We have seen that determining inert strength (S, σi) of a sample population is critical in determining lifetime. Equally critical is knowing the reliability of such strength determination.
For brittle materials, in which the most severe scratch in the population determines failure, a failure probability distribution developed by Walloddi Weibull1 has been found to be a more reliable predictor than the normal Gaussian curve distribution. While a very large data set may nicely fit both distributions, a Weibull distribution fits a curve to the data, and the normal distribution fits the data to a bell curve. The Weibull formulation is particularly preferred for glass and ceramics and, indeed, for most applications involving large scatter and fatigue life. It is also preferred for prediction of fracture in other brittle materials.
Online access to SPIE eBooks is limited to subscribing institutions.