On the toughening of brittle materials by grain bridging: promoting intergranular fracture through grain angle, strength, and toughness

The structural reliability of many brittle materials such as structural ceramics relies on the occurrence of intergranular, as opposed to transgranular, fracture in order to induce toughening by grain bridging. For a constant grain boundary strength and grain boundary toughness, the current work examines the role of grain strength, grain toughness, and grain angle in promoting intergranular fracture in order to maintain such toughening. Previous studies have illustrated that an intergranular path and the consequent grain bridging process can be partitioned into five distinct regimes, namely: propagate, kink, arrest, stall and bridge. To determine the validity of the assumed intergranular path, the classical penentration/deflection problem of a crack impinging on an interface is reexamined within a cohesive zone framework for intergranular and transgranular fracture. Results considering both modes of propagation, i.e., a transgranular and intergranular path, reveal that crack-tip shielding is a natural outcome of the cohesive zone approach to fracture. Cohesive zone growth in one mode shields the opposing mode from the stresses required for cohesive zone initiation. Although stable propagation occurs when the required driving force is equivalent to the toughness for either transgranular or intergranular fracture, the mode of propagation depends on the normalized grain strength, normalized grain toughness, and grain angle. For each grain angle, the intersection of single path and multiple path solutions demarcates strong grains that increase the macroscopic toughness and weak grains that decrease it. The unstable transition to intergranular fracture reveals that an increasing grain toughness requires a growing region of the transgranular cohesive zone be at and near the peak cohesive strength. The inability of the body to provide the requisite stress field yields an overdriven and unstable configuration. The current results provide restrictions for the achievement of substantial toughening through intergranular fracture.