Connecting the macro- and microstrain responses in technical porous ceramics: modeling and experimental validations

The relation between the macroscopic and the microscopic (lattice) strain response to external uniaxial stress has been investigated for porous ceramics. Analytical and finite element modeling (FEM) have been performed and neutron diffraction data on porous sintered alumina and extruded honeycomb SiC have been used to validate the theoretical approach. By FEM simulations, it is shown that in spite of the complex pore microstructure, shear stresses are small during uniaxial compression. Analytical modeling shows that while the average microscopic stress depends on the applied macroscopic stress only through the porosity p, the average microscopic strain depends on the macroscopic stress through the pore morphology factor m, as well. Novel relationships are proposed to describe this dependence. Analytical calculations and numerical modeling perfectly agree with each other, and both show good consistency with experiments. As predicted, it has been observed that the microscopic (diffraction) Young’s modulus does not depend on the pore morphology factor, and follows the rule-of-mixtures, while the microscopic Poisson’s ratio does not even depend on porosity, but is equal to the value for the dense material property. A practical implication of these findings is that it is not possible to attach a pore morphology factor to a material, unless the processing conditions are tailored to vary p without varying m. In fact, the different values of m found for the different porosities explain why many models can be used to rationalize the experimental data. With the proposed method, the factor m can be independently evaluated by the use of macro- and micro-elastic properties of the porous body. Analogously, the macroscopic elastic properties of the dense material can be obtained by macroscopic and microscopic values measured on the correspondent porous material.