Three‐Dimensional Effects in Microcrack Nucleation in Brittle Polycrystals

Stress concentration at vertices where grains of a polycrystal meet at a point is contrasted with stress concentration at two‐dimensional junctions where grains join along a line. Effects of thermal anisotropy and elastic anisotropy orientation mismatches from grain to grain are considered. Special geometries with moduli mismatches are also analyzed to shed light on three‐dimensional vs two‐dimensional behavior. Although there are exceptions, it is generally found that the stress concentration at vertices is more singular than that at junctions. Singularities which are stronger than cracklike singularities (i.e., stress α r − s where s > 1/2) are found, and the implication of such “super singularities” for microcrack nucleation is discussed. Conditions for propagation of microcrack flaws at vertices are analyzed and contrasted with those at junctions.