Strong influence of a small fiber on shear stress in fiber-reinforced composites

Abstract

In stiff fiber-reinforced composites, it has been known that the shear stress increases at the rate of 1/root epsilon as the distance e between adjacent fibers approaches 0. This paper reveals a strong influence of a combination of a triple fiber, as well as the distance between a pair of fibers, on the blow-up so that the stress concentration can be significantly accelerated by adding a small fiber in-between fibers. Specifically, if a fiber J(2) with a small diameter delta is located in-between fibers J(1) and J(3), epsilon(1) = dist(J(1), J(2)) and epsilon(2) = dist(J(2), J(3)), then the stress blows up at the exact rates of 1/root delta epsilon(1) and 1/root delta epsilon(2) between J(1) and J(2) and between J(2) and J(3), respectively. This estimate still holds even when a part of J(2) overlaps with J(3). The magnification factor 1/root delta yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods. (C) 2011 Elsevier Inc. All rights reserved.