Correction to the Fukuda-Kawata Young's modulus theory and the Fukuda-Chou strength theory for short fibre-reinforced composite materials

The theories for modulus and strength of short fibre-reinforced composite materials are based on the calculation of the force sustained by fibres crossing an arbitrary line perpendicular to the applied load, called the scan line, in a thin, rectangular specimen. The widely referenced Fukuda-Kawata modulus theory and the Fukuda-Chou strength theory are based on an apparently incorrect procedure for the calculation of the force sustained by the fibres crossing the scan line. The error is explained in detail by comparing the Fukuda-Kawata modulus theory and the Cox modulus theory. The magnitude of this error is calculated for specific cases.