An improved shear lag model for broken fibers in composite materials

A shear lag model is formulated to predict the stresses in a unidirectional fiber reinforced composite. The model is based on assumptions consistent w ith the finite element method and the principle of virtual work by assuming that the matrix displacements can be interpolated from the fiber displacem ents. The fibers are treated as one-dimensional springs and the matrix is m odeled as three-dimensional finite elements. The resulting finite element e quations for the system are transformed into differential equations by taki ng the discretization length to approach zero. The governing ordinary diffe rential equations are solved using Fourier transformations and an influence function technique. The technique is used to solve for the stresses around a single fiber break in an infinite square or hexagonal array of fibers. T he results are compared with previous shear lag models and finite element r esults. The model predicts stress concentrations that are in good agreement with more detailed finite element analyses.