Scalings in the statistical failure of brittle matrix composites with discontinuous fibers—I. Analysis and Monte Carlo simulations

Abstract

This paper addresses the statistical aspects of the failure of unidirectional composites having brittle matrices reinforced with discontinuous brittle fibers. The failure process involves quasi-periodic matrix cracking, frictional sliding of the fibers in fiber break zones and fiber bridging of matrix cracks in a global load-sharing framework. We consider a composite section of “characteristic” length and develop its distribution for strength in terms of certain characteristic stress and length scales. Continuous sections of the fibers follow the usual Weibull distribution for strength. We also introduce random discontinuities along the fiber, originating say from processing damage whose spacins follow a Poisson process where the rate α is the mean number of discontinuities per characteristic length of the fiber. We derive two approximations for the mean and standard deviation of such characteristics composites. A realistic Monte Carlo simulation model is developed to test these analytical results and to study the fiber pull-out properties. The composites turn out to be quite insensitive to initial damage. The mean pull-out length is found to increase with increasing α and becomes independent of the Weibull modulus for large values of α.