Analysis of Microscopic Stress and Strain in Ceramics

The macroscopic elastic constants of alumina are calculated by the finite element method based on a plane model of polycrystalline ceramics. The microscopic stress and strain in the uniaxial elastic deformation are also analyzed considering the pore in ceramics and the elastic anisotropy of the crystal grain. As the porosity increases, the macroscopic value of Young's modulus decreases and the calculated relation between them agrees with the well-known experimental equation. The microscopic stress and strain concentrations around a pore are affected by Young's modulus of the grain and are dependent on the position of the pore on the grain boundary. The maximum values of stress and strain change with the porosity, and the influence of the position of the pore is large when porosity becomes large. In the case when a pore exists on the grain boundary nearly perpendicular to the stress axis, the maximum values are at the region around the grain having a large value of Young's modulus.