Kinetic genesis of some statistic regularities of fracture

Abstract

The statistics of strength and longevity of solids has been the subject of investigation for many years. Some common regularities in fracture statistics have been experimentally revealed. These are Jhurkov's exponential and power-type longevity equations, Weibull's statistics of strength, and different types of size effect. However, the present notions on the nature of the observed statistic regularities are far from being complete. Here the object is to examine fracture statistics on the basis of a previously suggested kinetic approach. We consider the evolution of the statistical ensemble of cracks under static and steady-rate loading of a solid. The growth of an individual crack is therewith treated as a spasmodic stochastic process and presented by a time-dependent distribution density of a crack size. That function is used to construct the conditional longevity distribution with respect to the growth of an individual crack with the prescribed initial size. The final longevity distribution is found as the distribution of a minimum of conditional longevities. That procedure has been realized for both brittle and quasi-brittle cases. The obtained longevity and strength distributions were found to be in qualitative agreement with the observed statistic regularities. However, the conventional `weak link concept' and proposals for the statistics of dangerous defects are in conflict with the obtained results. It is moreover shown that, within the limits of the wide-spread concept, Jhurkov's longevity equation and Weibull's statistics of strength are mutually exclusive. Although the results were obtained from simple models, there is a good probability of kinetic origin for the basic statistic regularities of fracture.