Relation between structure and mechanical behaviour of fibre-reinforced composite materials at large strains

Abstract

A theory is presented for the mechanical behaviour of fibre-reinforced composite materials at large strains. It is based on the distribution of fibres within the material and uses only basic mechanical properties of the fibres and matrix. The angular distribution of fibres is described by an orientation distribution function, g ( θ, ϕ ), which changes as the material is stretched, becoming greater along the directions of greatest tensile strain. No assumption is made about stress transfer to the fibres, or their length, except that they are long enough for this to happen effectively. The analysis predicts the reorientation of the fibres with strain and shows good agreement with preliminary experimental results from spinal ligaments. The predicted stress-strain behaviour shows qualitative agreement with experiment but further analysis is needed to take account of the crimping of the collagen fibres which occurs in this material. The theory may also have application to reorientation effects observed in drawn polymers and this is demonstrated with reference to polyethylene and polyethylene terephthalate.