From statistical distribution of microcrack to statistical disribution of strength and toughness

Based on the idea of fracture caused by the statistical nucleation, growth and propagation of microcracks in the materials, the statistical distribution functions of brittle strength, fracture toughness and crack extension force of metals are derived from the solved statistical distribution function of microcracks. The forms of these three statistical distribution functions are similar, and the latter two can be derived from the former. The further approximation of these statistical distribution functions is not the Weibull distribution function but the Duxbury-Leath distribution function. The statistical distribution characteristics of fracture probability have been compared with experiment data.