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 ft and fracture toughness KIC. It was proposed in this study that the characteristic crack a*ch = 0.25(KIC/ft)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 ft and fracture toughness KIC. 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 ft becomes the sole parameter required to describe the entire fracture range.