Size and heterogeneity effects on the strength of fibrous composites

Abstract

Probabilistic fiber composite strength distributions and size scalings depend heavily on both the stress redistribution mechanism around broken fibers and properties of the fiber strength distribution. In this study we perform large scale Monte Carlo simulations to study the fracture process in a fiber composite material in which fibers are arranged in parallel in a hexagonal array and their strengths are given by a two-parameter Weibull distribution function. To calculate the stress redistribution due to several broken fibers, a realistic 3D shear-lag theory is applied to rhombus-shaped domains with periodic boundary conditions. Empirical composite strength distributions are generated from several hundred Monte Carlo replications, particularly for much lower values of fiber Weibull modulus γ, and larger composite sizes than studied previously. Despite the localized stress enhancements due to fiber failures, predicted by the shear-lag model, composite response displays a transition to equal load sharing like behavior for approximately γ≤1. Accordingly, the results reveal distinct alterations in size effect, failure mode, and weak-link scaling behavior, associated with a transition from stress-driven to fiber strength-driven breakdown.