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, mm, versus volume fraction porosity, PP, is extremely limited despite the importance of mm as a gauge of mechanical reliability. In Part I of this study, mm 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 mm versus PP plot is “U-shaped” with a wide band of mm values for P<0.1 (Region I) and P>0.55 (Region III), and a narrower band of mm values in the intermediate porosity region of 0.1, and the Young’s modulus EE for the HA specimens tested in Part I along with literature data for other brittle materials. Both <σf> and EE are power law functions of the degree of densification, ϕϕ, where ϕ=1−P/PGϕ=1−P/PG and PGPG is the green (unfired) porosity.

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► Weibull modulus, mm, versus porosity PP, examined: HA, 7 other brittle materials.
► 3-region mm versus PP “U”-shaped plot, represents more than 1560 fractured specimens.
► Unlike Regions I and III, Region II mm is banded, 4► Physical mechanisms: flaws, microstructure, temporal–spatial aspects of stress.