Effect of fibre shape on the stresses within fibres in fibre-reinforced composite materials

Abstract

Equations have been derived for calculating the stress distributions in a tapered reinforcing fibre in a composite material, i.e. for a fibre which does not have a uniform radius. In general, deformation of the matrix in a composite induces a radial (compressive) stress at the fibre surface and an axial (tensile) stress. The equations were solved for a circular conical, paraboloidal and ellipsoidal fibre embedded in a plastic matrix. Results were compared with the familiar results for a uniform cylindrical fibre (i.e. with a constant radius) for which the radial stress at the surface is zero. For a uniform cylinder, the axial stress increases linearly, from zero at the ends, to a maximum value at the centre. At the other extreme, the axial stress in a conical fibre was shown to be constant. The intermediate cases of a paraboloidal and an ellipsoidal fibre showed axial stress distributions lying between these two extremes.