Effect of Horizon Size on Crack Growth Path in Peridynamics for Brittle Materials

In the field of peridynamics (PD) theory, the material horizon plays a crucial role. This study investigates how the horizon size affects the crack growth paths and shapes in brittle materials. To achieve this, a pre-notched plate was modeled based on bond-based PD theory, with varying horizon sizes, and the development of cracks was observed. Duran ۵۰ glass is the brittle material employed in the models. The simulations were conducted in ۲D and plane stress, with damage and displacement contours extracted based on the damage criterion definition. In this study, five models were presented with different 𝛿/ℎ. What differs in the models is the horizon size (𝛿), while the distance between points (ℎ) remains constant and equals ۰.۲۵ mm. The results were compared to previous numerical and experimental studies. In all models except for the model with 𝛿=۲ℎ, bifurcation of the main crack was observed. Based on the results, the crack growth shape is inaccurate if 𝛿=۲ℎ. However, the models with 𝛿=۳ℎ and 𝛿=۶ℎ are more precise, indicating the bifurcation of the main crack properly without additional branching. In the model with 𝛿=۴ℎ, bifurcation is evident, but preceding that, there is a branching phenomenon. In general, the findings of this study align with previous research. Ultimately, peridynamics is a successful approach for simulating the branching of cracks in brittle materials.

Keywords:

Bond-based peridynamics , Brittle materials , Crack growth , Horizon size