Combined effects of the fibre distribution and of the fibre matrix or interphase matrix transverse modulus ratio on the possible fracture modes of unidirectional composites submitted to a transverse loading

Considering first the extreme cases of either a perfectly soft or perfectly rigid isolated fibre, the investigation of the effect of the transverse Young's modulus ratio on the stress field resulting from the applied transverse loading is then extended to intermediate fibre matrix and interphase matrix transverse modulus ratios representative of real composite materials. Regarding the effect of the randomness of the fibre distribution, the simplest arrangement of two isolated fibres is considered, the reference situations being those of either an isolated fibre or of a regular arrangement. In the case of the two isolated fibres, three values of the angle between the direction of the fibre alignment and that of the applied transverse loading are taken into consideration (0, 90 and 45°), this last critical situation being of essential interest, due to the “alignment effect” which tends to rotate the fibre pair towards the direction of the applied loading, thereby inducing a particular stress field. Simple analytical formulae are used to determine the stress field resulting from the applied transverse loading in the simplest case of an isolated fibre, i.e. a two-phase (fibre matrix) system, or a simplified (perfectly soft fibre) three-phase (fibre-interphase matrix) system. In the general three-phase system, and in the spatial fibre arrangement of either a fibre pair or a regular distribution, a global finite element numerical calculation is performed; thereby directly taking into account the mechanical interaction between the fibres. The representative mechanical quantities thus determined are discussed in relation with both the possible fundamental mechanisms of deformation and fracture and the actually observed phenomena.