Accurate predictions of dynamic fracture in perforated plates

Abstract

Dynamic brittle facture in materials with many pores/perforations has been shown experimentally to feature complex evolution of crack morphologies that include crack branching, micro-branches that arrest, cracks restarting from pores and branching soon after. Computational models of these problems need to accurately account for the dynamic interactions between strain waves and stress concentration zones induced by the perforated geometry. In this paper, we aim to improve the predictive capabilities of computational simulations of dynamic brittle/quasi-brittle fracture in samples with complex geometries, like perforated plates, by introducing a discretization method using non-uniform grids near a boundary (NB-NUG) for 2D peridynamic fracture modeling. The NB-NUG avoids the steps and the corresponding artificial stress concentrations created in PD models when using uniform grids over domains with curved boundaries. The new method also reduces numerical errors compared with general non-uniform grids used for PD models. We apply the model for dynamic fracture of thin PMMA plates with different arrangements of periodic pores/perforations. The results match the experimental observations for all of the cases considered. Fine features observed in the experiments (multiple cracks branching and cracks that arrest soon after splitting, number of branching events, etc.) are captured by the new approach and not by the other PD models with different types of grids. The results show that the high strain energy density regions created around perforations attract a nearby crack tip, deflecting the crack path, altering its propagation velocity, and promoting crack branching in its wake, thus dissipating more energy. Nonlocality of damage helps here in allowing its unrestricted evolution in problems in which complex crack morphology is sensitive to small changes in the geometrical arrangement of pores in the structure.