Prediction of ceramic fracture with normal distribution pertinent to grain size

Abstract Fracture of brittle ceramics initiated from shallow surface cracks comparable to their average grain sizes ( G ) can fluctuate significantly. Such fluctuations can contain crucial information on the inherent relations between the average grain size G and bulk ceramic properties such as the tensile strength f t and fracture toughness K IC . It was proposed in this study that the characteristic crack a * ch  = 0.25( K IC / f t ) 2  = constant ×  G , inspired by observations of strength distributions with different a * ch / G ratios. It was found that normal distributions with the smallest standard deviation exist around a * ch  = (2.5–3.5) ×  G , based on quasi-brittle fracture results of four different ceramics with G from 2 to 20 μm and shallow surface cracks from 100 nm to 650 μm. Using the average value of the relative characteristic crack a * ch / G  ≈ 3, the mean and standard deviation (σ) were determined by normal distributions for both the tensile strength f t and fracture toughness K IC . Quasi-brittle fracture of those fine-grained ceramics based on the mean values and standard deviations was thus predicted. The upper and lower bounds with 96% reliability (±2σ) specified by the normal distributions covered nearly all experimental data ranging from the strength-controlled to toughness-controlled asymptotic limits, and quasi-brittle fracture between the two. With the knowledge of the average grain size G , the tensile strength f t becomes the sole parameter required to describe the entire fracture range.