Fibre reinforcement in fibre composite materials : effect of fibre shape
The aim of this project was to investigate the effects of fibre shape on its ability to reinforce a fibre composite material. Analytical and finite element (FE) models of an axisymmetric fibre composite material were developed and used to achieve this aim. Fibres of cylindrical shape, ellipsoidal shape, with paraboloidal ends and with conical ends were considered: fibre geometry was further characterised by an axial ratio, q. The scope of this study covered elastic and plastic load transfer processes. The former corresponds to the initial loading stage whereby an applied tensile stress acting on a fibre composite causes stress in an elastic matrix to be transferred to an elastic fibre which is embedded in and adheres to the matrix. The latter corresponds to the next stage when, on progressive increase of the applied stress, the matrix yields and turns plastic and failure of adhesion at the fibre-matrix interface occurs. Two approaches were used to develop analytical models. In the first approach, equations were derived for calculating stress and displacement distributions in a general axisymmetric body. This approach was based on a stress function method for structural analysis of a statically indeterminate problem. The equations derived were implemented to model a fibre composite undergoing elastic load transfer by prescribing appropriate boundary conditions. However, the approach led to no useful solutions. In the second approach, first-order ordinary differential equations for solving axial, σz, and surface radial, σr, stresses in a fibre were formulated by considering forces at equilibrium in a stress element in a fibre subjected to a fibre-matrix interfacial stress. Equations for calculating these stresses to study plastic load transfer were derived from the differential equations by prescribing appropriate boundary conditions, σz was assumed to be constant in the radical direction of the fibre. For a cylindrical fibre, σz increases linearly, from zero at the ends, to a maximum value at the centre. At the other extreme, σz in a conical fibre was shown to be constant. The intermediate cases of a paraboloidal and an ellipsoidal fibre showed distribution of σz lying between these two extremes. The effectiveness of a fibre shape for reinforcement was defined for the plastic study. It was found that the conical fibre possessed the highest value; the cylindrical fibre gave the lowest value. From this study, it was concluded that: (1) an important property of all the tapers considered is to make the distribution of σz in a fibre more uniform; (2) fibres with conical ends are more effective for reinforcing fibre composite materials than cylindrical fibres.