Effective Stiffness of Randomly Oriented Fibre Composites

This paper is concerned with the theoretical derivation of the effective stiffness properties for two types of randomly oriented fibre systems: (a) A system with completely three-dimensional random orientation of fibres in an isotropic matrix phase; (b) A system with two-dimensional (planar) random orientation of fibres in an isotropic matrix phase, appropriate to thin sections in a state of plane stress. The formulas derived predict the effective isotropic properties of the composite in terms of the elastic properties of each phase and the volume concentration of the fibre phase. These results provide the theoretical limits with which experimental results can be compared to assess the effectiveness of bonds, dispersion of fibres and any other factors which may affect the performance. In the last section a comparison is made with experimental results. In addition, the relation of the present study to pre vious work on this topic is discussed.