Nanomechanics based theory of size effect on strength, lifetime and residual strength distributions of quasibrittle failure: A review

The paper reviews a series of studies at Northwestern University which led to the establishment of a theory of probability distributions of short-time strength, residual strength after static preload and lifetime of structures made of quasibrittle materials such as concrete, fiber composites and tough ceramics. The theory is based on the frequency of probability of interatomic bond breaks on the atomic scale and on the multi-scale transition of power-law probability tail. The conclusion is that if the failure is not perfectly brittle, the probability distribution of strength and lifetime is a graft of Gaussian and Weibull distributions and varies from nearly Gaussian at the scale of one RVE to Weibullian for very large structures consisting of many RVEs. As a consequence, the safety factors should depend on structure size. Numerous experimental comparisons and computational simulations are given.