SIMPLE GEOMETRICAL MODELS FOR YOUNGS MODULUS OF FIBROUS AND PARTICULATE COMPOSITES

The concept of fibres in a uniform square array is used to develop a simple model for the transverse modulus of a unidirectional composite. The model defines in a direct way the upper and lower bounds on transverse modulus at a fixed fibre-volume fraction and expresses them in terms of equivalent fibres of square cross-section. Modulus values between these bounds are accommodated by a single disposable parameter P, the 'relative volume fraction', easily understood as measuring the effective contribution to stiffness from the outer portions of a fibre. The model is more flexible than the frequently used Reuss model. The model is further developed to embrace particulate composites, upper and lower bounds being defined for the modulus of a cubic array of spherical particles dispersed in a continuous phase. The same disposable parameter as that referred to above is used for purposes of fitting to data. Applications of both models are illustrated by comparing their predictions with measured moduli for a series of cast polyester/urethane-acrylate blends, and for a series of unidirectional glass-fibre composites with those blends as matrices.