Fracture of Brittle Solids in the Presence of Thermoelastic Stresses

Abstract

A micromechanical model for strength behavior as a function of grain size in two‐phase materials with thermal expansion mismatch and in single‐phase materials with thermal expansion anisotropy is presented. The strength vs grain‐size plot is interpreted in terms of internal stresses and the ratio of grain to flaw size. The strength of thermally isotropic material is predicted to exhibit a weak grain‐size dependence with a negative grain‐size exponent normally different from 0.5. In thermally anisotropic poly crystalline solids, before the critical grain size for spontaneous cracking is reached, there will be a region of decreasing strength with increasing grain size due to an increase in the grain‐to‐flaw size ratio. When a critical grain size is reached, the ratio of grain to flaw size will decrease instantaneously and the strength will decrease in the same fashion. Very good agreement was obtained between predicted and experimentally observed strength behavior for TiO2 and MgO ceramics.