An Alternative to the Weibull Function for Some Cases

Doubt about the applicability of the Weibull function has been expressed by various workers, some of whom have suggested modifications to the Weibull function. Such modifications usually involve more parameters than the original Weibull function being thus much more flexible and thereby, in some cases, providing a good fit if the numerous (up to six) parameters can be estimated. These functions are not valid as asymptotic extreme-value distribution functions and thus represent a departure from the so-called weak-link principle. A fundamental problem with the Weibull approach, the lack of statistical independence of volume elements, will be briefly discussed. For cases where failure is caused by sharp defects a new extreme-value (weakest-link) function has been developed on the basis of the mechanics of the near-tip regions of such defects. The new function has only two statistical parameters which can be measured easily from plots, graphically or by least-squares fitting. Several large sets of data, fracture toughness, and fracture stress from several different materials will be shown, to which the new function provides a much better fit than the Weibull function.