A statistical approach for the assessment of reliability in ceramic materials from ultrasonic velocity measurement: Cumulative Flaw Length Theory

A primary objective of statistical fracture approach is to predict the probability of failure of a component for an arbitrary stress state when the failure statistics are known. This study introduces the fundamentals and application of a new approach to characterize the mechanical behaviour of high temperature ceramic materials, including refractory materials, by coupling non-destructive methods, in particular ultrasonic velocity measurement, and the Batdorf statistical fracture theory. A new approach, termed Cumulative Flaw Length Theory (CFLT), has been developed for the case of macroscopically homogeneous isotropic materials containing randomly oriented microcracks uniformly distributed in a location subjected to non-uniform multiaxial stresses. A function representing the number of cracks per unit volume is estimated based on the histograms of ultrasonic velocity measurements. This function is used without additional assumptions to determine the probability of fracture under an arbitrary stress condition. Two different cordierite-mullite high temperature ceramic materials were characterized under the assumptions of this theory to provide experimental evidence to support the model.