Abstract

A theoretical model is presented for the distribution of stresses on particle interfaces in a random three-dimensional distribution of spherical particles under tension. The particles are assumed to be rigid, and cylindrical pile-ups of prismatic loops are generated when the material is subjected to uniaxial tension. As the strain increases the length of each pile-up increases and it eventually comes into contact with pile-ups of neighbouring particles. The impingement of different pile-ups restricts the length of the pile-ups and thus increases the stress at the particle interfaces. The probability for pile-up interactions is calculated and expressions are derived for the distribution of pile-up lengths and stresses at the particle interfaces. Computations are performed for the distribution of stresses at interfaces in a random distribution of spherical particles of equal size. The probability for pile-up interactions in a distribution of particles of two different sizes is also calculated. It is found that the probability for increases of interfacial stresses due to pile-up interactions is larger for the larger particles in the size distribution.