Crack nucleation in brittle and quasi-brittle materials: A peridynamic analysis

Peridynamic (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. Bilinear and trilinear bond force-strain relationships have been proposed in the literature for crack propagation in quasi-brittle materials. In this paper we study crack nucleation in a plate with a hole under quasi-static loading using bilinear and trilinear PD models. We provide analytical formulas to calibrate the models to measurable material properties. We show convergence for both strength and fracture toughness. The bilinear PD constitutive model works well for both brittle (e.g. ceramics) and quasi-brittle (e.g. concrete) systems, while the trilinear version is more suited for quasi-brittle fracture behavior. We also find that for quasi-brittle fracture, a model that accounts, stochastically, for the presence of small-scale pores/defects performs better than a homogenized model. A wedge-splitting test in concrete and crack nucleation in a quasi-isotropic composite plate with a circular hole are used to demonstrate the model's performance. In contrast with other models, the current formulation does not depend on the sample geometry.