Statistical Mechanics of Safety Factors and Size Effect in Quasibrittle Fracture

Throughout most of the 20th century, it was widely believed that the size effect on structural strength has a purely statistical origin, explained by extreme value statistics based on the weakest link model, and described by Weibull statistical theory of random strength. However, beginning with the first suggestions made already in the early 1970s, it gradually transpired that, in quasibrittle materials (i.e. heterogeneous brittle materials with a non-negligible fracture process zone), the mean size effect is essentially deterministic, stemming from energy release caused by stress redistribution in a structure prior to maximum load. The quasibrittle energetic scaling bridges three simple asymptotic power-law scalingsthose of linear elastic fracture mechanics, plasticity, and Weibull theory. Renormalization group transformation does not suffice to handle the transitional nature of this quasibrittle size effect, often spanning several orders of magnitude of size. As is now widely accepted, quasibrittle materials including concrete, rock, tough ceramics, sea ice, snow slabs and composites exhibit major size effects on the mean structural strength that are largely or totally deterministic in nature, being caused by stress redistribution and energy release associated with stable propagation of large fractures or with formation of large zones of distributed cracking.