Abstract
The simulation method was developed to predict homogenized elastic moduli of ceramic materials from elastic stiffness of each grain within its microstructure. Polycrystalline Al_2O_3, ZrO_2 and Al_2O_3-ZrO_2 ceramics were produced as model samples. Elastic stiffness, c_<ij>, of single crystal cubic-ZrO_2 was measured by four-point bending method. Microstructures of model samples were modeled as two and three-dimensional heterogeneous bodies composed of Al_2O_3 and ZrO_2 grains. The crystallographic 3D-directions of each grain were assumed to be randomly distributed. Some square plates with a unit thickness that cut from the initial two-dimensional grain models and some cubes composed of geometeric cube grains were used to calculate apparent macroscopic elasitc moduli such as Young's modulus, Poisson's ratio and modulus of rigidity. An influence of the model size on apparent elastic moduli was examined by a finite element method. And then, the optimum model size was determined by comparing calculated elastic moduli to experimental data measured by a pulse-echo method. As a result, the scattering of apparent Young's modulus varies narrowly with increasing the number of anisotropic Al_2O_3 and ZrO_2 grains. The number of anisotropic grains within the optimum model was found to be about 400. The calculated elastic moduli for the optimum model coincided with the experimental data.
