Elastic constants versus porosity for a highly porous ceramic, perlite

The compressional and shear velocities of a set of sintered perlite bricks of varying porosity, η, were measured by the pulse transmission method. The porosities of the specimens ranged from 10 to 83%. The quantities (νp2ρ)η and (νs2ρ)η are compared with the theoretical relations of Mackenzie and of Hashin and Shtrikman and are found to be in fair agreement with these values at low porosities but to fall below these curves for intermediate and high porosities. These data are then compared with the curve of an empirical exponential formula. Compressional velocities were also measured through dry highly porous perlite powder samples. The values of (νp2ρ)η for the powder fall below the sintered sample data and vary much more slowly as a function of porosity. Consideration of these data and the empirical equation suggests the possibility of describing the effects of porosity on elastic constants by a family of curves in the elastic-constant-porosity plane.