Relation between Strength, Microstructure, and Grain‐Bridging Characteristics in In Situ Reinforced Silicon Nitride

The grain size of in situ Si 3 N 4 is varied, and its effects on strength‐flaw size relations are related to the behavior of a bridging zone behind the crack tip. The bridging‐zone properties are calculated from a Dugdale model assuming that the bridging zone has a constant bridging stress ( p *) and length ( D b ) at the moment of the critical fracture. The results show that as grain size increases, p * decreases while D b and the critical bridging zone opening ( u *) first increase and then decrease, resulting in a maximum for short‐crack fracture toughness at an intermediate grain size. The initial increase of u * and D b with grain size is attributed to an increase in debonding length, while the decrease of p * is attributed to a decrease in strength for bridging grains due to a statistical effect which also causes D b and u * to drop in the large‐grain regime. Implications on microstructure design are discussed.