Using theoretical models, we consider the elastic constants of ceramics containing proes. As an example, we consider alumina. However, the approach applies to all ceramics. As a point of departure, we consider spherical pores. For all the usual elastic constants - Young modulus, shear modulus, bulk modulus. Poisson ratio-we give relationships for both the forward and inverse cases: predicting the porous ceramic properties and estimating the pore-free ceramic properties. Following a suggestion by Hasselman and Fulrath that sintering or hot pressing can produce cylindrical pores, we derive a relationship for the elastic constants of a distribution of randomly oriented long cylinders (axial ratio goes to infinite, the prolate-spheroid limit). This model predicts elastic constants lower than for spherical pores, but well above observation. We obtain agreement with observation by assuming the proes are oblate spheroids. For alumina, the necessary aspect ratio equals one-ninth. Using this oblate spheroid pore-shape model, we give predictions for all of alumina's elastic constants versus pore volume fraction. Besides pore aspect ratio, the model requires only the pore-free alumina elastic constants. It contains no adjustable parameters.
Elastic Constants of Porous Ceramics
Handbook of Elastic Properties of Solids, Fluids, and Gases ,
, Lei, M.
and Datta, S.
Elastic Constants of Porous Ceramics, Handbook of Elastic Properties of Solids, Fluids, and Gases , , [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=851364
(Accessed February 25, 2024)