Stochastic failure of isotropic, brittle materials with uniform porosity

Porous materials present serious technological constraints on all applications, such as battery electrodes, solid oxide fuel cells, synthetic bone grafts, filters, pharmaceutical powder compacts and feed pellets. Despite the significance of reliability in brittle materials, current literature is limited in pore-pore interaction effects on fracture statistics of brittle porous materials (BPMs). In this paper, a two-dimensional finite element (FE) simulation-based approach was developed to assess the pore-pore interactions and their impact on fracture statistics of isotropic microstructures. The classical fracture mechanics approach was combined with FE simulations that account for the interactions to predict the decrease in the fracture stress with increasing porosity. Rules were directly compared against experimental data for porous polycrystalline alumina, hydroxyapatite, and all the other data combined in Fig. 6. The maximum reliability of BPMs was shown to be limited by the underlying pore-pore interactions. Weibull modulus decreased more than threefold for a change in porosity from 1 to 2 vol.%. The Weibull moduli were between 7 and 18 in the range of 2-31 vol.% porosity. Even the microstructures with the same porosity level and size of pores showed substantial differences in fracture strength.