Breakage of flawed particles by peridynamic simulations

In this paper, we use a 2D bond-based peridynamic model to investigate the strength of disk-shaped particles including pre-cracks. We use a diametral (or Brazilian) test to break the particles. For the flawless particles, we find that the stress distribution compares well with an analytical model accounting for the size of the contact zone, and the particle stiffness tends linearly to a well-defined value for increasingly resolved meshing. We then introduce cracks, which are numerically defined by reducing the Young modulus of the bonds crossing linear segments. We consider in detail the effect of a single vertical crack on the yield stress as a function of its position. We also consider a randomly distributed population of cracks with sizes generated from a Gaussian size distribution. For a parametric study with a hundred particles, we found a probability of failure that is well fit by a Weibull law. Finally, using an image analysis algorithm, we investigate the statistics of cracks and the resulting fragments.