An Improved Shear Lag Model for Broken Fibers in Composite Materials

Abstract

A shear lag model is formulated to predict the stresses in a unidirectional fiber reinforced composite. The model is based on assumptions consistent with the finite element method and the principle of virtual work by assuming that the matrix displacements can be interpolated from the fiber displacements. The fibers are treated as one-dimensional springs and the matrix is modeled as three-dimensional finite elements. The resulting finite element equations for the system are transformed into differential equations by taking the discretization length to approach zero. The governing ordinary differential 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. The results are compared with previous shear lag models and finite element results. The model predicts stress concentrations that are in good agreement with more detailed finite element analyses.