Part I: porosity dependence of the Weibull modulus for hydroxyapatite and other brittle materials.

Porous brittle materials are used as filters, catalyst supports, solid oxide fuel cells and biomedical materials. However the literature on the Weibull modulus, m, versus volume fraction porosity, P, is extremely limited despite the importance of m as a gauge of mechanical reliability. In Part I of this study, m is determined for 441 sintered hydroxyapatite (HA) specimens fractured in biaxial flexure for 0.08 ≤ P ≤ 0.62. In this study, we analyze a combined data set collected from the literature that represents work from a total of 17 different research groups (including the present authors), eight different materials and more than 1560 oxide and non-oxide specimens, the m versus P plot is "U-shaped" with a wide band of m values for P<0.1 (Region I) and P>0.55 (Region III), and a narrower band of m values in the intermediate porosity region of 0.1<P<0.55 (Region II). The limited range of m (~4<m<11) in Region II has important implications since Region II includes the P range for the majority of the applications of porous brittle materials. Part II of this study focuses on the P dependence of the mean fracture strength,<σ(f)>, and the Young's modulus E for the HA specimens tested in Part I along with literature data for other brittle materials. Both <σ(f)> and E are power law functions of the degree of densification, ϕ, where ϕ=1-P/P(G) and P(G) is the green (unfired) porosity.