Statistical distribution and size effect of residual strength after a period of sustained load

The present paper formulates the statistics of the residual strength of a quasibrittle structure after it has been subjected to a period of sustained loading. Here, quasibrittle structures (of positive geometry) are modeled by a finite (rather than infinite) chain of the weakest-link model. A strength degradation equation is derived based on the static crack propagation law which shows that the rate of strength degradation is not constant but continuously increasing. The cdf of residual strength of one RVE, representing one link in the chain, is shown to be closely approximated by a graft of Weibull and Gaussian (normal) distributions. In the left tail, the cdf is a three-parameter Weibull distribution consisting of the (n +1)th power of the residual strength, where n is the exponent of the crack propagation law and the threshold is a function of the applied load and the load duration. The finiteness of the threshold, which is typically small, is a new feature of quasibrittle residual strength statistics, contrasting with the previously established absence of a threshold for strength and lifetime. Its cause is that there is a non-zero probability that some specimens fail during the static preloading, and thus are excluded from the statistics of the overload. The predictions of the theory are validated by available test data on glass-epoxy composites and on borosilicate glasses. The size effect on the cdf of residual strength is also determined. The size effect on the mean residual strength is found to be as strong as the size effect on the mean initial strength.