Numerical analysis of crack path stability in brittle porous materials

Abstract

Porous materials are widely used in engineering applications because of their high stiffness, strength, and low density. Those advantages are mainly due to their open microstructures, which also makes it challenging to obtain a thorough understanding of their fracture mechanisms and to predict trustworthy crack paths. In this study, we analyse numerically fracture trajectories in brittle porous solids with varying porosity (or relative density) subject to different mixed-mode loading conditions using a phase-field theory for brittle fracture. The results reveal that the crack paths in porous solids with high porosity (low relative density) are very different from those in porous solids with low porosity (high relative density). The latter resemble stable crack paths in homogeneous solids, whereas the former seems somewhat arbitrary, more stochastic. In high porosity materials, the crack paths are governed by the local microstructure rather than by the global remote loading. A key observation is that there is a transition of the fracture behaviour in porous materials at relative densities of around 50%. At relative densities above 50%, the material behaves nearly as a classical continuum, and the crack paths are reasonably well captured by traditional fracture mechanics theories. The stochastic nature of the porous microstructure is also examined.