Asymptotic Characteristic of Exact Distribution of Fracture Strength Based on Gamma Distribution as Initial Flaw Size Distribution

Abstract

In this paper, an exact distribution of fracture strength was derived from extreme value statistics for an initial distribution of flaw size, via conversion to an exact distribution of largest flaw size. Gamma distribution was shown as a better function to approximate the initial distribution data measured by immersion liquid technique. The exact distribution of fracture strength was obtained as a function of the number of links in the weakest link theory. With increasing the number of links, the exact distribution gradually became linear on Weibull plot, and almost coincided to Weibull distribution at the number of links larger than 1000. Compared to actual distributions of fracture strength, the number of links in the specimens was estimated to be in the range from 104 to 105. The above discussion showed a verification of this theory.