Some problems have been posed in evaluating the strength of engineering ceramics. The relative strength of a smooth specimen has been observed to be lower than that expected from the fracture toughness criterion with decreasing flaw size at the fracture origin. Another problem was that the fracture toughness measured using a notched specimen depended on the notch width. Such anomalous behavior of small flaws and the notch width effect is explained by a new model proposed in this paper. The model was established assuming stable cracking due to separation per grain just ahead of a Raw, such as a crack and a notch, prior to the final unstable fracture. Based on the grain fracture model, the simulation was conducted to explain the anomalous behavior of small flaws and the notch width effect. For both situations, the analytical relations showed good correspondence with cxperimentai observations.
INTRODUCTrON
IT HAS been reported that the fracture originating from a small flaw in engineering ceramics occurs at a lower stress compared with the prediction based on the plane strain fracture toughness (K,,) criterion [l-4]. The dependence of the fracture toughness or the fracture energy on the flaw size in ceramic materials was also observed by several investigators [S-7]. They discussed such anomalous behavior in ceramics from the aspect of the relation between the flaw size and the grain size, and correlated the behavior with the fact that the fracture energy to propagate a crack in a single crystal is smaller than in a polycrystal. As an engineering treatment for the flaw size effect in ceramics, it was proposed that the constant a,, depending on microstructure, was added to the original length a of the crack in evaluating the stress intensity factor [3,4, S]. The constant a0 was assumed to be the size of a few grains. Another problem was that the fracture toughness depends on the notch width in the evaluation using notched specimens [9-E I]. This problem was also settled by assuming a fictitious crack at the notch root, whose size equals that of two grains . Experimenta evidence for such a fictitious crack has been suggested by the observation of acoustic emission [ 12, 131. However, there is no model to explain the process of formation of such a fictitious crack and its size.
In this paper, a new model of the cracking process is developed assuming the fracture of the grain just ahead of a flaw, such as a crack and a notch, during the loading process. Simulation based on the proposed model is also carried out to describe the anomalous behavior of small flaws and the notch width effect in ceramic materials as mentioned above.