Peridynamics simulation of crack propagation of ring-shaped specimen like rock under dynamic loading

The split Hopkinson pressure bar (SHPB) system with a spindle-shaped striker is widely used to test the characteristics of rock-like materials subjected to dynamic loading, and the crack propagation of ring-shaped specimens under dynamic loading is a research focus in rock mechanics. In this paper, a model of the SHPB system, including the striker, incident bar, specimen, and transmitted bar, is established based on peridynamics theory and is validated by comparing two kinds of stress waves obtained by a peridynamics simulation and experiment. Based on these results, the crack propagation of a ring-shaped specimen with an aperture is simulated, and the influences of the apertures of the specimen on the failure patterns are discussed. The results show that there are four cracks distributed on the specimen with an aperture of 24 mm: crack-1 first initiates at the end of the inner diameter near the incident bar, crack-2 then occurs at the end of the inner diameter near the transmitted bar, and then crack-3, also called a secondary crack, initiates on the upper and lower outer boundaries of the specimen; these secondary cracks are perpendicular to the other cracks. The sequence of starting velocities and average propagation velocities of cracks from high to low is crack-3, crack-2, and crack-1, and the failure of the ring-shaped specimen occurs due to tension. Controlled by the structure effect of the ring-shaped specimen, the loading rate and the peak stress decrease gradually, and the failure patterns of the specimens transform from splatted by one initial crack to broken by two cracks that are perpendicular to each other and then to asymmetrical failure with an increase in the apertures of the specimen. The comparison results of peak stresses and failure patterns between the peridynamics simulation and the experimental results verify the accuracy of peridynamics theory.