Peridynamic Models for Fatigue and Fracture in Isotropic and in Polycrystalline Materials

To improve design and reliability, extensive efforts has been devoted to understanding damage and failure of materials and structures using numerical simulation, as a complement of theory and experiment. In this thesis, peridynamics is adopted to study fatigue and dynamic failure problems. Fatigue is a major failure mode in engineering structures. Predicting fracture/failure under cyclic loading is a challenging problem. Classical model cannot directly be applied to problems with discontinuities. A peridynamic model is adopted in this work because of important advantages of peridynamics in allowing autonomous crack initiation and propagation. A recently proposed peridynamic fatigue crack model is considered and improved in terms of computational efficiency and numerical stabilities. We validated the fatigue crack model by comparing simulation results of a modified compact tension test with experiments. The proposed improvements add the fatigue limits to the propagation phase. We demonstrate that the model simulates all three phases of fatigue failure (initiation, propagation, and final failure) with an example in which a fatigue crack sinks into a cutout and re-initiates from a different location along the cutout, grows, and lead to final failure of the structure. Convergence studies show that the peridynamic results are correct once the nonlocal size is smaller compared with the size of relevant geometrical features. In the second part of this thesis, a 3D peridynamic model for cubic crystalline elastic and brittle materials is proposed. We use the model to simulate the Edge-on impact test of a transparent ceramic material, AlON. Experiments show that in ALON, damage transitions from a fast failure front (faster than the shear wave in the sample) to much slower localized cracks. Using the peridynamic model we explain, for the first time, the reasons behind this transition, and why failure front moves faster than the shear wave speed in the material. We also use the polycrystalline peridynamic model to predict crack nucleation sites in a Ni-based superalloy. Peridynamic results for a synthetic polycrystalline sample under tension are compared with finite element simulations. Results show that the model introduced captures the strain distribution and all strain concentration sites predicted by the FEM model, and in addition, it allows for initiation, growth, and interactions of cracks