Statistical kinetics of quasi-brittle fracture

The statistical laws of fracture under conditions of static fatigue and loading at a constant rate are discussed. Phenomenological crack-growth models are used to theoretically analyze the statistics of quasi-brittle fracture of solids that undergo static fatigue and whose experimentally measured strength is controlled by kinetic factors. The strength and longevity distributions that correctly reflect the main empirical dependences are constructed. It is shown that the often detected specific features of the statistics of quasi-brittle fracture are likely to be caused by the qualitative similarity between the asymptotic behaviors of the statistics of thermal fluctuations and “dangerous” structural defects, namely, by the exponential distribution of the strong-thermal-fluctuation expectation time, a large number of statistically equivalent dangerous defects in a sample, and a sharp decrease in the probability of defects whose sizes are larger than a certain limiting size. The results obtained suggest that the generally accepted theoretical interpretation of the Weibull distribution is likely to require revision, since the assumption regarding the power asymptotics of the size distribution of cracklike defects during quasi-brittle fracture is in conflict with the empirical data on static fatigue.