Investigation of Variability of Flaw Strength Distributions on a Brittle SiC Ceramic

Abstract

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens: 4-point bending as well as 3-point bending with different span lengths. Flaw strength is given by the elemental stress operating on the critical flaw at fracture of a test specimen. Fracture inducing flaws and their locations are identified by fractography. A single population of pores was found to dominate fracture. The construction of diagrams of p-quantile vs elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. Weibull cumulative probability distributions were derived from the mean and the standard deviation using the first moment equation. Agreement was obtained between both Weibull and normal flaw strengths distributions. The cumulative distributions for the different bending tests were predicted satisfactorily from the flaw strength density function using the elemental strength model. Flaw strength distributions that include potential weaker flaws encountered in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed about the pertinence of an intrinsically representative flaw strength distribution, about failure predictions, about size effects, and about the significance of flaw spatial distributions.