Application of peridynamic stress intensity factors to dynamic fracture initiation and propagation

A non-local formulation of the classical continuum mechanics theory called peridynamics is used to study initiation and propagation of dynamic fractures. The purpose of this study is twofold. First, we introduce a new post-processing technique to estimate stress intensity factors using peridynamic data. Second, the peridynamic stress intensity factors are used to study the influence of loading rate on key aspects of dynamic fracture. In particular attention is focused on examining the influence of loading rate and material properties on time to fracture and the local stress state at the fracture tip during initiation and propagation. In the first part of the paper emphasis is placed on using stress intensity factors to verify the numerical method. Simulations are performed on simplified test cases and the results are compared to relevant experimental and numerical studies found in the literature. Peridynamic stress intensity factors are then used to demonstrate the influence of loading rate on fracture initiation and propagation. To this end simulations are performed by partially loading the internal surfaces of a notch at various loading rates and monitoring the stress intensity at the tip of the notch. For each loading rate, the stress intensity factor increases smoothly to a value above the input fracture toughness at which point initiation occurs. After initiation, the stress intensity factor remains nearly constant in time. It is shown that the stress intensity factor at initiation and the time to fracture depend on the loading rate. Predictions show that the critical stress intensity is insensitive to loading rate when the fracture initiation time is below a material-dependent characteristic time scale. As loading rate increases, the time to fracture decreases and stress intensity at initiation increases markedly. The characteristic time-scale is shown to be only dependent on the material stiffness and independent of the strength of the singularity at the fracture tip. In our simulations, increasing the loading rate resulted in fracture branching. Also, the fracture speed increases with loading rate. However, the dynamic stress intensity factor of a propagating fracture is shown to be independent of loading conditions for a linear peridynamic solid with rate-independent input fracture toughness.