A statistical model for the time dependent failure of unidirectional composite materials under local elastic load-sharing among fibers

Abstract

In this paper we develop a statistical model for the time dependent failure of a unidirectional composite material under tensile loads. We consider probability distributions for lifetime in both stress-rupture and cyclic-fatigue and for strength under a linearly increasing load. We begin with a probability model for the failure of fibers which has its roots in the statistical kinetics of molecular failure, and we relate the parameters of our model to certain thermal activation quantities. At the micromechanical level we assume localized, elastic, load-sharing among failed and non-failed fiber elements in a cross section of the composite. As in earlier static versions we model the composite as a chain-of-short-bundles. Using asymptotic techniques we obtain accurate approximations to the probability distributions for composite lifetime with parameters that depend on certain fiber kinetic and variability parameters, fiber load-sharing constants, and on a “critical crack size” parameter that emerges as crucial.