Determination of the effective crack resistance in porous materials using a fracture phase-field model

Abstract

This work investigates the simulation-based determination of the effective fracture resistance of porous materials. Following the approach of Hossain et al. (2014), we conduct numerical experiments to identify effective crack resistance as a material parameter. Displacement boundary conditions corresponding to a steadily propagating macroscopic crack are applied to a representative microstructure. At the microscale, crack growth is simulated without prior assumptions regarding crack paths, continuity of propagation, or other features. The maximum value of the macroscopically acting J-integral defines the driving force required to advance the crack by a macroscopic length increment without arrest, which we refer to as the effective crack resistance. To simulate crack evolution in the microstructure without predefined growth assumptions, we employ a phase-field model. Phase field models are particularly well suited for this purpose. Our findings indicate that crack re-nucleation is a toughness determining failure mechanism in porous materials. We investigate the influence of various parameters on the characteristic length at which cracks re-nucleate, revealing a strong correlation with the internal length scale of the phase-field model. Finally, we analyze the effective crack resistance in simplified porous materials, with a specific focus on the effects of pore shape and pore spacing. Our results highlight their significant influence on crack resistance, providing insights into the failure behavior of porous structures.