Peridynamic Models for Crack Nucleation in Brittle and Quasi-Brittle Materials

Failure in materials initiates from the microscale (defects, pores, etc.) and can affect, sometimes catastrophically, the structure scale. In this thesis, peridynamics (PD) is adopted to study crack nucleation in brittle and quasi-brittle materials. PD models of bodies without pre-cracks, based on a single fracture parameter (associated with the critical fracture energy), produce different strengths when different horizon sizes are used to simulate crack nucleation under quasi-static conditions. To maintain the same strength and fracture energy under different horizon sizes, extra parameters have to be introduced in the failure model, leading to, e.g. bilinear and trilinear models. We study crack nucleation in a plate with a hole under quasi-static loading using these models. We provide analytical formulas to calibrate the models to measurable material properties. We show convergence for both strength and fracture toughness, for both brittle and quasi-brittle systems. We then introduce similar PD models to study crack nucleation and rupture in soft materials, by which one can capture crack nucleation sites and final rupture similar to those seen in the experiment. In this work, we also introduce a PD model for simulating brittle damage and fracture in elastic porous materials based on an Intermediate Homogenization (IH) approach. In this approach, instead of explicitly representing the detailed pore geometry, we use homogenization but maintain some information about the microstructure (porosity) in the model. Porosity is introduced as initial peridynamic damage, implemented by stochastically pre-breaking bonds to match the desired porosity. We use the IH-PD model to study the fracture behavior of notched sandstone-type samples under three-point bending tests. Results by the IHPD model, in contrast with those with a fully-homogenized model, agree very well with experiments: we obtain different failure modes depending on the length of the off-center pre-notch. The results show the importance of inserting some information about heterogeneities (like pores) into the models aimed to study brittle damage initiation and growth in porous materials