Microstructural Mechanics Model of Anisotropic‐Thermal‐Expansion‐Induced Microcracking

Thermal‐expansion‐induced microcracking in single‐phase ceramics has been simulated using a simple mechanics model based upon a regular lattice of brittle, elastic springs. Microcracks preferentially form at grain boundaries and propagate either into the bulk or along grain boundaries, depending on the toughness of the boundaries relative to the grain interiors. The present results show that anisotropic‐thermal‐expansion‐induced microcracking can be more severe for either large or small grain size samples depending on the damage measure employed. At very small misfit strains, the large grain microstructure develops microcracks before the small grain microstructure. However, over most of the misfit strain regime examined, the total length/area of all cracks in a sample is larger when the grain size is small. This is manifested in a larger decrement of the elastic modulus in small grain size samples as compared with large grain size samples at the same misfit (Δ T ). However, large grain sizes are more detrimental with regard to fracture properties. This is because the fracture stress scales as inversely with the crack length and large grain samples exhibit larger microcracks than small grain samples. Unlike in the unconstrained samples, when a sample is constrained during a temperature excursion, the stress created by the overall thermal expansion can directly lead to fracture of the entire sample.