Estimation of the maximum flaw size and the fracture strength distributions of a macroscopic body taking the local flaw-size data as an initial distribution

In this work a new theory for estimating the maximum flaw-size distribution and the fracture strength distribution of a macroscopic ceramic body is presented, without using any fracture data except the fracture toughness. First, Gamma function was selected as the most suitable distribution function for flaw-size. The unknown parameters were estimated using the local flaw-size data obtained by Yao et al.⁵, who used a small thin ceramic specimen. The maximum flaw-size distribution function for a macroscopic ceramic body, which has an arbitrary volume, was derived based on the extreme statistics by taking the local flaw-size data as an initial distribution. Finally, the strength distribution function was derived using fracture mechanics. The validity of this theory was examined by comparing the Weibull parameters estimated from the theory with the experimental ones by Yao et al.