Deviations from Weibull statistics in brittle porous materials

Brittle porous materials (BPMs) are used for battery, fuel cell, catalyst, membrane, filter, bone graft and pharmaceutical applications due to the multifunctionality of their underlying porosity. However, in spite of its technological benefits the effects of porosity on BPM fracture strength and Weibull statistics are not fully understood, limiting the wider use of these materials. By combining two-dimensional finite-element simulations and classical fracture mechanics we found that BPM fracture strength decreases at a faster rate under biaxial loading than under uniaxial loading. Three different types of deviation from classic Weibull behavior can be identified: P-type corresponding to a positive lower tail deviation, N-type corresponding to a negative lower tail deviation, and S-type corresponding to both positive upper and lower tail deviations. Pore-pore interactions result in either P-type or N-type deviation in the limit of low porosity, whereas S-type behavior occurs when low and high fracture strengths coexist in a set of fracture data.