A computational model of peridynamic theory for deflecting behavior of crack propagation with micro-cracks

Abstract

The critical effect of micro level defects should be examined at macro level to better understand the fracture behaviors of engineering materials. This study investigates the branching and deflecting behavior of a macro (main) crack in presence of multiple number of micro-cracks at the vicinity of the crack tip. For this purpose, a non-local continuum theory, known as Peridynamics (PD), is utilized based on the original set of bond-based PD equations. The main advantage of using PD is its characteristic superiorities on the modelling of dynamical fracture. Various example problems with inclined-linear and/or curvilinear micro-crack clusters are solved through the implementation of different numerical models to better understand the micro-crack toughening mechanisms. After validating the PD implementation with a benchmark case, several combinations of multiple micro-cracks with various locations are considered. To capture complex forms of crack branches, the positions of micro-cracks are designated to follow an encircling and spreading patterns at the vicinity of the main-crack tip. Hence, more internal energy is dissipated through the generation of new crack surfaces such that the main-crack deflects along a more twisting path. It has been observed that depending on the amount of dissipated energy, the propagation speed of main-crack alters. Also, it has been demonstrated that encircling potential crack propagation regions with micro-cracks provides an augmented toughness to the brittle materials. Overall, the efficiency and robustness of the PD theory are revealed for simulating crack propagation in brittle materials.