The strength of thin composites of finite width, with brittle matrices and random discontinuous reinforcing fibres

A new theory is proposed for the estimation of the tensile strength of a two-dimensional composite with a brittle matrix and randomly orientated discontinuous elastic fibrous reinforcement. The estimate is made by integrating the strengths of all fibres that cross a transverse crack. It is necessary to know the relationship between the length of embedment of a fibre and the force needed to break it or pull it out. No assumptions are made about the shape of the cross section of the fibre or about the magnitude or distribution of bond stresses. An important feature is the allowance made for the loss of effectiveness of fibres cut by the edges of a tensile specimen of finite width.