Stress Distribution and Effective Longitudinal Young's Modulus of Unidirectional Discontinuous Fibre Composites

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Abstract
In this article, stress and strain distributions in the elementary cell are studied in the case of unidirectional discontinuous fibre composites as functions of the geometrical arrangement of fibres. This arrangement is characterized by the volume frac tion of fibres, the fibre aspect ratio and the fibre spacing parameter. Thus, two extreme schemes are analyzed by the finite element method: one scheme with stresses imposed on the elementary cell and another scheme with an imposed deformation field. The first is related to a geometrical repartition of fibres without overlapping of fibre ends. The article shows that the second scheme can be associated with a hexagonal arrangement of fibres with a regular overlapping of fibre ends. The theoretical results obtained for Young's effec tive modulus of fibre composites show that modulus depends strongly on the geometrical arrangement of fibres, thus Young's modulus of discontinuous fibre composites cannot be derived from an isolated cell scheme. The article shows that the predominant factor is the overlap between the ends of adjacent fibres. For a regular overlapping of fibre ends, each elementary cell (fibre and matrix) stretches the neighbouring cells by a lateral transmis sion of load. Thus, the effective modulus is quite close to the bound given by the law of mixtures. On the other hand, in the case of a geometrical repartition without overlapping of fibre ends, the tensile load imposed to the composite is transferred by the alternating layers of matrix and matrix-fibre. In this case, the effective modulus then depends on the distance between fibre ends.