THEORETICAL EVALUATION OF FRACTURE-TOUGHNESS OF POLYCRYSTALLINE MATERIALS FROM CRACK DEFLECTION MECHANISM

A crack deflection model was constructed to explain the fracture behavior in polycrystalline ceramics consisting of isotropic ideal grains. From the considerations of the competition criterion between penetration and deflection of crack at grain boundaries, a 3-dimensional fracture process was modelled where the crack path is affected by adjacent crack planes. Cracks in polycrystals were divided into 3 types, that is, transgranular, intergranular and a mixture of the two. The macroscopic fracture toughness, K(ca), and the transgranular fracture ratio, T(f), were calculated as a function of the grain boundary toughness, K(cb). The maximum K(ca) of polycrystals is about 3 times that of single crystals, K(ct), at K(cb) = 0.9K(ct), and the crack path restriction at triple or quadruple points indicating a forced fracture in the connecting plane was found to be the primary reason for the increased fracture toughness of polycrystals over that of single crystals. In this analysis, the theoretical relationships between K(ca) and T(f) were also obtained where the maximum K(ca) is at T(f) = 75%. On the other hand, the calculations on both the plane strain and plane stress states showed that the fracture toughness of ceramics is not dependent on stress states.