Stochastic models for the tensile strength, fatigue

The time-to-failure of a single fiber is modeled as a functional of the fiber load history and reasonable forms for this functional are proposed. Earlier models by Daniels and Coleman are shown to be special cases of the proposed model and apparent disparities in their behavior are discussed. Techniques are presented for determining analytically the asymptotic distributions of the tensile strength and time-to-failure for bundles of a large number of fibers. For smaller bundles, exact results are far too cumbersome to be of use so that efficient Monte Carlo simulation procedures are proposed.