In many engineering applications, the risky overload would not occur right at the first load application. This chapter, based mostly on Salviato, Kirane, & Bažant (2014), deals with the residual strength of a structure at an accidental sudden overload that occurs later, after a period of sustained load high enough to weaken the structure. The residual strength is also important in the laboratory since, as will be shown, it is advantageous to replace lifetime tests by residual strength tests.

Practical examples of overload include an earthquake, a sudden excessive traffic load on a bridge, an excessive rise of water level behind a dam, accidental impact, or sudden overheating of an electronic component. Knowledge of the statistics of residual strength should allow improvements in the safety factors, taking into account the strength degradation of the structure depending on the load history and duration. It should also allow meaningful estimates of the remaining service life of structures for which maintenance design is a primary concern. This is of paramount importance from the perspective of cost reduction and safety, especially for modern large aircraft made of load-bearing quasibrittle composites (Lee, Ma, Thimm, & Verstraeten 2008).

The residual strength of different materials has been widely studied phenomenologically, but mainly for the case of cyclic loading. For example, Yang and Liu proposed a model for residual strength degradation and periodic proof tests for graphite-epoxy laminates under cyclic loading (Yang & Liu 1977; Yang 1978). A mechanistic attempt was provided by Halpin, Johnson, & Waddoups (1972), based on the kinetics of fracture growth. There have been some experimental studies, e.g., for concrete (Award & Hilsdorf 1972), but strictly deterministic. Unfortunately, no information exists in the literature on the residual strength in the statistical sense. In those few attempts that provided a statistical perspective (Kirchner & Walker 1971; Evans 1974; Hahn & Kim 1975; Thomas, Verrilli, & Calomino 2002; Duffy et al. 2003), the quasibrittleness of the structure was not considered.