Fracture model of meso-ceramics based on relative size and prediction of fracture toughness and bending strength

Abstract

Based on grain size effect of ceramics and boundary effect model, the concept of relative size is introduced. In addition, meso-fracture model of ceramics with different relative sizes is established. Experimental data of nine ceramic materials with different relative sizes are statistically analyzed. It is found that fictitious crack growth length Δafic is k (W − a0) (where k is a constant, W is the specimen depth, and a0 is the initial crack length). Furthermore, k value is 0.02 when relative size is less than 200, while it is 0.2 when relative size is in the range from 200 to 1500. Fracture parameter values determined by considering relative size are basically consistent with fracture parameter values reported in the literature. Combined with normal distribution, full fracture failure curves of ceramics with different relative sizes are constructed. No brittle failure controlled by fracture toughness occurs in ceramic specimens with relative size less than 200, while brittle failure controlled by fracture toughness occurs in ceramic specimens with relative size ranging from 200 to 1500. Main reasons for the occurrence of brittle failure controlled by fracture toughness are that with increasing relative size, grain size is reduced, the number of grain boundaries increases, crack growth length increases gradually, and the interaction between fracture process zone of ceramics and the boundary of specimens becomes stronger. At the same time, an expression for predicting the peak load Pmax of ceramics with relative size (W–a0)/dav≤1500 is established. It is found that peak load can be predicted based on relative size and geometric parameters of ceramics, which is of great significance for conveniently and accurately obtaining fracture parameters of ceramics.