A micromechanical basis for predicting the evolution of grain bridging

A micromechanical model is developed for grain bridging in monolithic ceramics. Specifically, bridge formation of a single, non-equiaxed grain spanning adjacent grains is addressed. A cohesive zone framework enables crack initiation and propagation along grain boundaries. The evolution of the bridge is investigated through a variance in both grain angle and aspect ratio. The bridging process can be partitioned into five distinct regimes of resistance: propagate, kink, arrest, stall, and bridge. Although crack propagation and kinking are well understood, crack arrest and subsequent "stall" have been largely overlooked. Resistance during the stall regime exposes large volumes of microstructure to stresses well in excess of the grain boundary strength. Bridging can occur through continued propagation or reinitiation ahead of the stalled crack tip. The driving force required to reinitiate is substantially greater than the driving force required to kink. The marked increase in crack resistance occurs prior to bridge formation and provides an interpretation for the rapidly rising resistance curves which govern the strength of many brittle materials at realistically small flaw sizes.; To determine the validity of an assumed intergranular path, the classical penetration/deflection problem of a crack impinging on an interface and various stalled crack configurations are reexamined within a cohesive framework for intergranular and transgranular fracture. Simulations of either mode of propagation reveal that shielding is a natural outcome of a cohesive approach to fracture. Findings considering both modes of propagation, i.e., a transgranular and intergranular path, suggest that the crack propagates when the required driving force is equivalent to the resistance for either intergranular or transgranular fracture. The mode of propagation is dictated by the grain strength, toughness, and orientation. For each grain angle, the intersection of intergranular and transgranular/intergranular solutions demarcates strong grains that increase the macroscopic toughness and weak grains that decrease the macroscopic toughness. Findings in the stall regime confirm that reinitiation ahead of the primary crack tip is admissible for sufficiently strong and tough grains. The current results provide restrictions for the achievement of substantial toughening through crack deflection and stalling prior to actual crack bridge formation.