Strength distributions and size effects for 2D and 3D composites with Weibull fibers in an elastic matrix

摘要

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 f 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 the delta-bundle failure models are 1D and 2D, respectively. Fiber elements have random strengths following either a Weibull or a power-law distribution with shape and scale parameters rho and sigma_(delta), respectively. Under Weibull fiber strength, failure simulations for 2D delta-bundles, reveal two regimes: Wen fiber strength variability is low (roughly rho >2) the dominant failure mode is by growing clusters of fiber breaks, one of which becomes catastrophic. When this variability is high (roughly 0 < rho < 2) cluster formation is suppressed by a dispersed failure mode due to the blocking effects of a few strong fibers. For 1D delta-bundles or for 2D delta-bundles under power-law fiber strength, the transitional value of rho drops to 1 or lower, and overall, it may slowly decrease with increasing bundle size. For the two regimes, closed-form approximations to the distribution of delta-bundle strength 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.