The Influence of Grain Size on the Toughness of Monolithic Ceramics

Experiments have shown that there may be an optimal grain size which maximizes the toughness of polycrystalline ceramics. In this paper, we attempt to develop a theoretical model which can predict the effect of grain size on the toughness of ceramics. We assume that three principal mechanisms affect the toughness of the material: distributed microcracking; crack trapping by tough grains; and frictional energy dissipation as grains are pulled out in the wake of the crack. The grain size influences these mechanisms in several ways. The energy dissipated due to frictional crack bridging increases with the size of the bridging grains, tending to improve toughness. However, as the grain size increases, the density of microcracks in the solid also increases, which eventually weakens the material. In addition, the level of inter-granular residual stress is also reduced by microcracking, which as a detrimental effect on the toughening due to bridging. We have developed a simple model to quantify these effects. However, the model does not predict the dramatic loss of strength which has been observed to occur beyond a critical grain size. We have therefore proposed an alternative explanation for the apparent decrease in toughness in coarse grained ceramics. Calculations indicate that in a coarse grained material, the main contribution to toughness is due to frictional crack bridging. However, to produce this toughening, the bridging zone must be over 500 grains long. In practice, the length of the bridging zone in a coarse grained solid may be comparable to the dimensions of the specimen used to measure its toughness. Under these conditions, it is not appropriate to use the concept of a geometry independent toughness to characterize the strength of the specimen. We have therefore developed a simple model of a double cantilever beam fracture specimen, which accounts for the effects of large scale bridging. Using this model, we are able to predict the apparent decrease in toughness measured in coarse grained specimens.