SIZE EFFECTS IN THE TENSILE STRENGTH OF UNIDIRECTIONAL FIBER COMPOSITES

Abstract

Monte Carlo simulation and theoretical modeling are used to study the statistical failure modes in unidirectional composites consisting of elastic fibers in an elastic matrix. Both linear and hexagonal fiber arrays are considered, forming 2D and 3D composites, respectively. Failure is idealized using the chain-of-bundles model in terms of {delta}-bundles of length {delta}, which is the length-scale of fiber load transfer. Within each {delta}-bundle, fiber load redistribution is determined by local load-sharing models that approximate the in-plane fiber load redistribution from planar break clusters as predicted from 2D and 3D shear-lag models. As a result these models are 1D and 2D, respectively. Fiber elements have random strengths following either the Weibull or the power-law distribution with shape and scale parameters {rho} and {sigma}{sub {delta}}, respectively. Simulations of {delta}-bundle failure, reveal two regimes. When fiber strength variability is low (roughly {rho} > 2) the dominant failure mode is by growing clusters of fiber breaks up to instability. When this variability is high (roughly 0 < {rho} < 1) cluster formation is suppressed by a dispersed fiber failure mode. For these two cases, closed-form approximations to the strength distribution of a {delta}-bundle are developed under the local load-sharing model and an equal load-sharing model of Daniels, respectively. The results compare favorably with simulations on {delta}-bundles with up to 1500 fibers. The location of the transition in terms of {rho} is affected by the upper tail properties of the fiber strength distributions as well as the number of fibers