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 implantation 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.

Dynamic Crack Propagation and Its Interaction With Micro-Cracks in an Impact Problem

“…Brittle materials have advantages such as hardness and wear resistance, but their deficiencies in terms of toughness and brittleness significantly restrain their usage in practice. This is the main reason that the problem of crack propagation at both macro and micro levels is a problem of frequent discussion in the recent literature [1][2][3][4].…”

“…Recent studies have stated that the micro-cracks and as a consequence, the shielding increases material toughness [7,8]. This phenomenon is called as "micro-crack toughening" [4]. Location, orientation, and density of micro-cracks significantly alter the toughening mechanism and crack propagation due to changes in stress intensity around the main crack [9][10][11].…”

“…Location, orientation, and density of micro-cracks significantly alter the toughening mechanism and crack propagation due to changes in stress intensity around the main crack [9][10][11]. Examining the effect of non-uniformly arranged micro-cracks with analytical approaches is rather complicated due to complex mechanical behavior [4]. Some analytical solutions were presented for uniformly distributed micro-cracks [12][13][14][15][16].…”

“…Braun and Fernández-Sáez [35] suggested a 2D discrete model and applied it to the benchmark problem in [36], though crack paths were lattice dependent for coarse meshes. Therefore, a more comprehensive and robust approach is a considerable requisite to determine crack nucleation, propagation, and interactions [4]. Silling and Askari [37] presented Peridynamics (PD) method, which naturally involves crack modeling, nucleation, and progression in a continuum, and thus overcomes the deficiencies of classical numerical approaches.…”

Topology optimization of cracked structures using peridynamics

“…PD improves the simulation of the crack growth compared to the weakly nonlocal approaches reported in the literature [63][64][65][66]. Most recently, PD is also utilized for toughness enhancement and material design of brittle materials by introducing micro-cracks in the vicinity of the macro-cracks [67].…”